a) dcam part 66 - module 3

PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS

For Training Purposes Only Issue 1 Revision 0 Jan 2011 Page i

MODULE 3: ELECTRICAL FUNDAMENTALS

(PART 66 CAT B1.1/B2)

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MAS Engineering Training

PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS

For Training Purposes Only Issue 1 Revision 0 Jan 2011 Page ii

WARNING

This document is intended for the purposes of training only. The information contained herein is as accurate as

possible at the time of issue, and is subject to ongoing amendments where necessary according to any

regulatory journals and documents. Where the information contained in this document is in variation with other

official journals and/or documents, the latter must be taken as the overriding document. The contents herein

shall not be reproduced in any form without the expressed permission of ETD

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS TABLE OF CONTENTS

For Training Purposes Only Issue 1 Revision 0 Jan 2011 Page ii

3.1 ELECTRON THEORY (EASA Ref: 3.1) Level 1 ............................................................................................................................................. 1

3.1.1 Atomic Structure....................................................................................................................................................................................... 1

3.1.2 Atomic Number......................................................................................................................................................................................... 3

3.1.3 Ionisation.................................................................................................................................................................................................. 5

3.1.4 Molecular structure of conductors, semiconductors and insulators .................................................................................................................. 7

3.2 STATIC ELECTRICITY AND CONDUCTION.......................................................... … 10

3.2.1 Static electricity and distribution of electrostatic charges ......................................................................................................................... 9

3.2.1.1Friction..................................................................................................................... 10

3.2.2 Electrostatic laws of attraction and repulsion ......................................................................................................................................... 10

3.2.3 Units of charge, Coulomb's Law............................................................................................................................................................. 13

3.2.4. Conduction of Electricity in solids, liquids, gases and vacuum.............................................................................................................. 13

3.3 ELECTRICAL TERMINOLOGY, UNIT AND AFFECTING FACTORS .......................................................................................................... 15

3.3.1 Potential Difference ................................................................................................................................................................................ 15

3.3.2 Electromotive Force (EMF) .................................................................................................................................................................... 17

3.3.3 Voltage ................................................................................................................................................................................................... 20

3.3.4 Current ................................................................................................................................................................................................... 21

3.3.5 Resistance ............................................................................................................................................................................................. 23

3.3.6 Conductance .......................................................................................................................................................................................... 25

3.3.7 Electric Charge....................................................................................................................................................................................... 26

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3.3.8 Conventional Current Flow..................................................................................................................................................................... 26

3.3.9 Electron Flow.......................................................................................................................................................................................... 28

3.4 GENERATION OF ELECTRICITY................................................................................................................................................................ 31

3.4.1 Friction ................................................................................................................................................................................................... 33

3.4.2 Magnetism.............................................................................................................................................................................................. 35

3.4.3 Heat........................................................................................................................................................................................................ 37

3.4.4 Pressure................................................................................................................................................................................................. 39

3.4.5 Light ....................................................................................................................................................................................................... 41

3.4.6. Chemical ............................................................................................................................................................................................... 43

3.5 DC SOURCES OF ELECTRICITY................................................................................................................................................................ 45

3.5.1 Basic chemical action............................................................................................................................................................................. 45

3.5.2 Primary and Secondary Cells ................................................................................................................................................................. 49

3.5.3 Cells connected in series and parallel .................................................................................................................................................... 50

3.5.3.1 Series Connection .................................................................................................. 54

3.5.3.2 Parallel Connection ................................................................................................ 58

3.5.4 Internal resistance and its effect on a battery......................................................................................................................................... 55

3.5.4.1 Internal Resistance................................................................................................. 61

3.5.4.2 Effects of Internal Battery Resistance..................................................................... 65

3.5.5 Aircraft batteries ..................................................................................................................................................................................... 60

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3.5.5.1 The dry cell (Leclanché cell) ........................................................................................................................................................... 61

3.5.5.2 Secondary cell ................................................................................................................................................................................ 65

3.5.5.3 Lead Acid Types......................................................................................................................................................................... 67

3.5.5.4 Lead Acid Battery Construction .................................................................................................................................................... 68

3.5.5.5 Lead Acid Battery Construction .................................................................................................................................................... 69

3.5.5.6 Specific Gravity Test Procedure (HYDROMETER) ...................................................................................................................... 71

3.5.5.7 Lead Acid Battery Inspection and Service .................................................................................................................................... 73

3.5.5.8 Alkaline Battery……………………………………………………………………………………………………………………………… 76

3.5.5.9 Alkaline Battery Inspection ........................................................................................................................................................... 78

3.5.5.10 Battery Charging......................................................................................................................................................................... 79

3.5.6 Thermocouples....................................................................................................................................................................................... 81

3.5.6.1 System Operation......................................................................................................................................................................... 81

3.5.6.2 Types of Thermocouple............................................................................................................................................................. 87

3.5.7 Photocells............................................................................................................................................................................................... 89

3.5.7.1 Construction of Photo-cells........................................................................................................................................................... 89

3.6 DIRECT CURRENT (DC) ELECTRICAL CIRCUITS (EASE Ref 3.6) Level 2............................................................................................... 95

3.6.1 Introduction ........................................................................................................................................................................................ 95

3.6.1.1 Simple circuit ................................................................................................................................................................................ 95

3.6.1.2 Power source, Voltage, current and resistance ............................................................................................................................ 97

3.6.1.3 Conductors ................................................................................................................................................................................... 97

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3.6.1.4 Series DC circuit........................................................................................................................................................................... 97

3.6.1.5 Schematic..................................................................................................................................................................................... 99

3.6.1.6 Parallel DC circuit ....................................................................................................................................................................... 100

3.6.2 Ohm’s Law ........................................................................................................................................................................................... 103

3.6.2.1 Using equation ............................................................................................................................................................................... 97

3.6.2.2 An analogy for Ohm's Law.......................................................................................................................................................... 111

3.6.3 Kirchhoff's Voltage and Current Law............................................................................................................................................... 115

3.6.3.1 Kirchhoff's Current Law .............................................................................................................................................................. 115

3.6.3.2 Kirchhoff's Current Law in action ................................................................................................................................................ 116

3.6.3.3 Kirchhoff's Voltage Law .............................................................................................................................................................. 117

3.6.3.4 Positive and Negative Signs in Kirchhoff's Voltage Law............................................................................................................. 119

3.6.4 Significance of the internal resistance of a supply ........................................................................................................................... 121

3.7 RESISTANCE AND RESISTOR (EASA Ref: 3.7) Level 1 and 2 ................................................................................................................ 125

3.7.1 Fundamentals....................................................................................................................................................................................... 125

3.7.1.1 (a) Resistance and affecting factors ............................................................................................................................................. 125

3.7.1.2 (a) Variables Effecting Electrical Resistance ............................................................................................................................. 127

3.7.1.3 (b) Positive and negative temperature coefficient conductance ................................................................................................. 129

3.7.2 (a) Specific resistance ........................................................................................................................................................................ 130

3.7.3 ( a ) Resistor identification.................................................................................................................................................................. 138

3.7.3.1 ( a ) Resistor colour code ........................................................................................................................................................... 139

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3.7.3.2 (a) Wattage ratings ..................................................................................................................................................................... 144

3.7.4 (a ) Resistors in series, parallel and series parallel combination....................................................................................................... 147

3.7.4.1 (a) Resistors in series................................................................................................................................................................. 148

3.7.4.2 (a) Resistors in parallel............................................................................................................................................................... 152

3.7.4.3 (a) Resistors in Series Parallel Combinations ............................................................................................................................ 157

3.7.5 (b) Fixed resistors............................................................................................................................................................................... 167

3.7.6 (b) Tolerance and limitations .............................................................................................................................................................. 168

3.7.7 (b) Stability ........................................................................................................................................................................................... 168

3.7.8 (b) Methods of construction of Fixed Resistors .................................................................................................................................. 169

3.7.8.1 (b) Types of fixed resistors: Low power resistors ....................................................................................................................... 169

3.7.8.2 (b) Types of fixed resistors: High power resistors....................................................................................................................... 170

3.7.9 (b) Variable resistors .......................................................................................................................................................................... 171

3.7.9.1 (b) Variable Resistors - Construction......................................................................................................................................... 172

3.7.9.2 (b) Construction of potentiometers ............................................................................................................................................. 177

3.7.10. (a) Operation and use of potentiometers and rheostats ................................................................................................................. 181

3.7.11 (b) Thermistors ................................................................................................................................................................................. 188

3.7.11.1 Benefits of Using Thermistors .................................................................................................................................................... 189

3.7.12 (b) Voltage dependent resistors ....................................................................................................................................................... 189

3.7.13 (b) Construction of Wheatstone bridge............................................................................................................................................ 190

3.7.13.1 (a) Operation of Wheatstone bridge ......................................................................................................................................... 191

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3.7.13.2 (b) Applications of the Wheatstone bridge…………………………………….............................................................................. 192

3.8 POWER (EASA 3.8) Level 2....................................................................................................................................................................... 194

3.8.1 Power and Energy................................................................................................................................................................................ 195

3.8.2 Energy.................................................................................................................................................................................................. 195

3.8.3 Power Formula ..................................................................................................................................................................................... 199

3.8.4 Maximum Power Transfer .................................................................................................................................................................... 201

3.9 CAPACITANCE AND CAPACITOR (EASA Ref. 3.9) Level 2 ..................................................................................................................... 203

3.9.1 Operation and Function of a capacitor ................................................................................................................................................. 203

3.9.2 Factors affecting capacitance ......................................................................................................................................................... 215

3.9.3 Capacitor types, Construction, and Function........................................................................................................................................ 224

3.9.3.1 Polarized capacitors (large values, 1pF +) ................................................................................................................................. 225

3.9.3.2 Unpolarised capacitors (small values, up to 1pF) ....................................................................................................................... 228

3.9.4 Capacitor Color Coding ........................................................................................................................................................................ 237

3.9.5 Calculations of capacitance and voltage in series circuits and parallel circuits ................................................................................ 251

3.9.5.1 Capacitor in Series ..................................................................................................................................................................... 251

3.9.5.2 Capacitors in Parallel.................................................................................................................................................................. 255

3.9.6 Exponential charge and discharge of a capacitor ............................................................................................................................ 260

3.9.6.1 Charging a Capacitor.................................................................................................................................................................. 261

3.9.6.2 Discharging a Capacitor ............................................................................................................................................................. 266

3.10.9.3 (b) Magnetic Flux and Flux Density ........................................................................................................................................ 311

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3.10.9.4 (b) Permeability ........................................................................................................................................................................ 312

3.10.9.5 (b) Hysteresis loop.................................................................................................................................................................... 313

3.10.9.6 (b) Retentivity ........................................................................................................................................................................... 315

3.10.9.7 (b) Coercive force ..................................................................................................................................................................... 315

3.10.9.8 (b) Reluctance .......................................................................................................................................................................... 316

3.10.9.9 (b) Saturation points ................................................................................................................................................................. 317

3.10.9.10 (b) Eddy currents .................................................................................................................................................................... 319

3.10.10 (b) Protection for care and storage of magnets ............................................................................................................................. 319

3.10.11 (b) Magnetic Field Strength/Flux Density Curve (B-H Curve) ......................................................................................................... 321

3.10.12 (b) Characteristics of Ferromagnetic Materials............................................................................................................................... 326

3.11 INDUCTANCE/INDUCTOR (EASA Ref 3.11) Level 2............................................................................................................................... 331

3.11.1 Electromagnetic Induction .................................................................................................................................................................. 331

3.11.2 Action of inducing a voltage in a conductor moving in a magnetic field.............................................................................................. 331

3.11.3.1 Effect of the following on the magnitude of an induced voltage: magnetic field strength ............................................................ 333

3.11.3.2 Effect of the following on the magnitude of an induced voltage: rate of change of flux .............................................................. 334

3.11.4 Force on a Current-carrying Conductor in a magnetic Field............................................................................................................... 339

3.11.5 Lenz's Law ......................................................................................................................................................................................... 342

3.11.6 Polarity determining rules................................................................................................................................................................... 345

3.11.7 Back EMF and Inductance ................................................................................................................................................................. 347

3.11.8 Saturation Point................................................................................................................................................................................ 350

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3.11.8.1 Time Constant .......................................................................................................................................................................... 354

3.11.8. 2 Inductance in Series and Parallel ............................................................................................................................................ 361

3.11.9 Mutual Induction ............................................................................................................................................................................... 367

Refer Figure 182, .............................................................................................................................................................................................. 369

3.11.9.1 The effect the rate of change of primary current and mutual inductance has on induced emf ................................................... 371

Factors affecting Mutual Inductance......................................................................................................................................................... 371

3.11.10 Principle Uses of Inductors............................................................................................................................................................... 372

3.11.10.1 Types of Inductors .................................................................................................................................................................. 372

3.11.10.2 Types of Cores ....................................................................................................................................................................... 374

3.12 DC MOTOR / GENERATOR THEORY (EASA Ref 3.12) Level 2............................................................................................................. 377

3.12.1 Basic Generator Theory ..................................................................................................................................................................... 377

3.12.1.1 Basic DC Generator ................................................................................................................................................................... 381

3.12.1.2 Principle of DC Generator ........................................................................................................................................................ 382

3.12.2 Construction and Components in a DC Generator ............................................................................................................................. 386

3.12.2.1 Commutation .............................................................................................................................................................................. 393

3.12.2.2 Armature Reaction...................................................................................................................................................................... 397

3.12.3 Types of DC Generators .................................................................................................................................................................... 399

3.12.3.1 Series –wound DC Generator .................................................................................................................................................... 399

3.12.3.2 Shunt-wound DC Generator ....................................................................................................................................................... 401

3.12.3.3 Compound wound Generator ..................................................................................................................................................... 403

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3.12.3.4 Generator Ratings and Terms .................................................................................................................................................. 405

3.12.4 Basic Motor Theory .......................................................................................................................................................................... 409

3.12.4.1 Fleming’s Left Hand Rule ........................................................................................................................................................... 413

3.12.4.2 Action of a Basic Electric Motor ................................................................................................................................................ 415

3.12.5 A Practical DC Motor........................................................................................................................................................................ 416

3.12.5.1 Back emf .................................................................................................................................................................................... 416

3.12.5.2 Torque ........................................................................................................................................................................................ 418

3.12.5.3 Power ......................................................................................................................................................................................... 419

3.12.5.4 Reactive Sparking and Armature Reaction................................................................................................................................. 419

3.12.5.5 Speed control of a DC motor ...................................................................................................................................................... 421

3.12.5.6 Reversal of Rotation of a DC Motor............................................................................................................................................ 422

3.12.6 Types of DC Motors ........................................................................................................................................................................... 424

3.12.6.1 Series Motor ............................................................................................................................................................................... 425

3.12.6.2 Shunt Motor ................................................................................................................................................................................ 427

3.12.6.3 Compound Wound Motor ........................................................................................................................................................... 429

3.12.7 Starter Generator ............................................................................................................................................................................... 433

13 AC THEORY................................................................................................................................................................................................ 435

3.13.1 Fundamentals..................................................................................................................................................................................... 435

3.13.2 AC Generation.................................................................................................................................................................................... 435

3.13.3 Waveform and Instantaneous Value .................................................................................................................................................. 439

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3.13.4 Sine Wave Characteristics ................................................................................................................................................................. 445

3.13.4.1 Peak Value ................................................................................................................................................................................. 445

3.13.4.2 Peak--to--Peak Value ................................................................................................................................................................. 447

3.13.4.3 Root Mean Square Value ........................................................................................................................................................... 449

3.13.4.4 Period and Cycle ........................................................................................................................................................................ 453

3.13.4.5 Frequency .................................................................................................................................................................................. 455

3.13.4.6 Angular Velocity.......................................................................................................................................................................... 465

3.13.4.7 Phase ......................................................................................................................................................................................... 467

3.13.4.8 Phase Difference ........................................................................................................................................................................ 469

3.13.5 Triangular/Square waves ................................................................................................................................................................... 471

3.13.6 Single/ Three phase principles ........................................................................................................................................................... 475

3.14 RESISTIVE (R), CAPACITIVE (C) AND INDUCTIVE (L) CIRCUITS (EASA 3.14) LEVEL 2 .................................................................... 481

3.14.1 Introduction......................................................................................................................................................................................... 481

3.14.1.1 Pure Resistance in AC Circuits................................................................................................................................................... 481

3.14.1.2 Power in Pure Resistive Circuits................................................................................................................................................. 483

3.14.1.3 Pure Inductance in AC Circuits................................................................................................................................................... 487

3.14.1.4 Power in Pure Inductive Circuits................................................................................................................................................. 489

3.14.1.5 Pure Capacitance in AC Circuits ............................................................................................................................................... 491

3.14.1.6 Power in Pure Capacitive Circuits .............................................................................................................................................. 493

3.14.2 Resistor and Inductor in Series ......................................................................................................................................................... 495

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3.14.3 Resistor and Capacitor in Series ...................................................................................................................................................... 499

3.14.4 Resistor, Inductor and Capacitor in Series ....................................................................................................................................... 504

3.14.5 Series Resonance ............................................................................................................................................................................ 507

3.14.7 Parallel Resonance ............................................................................................................................................................................ 515

3.14.8 Power in an AC Circuits ..................................................................................................................................................................... 520

3.14.8.1 True or Real, Apparent and Reactive Power .............................................................................................................................. 523

3.14.8.2 Power Factor .............................................................................................................................................................................. 525

3.15 TRANSFORMER (EASA Ref. 3.15) Level 2 ......................................................................................................................................... 42527

3.15.1 Transformer principles, construction, and operation........................................................................................................................... 423

3.15.1.1 Transformer Principles ............................................................................................................................................................... 423

3.15.1.2 Basic Construction of a Transformer ....................................................................................................................................... 424

3.15.2 Basic Operation of a Transformer ...................................................................................................................................................... 427

3.15.2.1 Schematic Symbols for Transformers........................................................................................................................................ 428

3.15.3 Transformer losses............................................................................................................................................................................. 429

3.15.4 Methods of overcoming losses........................................................................................................................................................... 430

3.15.5 Transformer action Under No Load and On Load Conditions ............................................................................................................ 432

3.15.6 Transformer Connections and Polarity Marking ................................................................................................................................. 435

3.15.7 Efficiency and Regulation................................................................................................................................................................... 437

3.15.8 Three Phase Transformers ................................................................................................................................................................ 438

3.15.9 Turns Ratio......................................................................................................................................................................................... 442

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3.15.10 Autotransformers.............................................................................................................................................................................. 445

3.16 FILTERS (EASA Ref 3.16) Level 1 ........................................................................................................................................................... 448

3.16.1 Introduction..................................................................................................................................................................................... 56548

3.16.2 The Cut-off Frequency ................................................................................................................................................................. 56950

3.16.3 Operation, application and uses: low-pass..................................................................................................................................... 57051

3.16.4 Operation, application and uses: high-pass ................................................................................................................................. 57553

3.16.5 Operation, application and uses: band-pass............................................................................................................................... 57958

3.16.6 Operation, application and uses of the following filters: band stop............................................................................................... 58260

3.17 AC GENERATORS (EASA Ref 3.17) Level 2...................................................................................................................................... 58563

3.17.1 Rotation of a Loop in a Magnetic Field and Waveform Produced................................................................................................. 58563

3.17.2 Rotating-Armature Alternators....................................................................................................................................................... 58563

3.17.3 Rotating-Field Alternators............................................................................................................................................................. 59169

3.17.4 Three Phase Star and Delta Connections ...................................................................................................................................... 59575

3.17.5 Permanent Magnet Generator....................................................................................................................................................... 59978

3.17.6 Prime Movers ................................................................................................................................................................................ 60180

3.17.7 Alternator Rotors ........................................................................................................................................................................... 60180

3.17.8 Alternator Characteristics and Limitations ..................................................................................................................................... 60382

3.17.9 Power in a Three Phase System ................................................................................................................................................... 60483

3.18 AC MOTORS (EASA Ref 3.18) Level 2 ................................................................................................................................................ 60685

3.18.1 Introduction..................................................................................................................................................................................... 60785

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3.18.2 Rotating Magnetic Fields........................................................................................................................................................... 60986

3.18.2.1 Two-Phase Rotating Magnetic Fields ................................................................................................................................... 60986

3.18.2.2 Three-Phase Rotating Fields.................................................................................................................................................. 61389

3.18.2.3 Rotor Behavior in a Rotating Field.......................................................................................................................................... 61590

3.18.3 Construction, Principles of operation and Characteristics of AC Synchronous Motor .................................................................... 61792

3.18.4 Construction , Principles of operation and Characteristics of AC Induction Motor......................................................................... 62196

3.18.5 Two Phase Induction Motor................................................................................................................................................................ 500

3.18.6 Single-Phase Induction Motors........................................................................................................................................................... 501

3.18.6.1 Single-phase Induction Motors ................................................................................................................................................... 503

3.18.6.2 Split-phase Induction Motor........................................................................................................................................................ 504

3.18.6.3 Split-Phase Induction Motors...................................................................................................................................................... 506

3.18.6.4 Capacitor-Start .......................................................................................................................................................................... 506

3.18.6.5 Resistance-Start ......................................................................................................................................................................... 508

3.18.6.6 Shaded-Pole Induction Motors ................................................................................................................................................... 510

3.18.7 Speed of Single-Phase Induction Motors ........................................................................................................................................... 514

3.18.8 Speed Control of AC Motor ............................................................................................................................................................... 515

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS ELECTRON THEORY (DCAM 3.1 L1)

For Training Purposes Only Issue 1 Revision 2 June 2011 Page 1

3.1 ELECTRON THEORY (EASA Ref: 3.1) Level 1

3.1.1 Atomic Structure

An atom is the smallest part of an element (e.g. carbon, copper, silver) and is built up such as a small solar system.

The nucleus in its centre consists of protons and neutrons. Spinning around the nucleus are the electrons. The structure of the nucleus and

the number of spinning electrons decide the type of element. The nucleus of the atom and the electrons has different electric charges as

shown in Figure 1:

• the protons are positively charged

• the electrons are negatively charged

• the neutrons are electrically neutral.

These different electrical charges create forces which combine to hold the atom together. Protons and neutrons comprise almost the total

mass of an atom.

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FIGURE 1: The Atomic Structure

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3.1.2 Atomic Number

The number of planetary electrons in an atom varies with the element and gives the atomic number of the element.

Figure 2 shows two examples of atomic structures. The atomic number of carbon is six, indicating that the carbon atom has six electrons in

orbit. Copper has an atomic number of 29 and therefore contains 29 electrons. An atom under normal conditions is electrically neutral. The

numbers of electrons and protons are equal and, since the negative charge of an electron is neutralized by the equal positive charge on a

proton, the atom as a whole has zero charge.

The neutron increases the mass of the atom but does not contribute to its charge. The chemical and electrical characteristics of an element

(atom) depend upon the action of ’free’ electrons. ’Free’ electrons are those electrons that appear in the outermost orbit (shell) of an atom as

depicted in Figure 3.

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FIGURE 2: Atomic Number of Elements

FIGURE 3: Free Electrons of Atoms

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3.1.3 Ionisation

Atoms are affected by many outside forces such as heat, light, electric fields, magnetic fields and chemical reaction. Often the balanced state

of the atom is upset by one or more of these forces. As a result an atom can lose or gain an outer electron. When this happens the atom is no

longer in a neutral state, and becomes an ion.

Figure 4, (detail a) shows an atom that is neutral because it contains an equal number of protons and electrons. Figure 4, (detail b) shows

the condition that exists when an atom loses an electron. The atom now has one more proton than electrons. Thus there is one positive

charge that is not cancelled by a negative charge. Therefore the atom has a net positive charge and is known as a ’positive ion’. If an atom

has ’collected’ a stray electron there is one negative charge which is not offset by a corresponding positive charge. Therefore the atom has a

net negative charge and is known as a negative ion Figure 4, (detail c).

In certain materials these outer electrons are so weakly bound to their nucleus that they can easily be forced away and left to wonder among

other atoms at random. Such electrons are the ’free’ electrons as described before. The movement of ’free’ electrons allow electric current to

flow.

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FIGURE 4: Ionisation of Atoms

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3.1.4 Molecular structure of conductors, semiconductors and insulators

3.1.4.1 Conductors and Insulators

A conductor is a substance in which there is a constant exchange of ’free’ electrons between atoms. Pure metals are good conductors, silver

being the best and copper ranking second.

An insulator is a substance in which there is practically no random movement of ’free’ electrons. In this case the outer orbital electrons are

tightly bound to their parent nuclei and will not normally break away.

Good insulators are:

• porcelain

• mica

• ebonite

• dry air

• rubber.

No firm line can be drawn between conductors and insulators. Silver is a very good conductor; rubber is a very good insulator. Between these

extremes lies a group of material which are neither good insulators nor conductors. This group is termed semi--conductors. Semi--conductors

possess some very important properties, which are used in transistors and other solid state devices. Figure 5 shows groups of conductor,

semiconductor and insulator.

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FIGURE 5: Conductors and Insulators

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS STATIC ELECTRICITY AND CONDUCTION (DCAM 3.2 L2)

For Training Purposes Only Issue 1 Revision 0 Jan 2011 Page 9

3.2 STATIC ELECTRICITY AND CONDUCTION

3.2.1 Static electricity and distribution of electrostatic charges

3.2.1.1Friction

A good example to explain static electricity is, to generate electricity by friction. This is done by separating electrons from their parent atoms. If

two different materials are rubbed together, electrons may be forced out of their orbits in one material and transferred to the other material.

The material which captures electrons acquires a negative charge of course. The material which loses electrons acquires a positive charge.

The resulting distribution of electric charges is known as static electricity. Both materials retain the static charges they have acquired, until

something occurs to ’discharge’ them. Materials easily acquire a charge of static electricity include glass, amber, hard rubber, waxes, flannel,

silk, rayon and nylon.

Example:

When a hard rubber rod is rubbed with fur, the fur loses electrons to the rod. The rod becomes negatively charged and the fur positively

charged.

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NOTES

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3.2.2 Electrostatic laws of attraction and repulsion

There is a basic law which states that, like charges repel and unlike charges attract (coulomb’s law). Because like charges repel, two electrons

repel each other Figure 6, (detail a) as do two protons Figure 6, (detail b). It can be seen how the lines of force interact between two

electrons or protons. The next effect is that the electrons or protons attempt to move apart.

In Figure 6, (detail c) an electron and a proton are shown. Here, the two fields interact in such a way that the two charges attract and tend to

move together. Coulombs law holds true for concentration of charges as well.

A shortage of electrons causes a positive charge and is called a positive potential. An excess of electrons causes a negative charge or

negative potential.

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FIGURE 6: Behaviour of Like and Unlike Charges

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3.2.3 Units of charge, Coulomb's Law

The charge of an electron (or proton) is extremely small and is inconvenient for practical measurements. The practical unit of charge or

quantity of electricity is the coulomb. The symbol for coulomb is Q. A charge of one coulomb is equal to the charge of 6.29 x 1018 electrons.

A difference in potential (voltage) will cause electrons to flow from the negative potential to the positive potential if a conductor is connected

between the two potentials. The electrons are in effect attracted or pulled to the positive potential and repelled or pushed away from the

negative potential.

3.2.4. Conduction of Electricity in solids, liquids, gases and vacuum

Solids – Electrons

Liquids – Ions (both positives and negatives)

Gases or Vacuum – (both electrons and ions)

Refer Figure 7,

Current flows in solid. A free electron travels only a short distance before it combine with the positive ion

Current flows in gas. Both electrons and ions serve as current carrier.

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FIGURE 7: Conduction of Electricity in Solids, liquids, gases and vacuum

Direction of Current

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS ELECTRICAL TERMINOLOGY, UNIT AND AFFECTING FACTORS (DCAM 3.3 L2)


3.3 ELECTRICAL TERMINOLOGY, UNIT AND AFFECTING FACTORS

3.3.1 Potential Difference

The difference between positive and negative charge is called a potential difference (PD) and is measured in Volts (V). Figure 8,

(detail a) shows a PD of 100 V between a positive charge and a neutral charge, whereby the neutral charge is negative with respect to the

positive charge.

In Figure 8, (detail b) a PD of 100 V between a neutral charge and a negative charge is shown. The neutral charge is positive with respect to

the negative charge. A PD of 200 V is shown on Figure 8, (detail c) between a negative charge of -100 Volts and a positive charge of +100 V.

The neutral charge between positive and negative is negative with respect to +100 V and positive with respect to -100 V.

A difference in potential (voltage) will cause electrons to flow from the negative potential to the positive potential if a conductor is connected

between the two potentials. The electrons are in effect attracted or pulled to the positive potential and repelled or pushed away from the

negative potential.

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FIGURE 8: Potential Differences

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3.3.2 Electromotive Force (EMF)

An electromotive force (EMF) is an electrical pressure that is able to force electrons to move a current flow around a circuit. This means that a

cell, battery or generator can generate an EMF that can force a current to flow around a circuit.

A simple closed electrical circuit such as a conductor and a lamp connected between the terminals of a battery provides two concurrent

energy transformations. Chemical energy is converted to electrical energy by the battery, and electrical energy is converted to light energy in

the lamp.

Note: Beside the light energy a part of the electrical energy is converted into heat energy that is also radiated by the lamp.

Figure 9 shows a simple electric circuit which consists of a battery, a switch and a resistor (component that consumes energy). The battery

generates an EMF to force a current flow when the switch is closed. In this case, a potential difference (PD) exists across the resistor. The PD

is the difference in electrical pressure or voltage between two points.

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FIGURE 9: Electromotive Force (EMF)

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The EMF can only be measured when no current flows Figure 10, (detail a). When current flows, the EMF cannot be measured, only the PD

can be determined. The reason for this is that a voltage is dropped across the internal resistor of the battery Figure 10, (detail b).

When a current flows is: When no current flows is:

EMF = PD + internal voltage drop. EMF = PD

EMF and PD are both measured in volts (V).

FIGURE 10: Electromotive Force (EMF) and Potential Difference (PD)

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3.3.3 Voltage

Voltage is an electrical pressure which causes an electric current to flow through a complete electric circuit as shown as shown in Figure 11.

Electric potential is energy per unit charge. Measured in joules per coulomb (= volts)

FIGURE 11: Voltage

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3.3.4 Current

Current is the flow of electrons from a negative charge to a positive charge. In order to measure current flow, the number of electrons passing

a point in a specific time must be measured. This measurement requires a unit and is known as the ampere (A).

One coulomb is equal to 6.29 x 1018 electrons. An ampere is equal to one coulomb per second.

When 6.29 x 1018 electrons flow through a wire each second, the current flow is one ampere. If twice the numbers of electrons flow each

second, the current is two amperes. This relationship is expressed by the equation:

Q (coulombs) = I (ampères) x t (seconds) or I =Q/t (ampères)

The symbol for quantity of current is I. The unit of current (to measure current) is ampere (A). The name ’ampere‘is often shortened to

’Amp ‘and is further abbreviated to ‘A‘. Often, the ampere is a too large unit. In these cases metric prefixes are used to denote smaller units.

One thousandth (0.001) of an ampere is one milli-ampere (1 mA). One millionth (0.000001) of an ampere is one microampere (1 µA). The rate

of flow of electrons can be in one of three forms known as direct current (DC), pulsating current and alternating current (AC).

A direct current is formed when an electric current is flowing continuously in one direction at a steady rate Figure 12, (detail a).

A pulsating current is formed when current flows in one direction, but undergoes regular, recurring variations in magnitude Figure 12,

(detail b).

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An alternating current is formed by an electric current which alternatively reverses its direction in a circuit in a regular manner. One cycle is a

complete variation Figure 12, (detail c).

The number of such cycles occurring in one second is termed frequency. The unit of frequency is the hertz (Hz).

FIGURE 12: Forms of Current

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3.3.5 Resistance

Resistance is a property which opposes current flow. Some materials such as glass and rubber, offer a great deal of opposition to current flow;

they are said to have ’a very high resistance’. Other materials, such as silver or copper, offer very little opposition to current flow. Therefore

they have ’a very low resistance’. The schematic symbol of resistance is R.

The unit of resistance is the Ohm ().

For smaller and larger resistance values the following terms are used:

1

1000000 Ohm = 1 micro-Ohm = 1 µ

1

1000 Ohm = 1 milli-Ohm = 1 m

1000 Ohm = 1 kilo-Ohm =1 k

1000000 Ohm = 1 Mega-Ohm =1 M

Resistance is deliberately added to electric circuits to limit currents or to divide voltages.

The devices used to add known resistance to a circuit are called resistors.

Resistors in circuit diagrams are sketched down by symbols as shown in Figure 13.

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FIGURE 13: Resistor Symbols

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Three factors affecting resistance:

1. Length of resistance material, whereby the resistance is proportional to length.

2. Cross--sectional area of resistance, whereby the resistance is inversely proportional to cross--sectional area.

3. Resistance material. Each material has a characteristic resistance or resistivity (symbol pronounced rho). Rho is normally the resistance

of a metre length of material with a cross--sectional area of one millimetre squared (1 mm2).

3.3.6 Conductance

Conductance is the opposite of resistance and is defined as the ease with which a material passes current. Conductance is the reciprocal of

resistance:

Conductance = 1

Resistance

The unit of conductance is the Siemens (S). Therefore is G = 1 or R = 1

R G

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3.3.7 Electric Charge

Electric charge is a characteristic of subatomic particle that will gives materials their electromagnetic properties.

A nucleus consists of neutron, proton and electron which have their properties of electric charge as below:

Proton – Positive charge

Electron – Negative charge

Neutron – Zero charge / Neutral

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3.3.8 Conventional Current Flow

The direction of moving positive charge opposite from electron flow. Refer Figure 14. The direction of conventional current is the direction of

positive charges in motion

FIGURE 14: Conventional Current Flow

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3.3.9 Electron Flow

The direction of the electron drift is from the negative side of the battery to the positive side via a local resistance (R) as in Figure 15.

While in Figure 16, the electrons inside the battery move from the positive terminal to the negative terminal because of the potential difference

FIGURE 15: Electron Flow

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NOTES

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FIGURE 16: Electron Flow

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS GENERATION OF ELECTRICITY (DCAM 3.4 L1)


3.4 GENERATION OF ELECTRICITY

For an electron to move (electric current), it must be given force from somewhere. This force is converted into electricity when electrons move.

The six basic means to bring about the movement of electrons and thus generate electricity are friction, magnetism, and heat, and pressure,

light and chemical action.

Figure 17 shows all methods available to generate electricity.

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FIGURE 17: Sources of Electricity Generation

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3.4.1 Friction

A good example to explain static electricity is, to generate electricity by friction. This is done by separating electrons from their parent atoms.

If two different materials are rubbed together, electrons may be forced out of their orbits in one material and transferred to the other material.

The material which captures electrons acquires a negative charge of course. The material which loses electrons acquires a positive charge.

The resulting distribution of electric charges is known as static electricity. Both materials retain the static charges they have acquired, until

something occurs to ’discharge’ them. Materials easily acquire a charge of static electricity include glass, amber, hard rubber, waxes, flannel,

silk, rayon and nylon.

In Figure 18, when a hard rubber rod is rubbed with fur, the fur loses electrons to the rod. The rod becomes negatively charged and the fur

positively charged.

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FIGURE 18: Generation of Static Electricity by Friction Proprietary of




3.4.2 Magnetism

The movement of a magnet in a coil causes an induced voltage in the latter as in Figure 19. This depends on the direction of the magnet field

and the speed of movement of the magnet in the coil. When a bar magnet is moved into and out of a coil a measuring instrument connected to

the coil indicates a voltage (induced voltage).This process is called induction shown in Figure 20.

During the induction process, mechanical energy is converted into electrical energy. The direction of the induced voltage depends on the

direction of movement of the magnet and on the direction of the magnet field. The value of the induced voltage increases with the speed of the

magnet. The generation of induced voltages can be explained by the fact that the ’free’ electrons, present in the wire of the coil, are moved by

the movement of the magnet towards one end of the coil if the magnetic flux increases.

FIGURE 19: Induced Voltage

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FIGURE 20: Induction ProcessProprietary of




3.4.3 Heat

Refer to Figure 21

A thermo--electric effect is caused by heat being applied to two conductors of different metals (e.g. iron and copper) connected together. The

generated voltage depends upon the material used and the difference in temperature between the hot and the cold junctions.

The thermo--electric effect is used to measure temperature in a thermocouple instrument of engines, exhaust gases, ovens and furnaces.

It can be also used to measure current flow (the current heats a resistor in which the hot junction is placed) where direct measurement of a

current (radio frequency currents for example) is not possible.

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FIGURE 21: Thermoelectric Effect

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3.4.4 Pressure

Refer to Figure 22

When a quartz plate is compressed, electric charges are generated on its faces. Tension generates charges of the opposite sign. This effect is

known as electro-striction or piezoelectric effect. This electro-striction or piezoelectric property is reciprocal.

When a voltage is applied between two faces of quartz it contracts or expands a little, according to which face is made positive and which is

made negative. These effects are used for transmission and reception of ultrasonic vibrations in water (sonar, echo sounder).

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FIGURE 22: Piezoelectric Effect

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3.4.5 Light

Refer to Figure 23

A photo--electric effect occurs when light strikes a photo voltaic material and causes electrons to be emitted. The result is an electric voltage.

This effect is used in photo--diodes, photo--transistors, solar cells and silicon cells.

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FIGURE 23: Photoelectric Effect

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3.4.6. Chemical

Refer to Figure 24

Dissimilar substances have opposite polarities with respect to one another and that, when two such substances are rubbed together, one will

have a positive charge and the other a negative charge.

Dissimilar metals also have this property, and when two such metals are placed in contact with each other, there will be a momentary flow of

electrons from the one having a negative characteristic to the one having a more positive characteristic.

If two plates of dissimilar metals are placed in a chemical solution called an electrolyte, opposite electric charges will be established on plate A

and plate B. The result is an electrical voltage (potential difference).

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FIGURE 24: Chemical Effect

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS DC SOURCES OF ELECTRICITY (DCAM 3.5 L2)


3.5 DC SOURCES OF ELECTRICITY

3.5.1 Basic chemical action

Refer to Figure 25

If two plates of dissimilar metals are placed in a chemical solution called an electrolyte, opposite electric charges will be established on plate A

and plate B. The result is an electrical voltage (potential difference). This arrangement of plates in an electrolyte is known as simple cell. If two

or more cells are connected in series a battery is created. All cells and batteries use some form of electrolyte. If certain substances are

dissolved in water they will ionise, i.e. they will give off positive and negative ions. This is known as electrolytic dissociation. These substances

are known as electrolytes, and conduct electric current. Electrolytes used in cells or batteries are either acids or alkaline.

The relationship between dissimilar metals is known as the electrochemical series. If two electrodes made of different materials are immersed

in an electrolyte, an electrical voltage is formed between them.

Example:

The voltage of a Zn - Cu cell.

Potential (voltage) of the Cu electrode = +0.34 V.

Potential (voltage) of the Zn electrode = - 0.76 V.

The voltage (potential difference) of this cell is:

+0.34 V - (- 0.76 V) = 1.1 V

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FIGURE 25: Electrochemical Series

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Refer to Figure 26 and 27

A simple cell comprises zinc and a copper electrode immersed in a solution of sulphuric acid electrolyte. The function of the cell is to provide a

source of DC power. The cell achieves this by an energy conversion process which converts chemical energy into electrical energy.

As the zinc dissolves in the acid, positive ions move towards the copper electrode, causing the zinc to become negative with respect to the

electrolyte. The positive ions attach themselves to the copper electrode, causing it to be positive with respect to the electrolyte. In electrical

engineering a negative electrode is called cathode and a positive electrode is called anode.

A potential difference of approximately 1 V then exists between the anode and the cathode. The potential difference depends on the plate (or

electrode) materials. The voltage of the various materials is listed in the electro--chemical series.

If an electrical connection is now made between the anode and cathode, the potential difference existing across will cause a current flow in the

external circuit. The current flow is proportional to the plate area (and to a lesser extent internal resistance and temperature). More zinc will

dissolve and ions will continue to pass through the electrolyte to the copper. Electrons will flow in the external circuit from zinc to copper, while

the conventional current flows from copper to zinc

An electric current will continue to flow in the external circuit until one of several things happen:

• all the zinc has been dissolved or

• the electrolyte has become exhausted i.e. the supply of ions has been used up.

Once one more of these conditions have arisen the cell will no longer generate electric current and its useful life is finished.

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When a cell is generating an electric current, bubbles of hydrogen gas form at the anode. A film of hydrogen is slowly formed and acts as a

barrier to the chemical process. After a certain time the barrier effectively becomes a kind of insulator preventing further current passing. This

has the effect of causing reduced potential difference across the anode and cathode and increased internal resistance of the cell or battery.

The formation of a film of hydrogen at the anode of a cell when it is connected to an external circuit is termed polarization.

FIGURE 26: Unloaded Simple Cell FIGURE 27: Loaded Simple Cell

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3.5.2 Primary and Secondary Cells

Cells or batteries fall into two classes:

• primary cells

• Secondary cells.

Primary cells are not re-chargeable. These cells are generally sealed units which must be disposed of as scrap when they become

discharged. Secondary cells are re-chargeable units which can be regularly serviced to restore the chemical energy. When discharged the

cells are connected to an electrical supply of suitable voltage and current.

A primary cell is one in which the chemical reaction eats away one of the electrodes, usually the negative electrode. When this happens, the

electrode must be replaced or the cell must be discarded. In this galvanic-type cell, the zinc electrode and the liquid electrolyte usually

replaced when this happen. In the case of dry cell, it is usually cheaper to buy a new cell.

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NOTES

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3.5.3 Cells connected in series and parallel

3.5.3.1 Series Connection

Positive of one cell connected to negative of the next cell. Higher output voltage and capacity output of one cell only (remains the same)

Example:

A 12V lead acid battery contains 6 cells connected in series with each cell having a potential difference of 2V.

FIGURE 28: Cells Connected in Series

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FIGURE 29: Schematic Diagram: Cells in Series

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3.5.3.2 Parallel Connection

Cells or batteries connected in parallel have their like terminals connected together. Positive of one cell connected to the positive of the

next cell. Negative of one cell connected to the negative of the next cell The overall voltage remains the same The parallel connection is

equivalent to the increasing the size of the electrodes and electrolyte, which increase the current capacity

E.g. two 12-V lead acid batteries were connected in parallel; overall voltage is 12V and twice the current capacity.

FIGURE 30: Cells in Parallel

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FIGURE 31: Cells Connected in Parallel

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3.5.4 Internal resistance and its effect on a battery

3.5.4.1 Internal Resistance

Any source of supply must posses some ’Internal Resistance’ (Ri) and when a current flows in the circuit a voltage drop is developed across

this internal resistance. The internal resistance of the supply is 0.5 and the external resistance of the circuit is 5.5 . Refer Figure 32.

The total resistance of the circuit is:

RT= Ri + R1

RT= 0.5 + 5.5

RT= 6

The total current through the circuit is:

IT = EMF / RT

IT = 12 V / 6

IT = 2 A

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Therefore two amperes have flowed through the two resistances in series developing a voltage drop each.

URi = IT x Ri

URi = 2 A x 0.5

URi = 1 V

The polarity of URi is as shown in Figure 32 and is such as to subtract from the EMF.

The terminal voltage (PD) of the supply (sometimes named applied voltage) between terminals ’A’ and ’B’ is therefore:

PD= EMF − URi

PD= 12 V − 1 V

PD= 11 V

The current IT is checked again by the use of PD and R1:

IT = PD / R1

IT = 11 V / 5.5

IT = 2 A

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When a current is taken from a supply, the PD is equal to the EMF minus the voltage drop across the internal resistance of the supply.

EMF = PD + URi

EMF = IT x RT

PD = IT x R (external resistance)

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FIGURE 32: Internal Resistance

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3.5.4.2 Effects of Internal Battery Resistance

FIGURE 33: Effects of Internal Battery Resistance

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3.5.5 Aircraft batteries

A battery is a device composed of two or more cells that convert chemical energy into electrical energy

The chemical nature of the battery components provides:

• An excess of electrons at one terminal

• A deficiency at the other

When the two terminals are joined by a conductor, electrons flow causes the chemical composition of the active material changes

Battery output – a steady D.C. voltage.

In an aircraft, batteries are used for APU starting and to provide standby power for the aircraft.

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3.5.5.1 The dry cell

The dry cell is the most popular type of primary cell. It is ideal for simple applications where an inexpensive and non-critical source of

electricity is all that is needed. The dry cell is not actually dry. The electrolyte is not in a liquid state, but is a moist paste. If it should become

totally dry, it would no longer be able to transform energy to electrical energy.

The construction of a common type of dry cell is shown in Figure 34A. These dry cells are also referred as Leclanche’ cells. The internal parts

of the cell are located in a cylindrical zinc container. The zinc container serves as the negative electrode (cathode) of the cell. The container is

lined with a non-conducting material, such as blotting paper, to separate the zinc from the paste. A carbon electrode is located in the centre,

and it serves as the positive terminal (anode) of the cell. The paste is a mixture of several substances such as ammonium chloride, powdered

coke, ground carbon, manganese dioxide, zinc chloride, graphite and water.

The electrolyte paste also serves to hold the anode rigid in the centre of the cell. When the paste is packed in the cell, a small space is left at

the top for expansion of the electrolyte paste caused by the depolarisation action. The cell is then sealed with a cardboard or plastic seal.

Since the zinc container is the cathode, it must be protected with some insulating materials to be electrically isolated. Therefore, it is common

practice for the manufacturer to enclose the cells in cardboard and metal containers.

The action of the water and the ammonium chloride in the paste, together with the zinc and carbon electrodes, produces the voltage of the

cell. Manganese dioxide is added to reduce polarization when current flows and zinc chloride reduces local action when the cell is not being

used.

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A cell that is not being used (sitting on the shelf) will gradually deteriorate because of slow internal chemical changes (local action) this

deterioration is usually very slow if cells are properly stored. If unused cells are stored in cool place, their shelf life will be greatly preserved.

Therefore, to minimize deterioration, they should be stored in refrigerated spaces. The cell is sealed at the top to keep air from entering and

drying the electrolyte. Care should be taken to prevent breaking this seal.

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The Leaclanche’ Cell

The dry cell, invented in 1867 by the French engineer Georges Leclanché (1839 - 1889)

Widely used as a source of electric energy in:

• electric torches

• small appliances such as transistor radios.

Once it is discharged it cannot be recharged, and must be discarded.

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FIGURE 34: Dry cell, cross sectional view

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3.5.5.2 Secondary cell

Batteries consisting of secondary cells are called storage batteries. The chemical action that releases electron flow is reversible (can be

recharged or restored). Secondary cells do not produce electrical energy, but store it in chemical form. Secondary cells can be charged and

discharged many times before they deteriorate to the point at which they must be discharged.

E.g. Lead-Acid Batteries and Nickel-Cadmium Batteries

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FIGURE 35: Theory of the Lead Acid Cell

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3.5.5.3 Lead Acid Types

• Positive plates made of lead peroxide (PbO2)

• Negative plates made of pure spongy lead (Pb)

• Electrolyte 30% sulphuric acid and 70% distilled water

Separators are used to keep the plate separated thus prevent internal short circuit. The material of the separators must be very porous

to offer minimum resistance to the current passing through. The separators are saturated with electrolyte.

FIGURE 36: Lead acid battery

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3.5.5.4 Lead Acid Battery Construction

• A lead acid battery consists of group of lead-acid cells connected in series.

• Each cells of a storage battery has positive and negative plates.

• A positive plate group consists of a number of positive plates connected to a plate strap.

• A negative group also connected in the same manner.

• These two groups meshed together with the separators between the positive and negative plates.

FIGURE 37: Lead acid battery construction

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3.5.5.5 Lead Acid Battery Operation

When the cell elements are assembled, they are placed in the cell container (made of hard rubber or plastic composition)

Cover made of material similar to cell container, sealed in with a special sealing compound to prevent spillage and loss of electrolyte.

The cell ventilation cap is necessary to provide a means where by gasses can escape. The type of cell construction permits the electrolyte to

circulate freely and also provides a path for sediment to settle at the bottom of the cell. When an external circuit is connected to a fully charged

cell, electron flows from the negative lead plates, via the circuit to the positive lead peroxide plates.

As an electron arriving at the positive plates, from the external circuit, drive negative oxygen ions from the lead peroxide into the electrolyte.

These combine wit hydrogen, which has lost sulphate ions to form water. The positive lead ions that are left on the positive plates also attract

and combine with sulphate ions from the electrolyte to form lead sulphate on the positive plates. Once lead sulphate collects on both the

positive and negative plates and the electrolyte becomes diluted by the water, which has formed in it, the cell is considered discharged. A

discharged cell is recharged using a direct current of the correct voltage.

When the positive plates of the cell are connected to the positive of the charging source and the negative plates to the negative of the source,

electrons are drawn from the positive plates and forced onto the negative plates. Electrons arriving at the negative plates drive negative

sulphate ions out of the lead sulphate back into the electrolyte. The sulphate ions join with hydrogen to form sulphuric acid. When the

electrons flow from the positive plates they leave positively charged lead ions. These attract oxygen from the water in the electrolyte to form

lead peroxide on the plates. When the cell is fully charged the positive plates again become lead peroxide and the negative plates lead. The

electrolyte becomes a high concentration of sulphuric acid.

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During the charging of the cell hydrogen gas released from the electrolyte and bubbles top the surface. As the cell nears full charge more

hydrogen is released and the bubbling increases. A vent is, therefore, incorporated in the cell cap. The voltage of a fully charged cell is

approximately 2.2 volts (2 volts nominal) and in the discharged state 1.8 volts.

FIGURE 38: Lead acid battery construction

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3.5.5.6 (HYDROMETER)

A hydrometer is a glass syringe with a float inside it. The float is a hollow glass tube sealed at both ends and weighted at the bottom end, with

a scale calibrated in specific gravity marked on its side. To test an electrolyte, draw it into the hydrometer using the suction bulb. Draw enough

electrolytes into the hydrometer to make the float rise. Do not draw in so many electrolytes that the float rises into the suction bulb. The float

will rise to a point determined by the specific gravity of the electrolyte. If the electrolyte contains a large amount of active ingredient, its specific

gravity will be relatively high. The float will rise higher than it would if the electrolyte contained only small amount of ingredient.

To read the hydrometer, hold it in a vertical position and read the scale at the point that surface of the electrolyte touches the float. Refer to

the manufacturer’s technical manual to determine whether or not the battery’s specific gravity is within specifications.

Specific Gravity Test Procedure:

1. Wear suitable eye protection.

2. Remove vent caps or covers from the battery cells.

3. Squeeze the hydrometer bulb and insert the pickup tube into the cell closest to the battery's positive (+) terminal.

4. Slowly release the bulb to draw in only enough electrolytes to cause the float to rise. Do not remove the tube from the cell.

5. Read the specific gravity indicated on the float. Be sure the float is drifting free, not in contact with the sides of top of the barrel. Bend down

to read the hydrometer at eye level. Disregard the slight curvature of liquid on the float.

6. Record your readings and repeat the procedure for the remaining cells.

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Note: Hydrometer should be flushed with fresh water after each use to prevent inaccurate readings. Storage battery hydrometers must be not

used for any other purposes.

FIGURE 39: Specific gravity test procedure (Hydrometer) Proprietary of




3.5.5.7 Lead Acid Battery Inspection and Service

General guide for inspection and service of batteries:

1. Inspect the battery.

• Ensure no crack on supporting structure.

2. Remove battery cover.

• Look for evidence of leakage and corrosion.

3. Check electrolyte level and add distilled water if required.

4. If the battery is suspected being defective, perform load test or a hydrometer test.

5. Inspect the battery terminal.

• Ensure the terminals are free from corrosion.

6. Inspect the battery cable.

7. Inspect the ventilation system of the Aircraft and battery box.

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3.5.5.8 Alkaline Battery

The Nickel-Cadmium Cell

Aircraft engines, particularly turbines, require extremely high current for starting. High rate discharge of lead acid batteries causes their output

voltage to fall, due to the increased internal resistance caused by the build-up of sulphate deposits. This drawback led to the development of

the alkaline cell for aircraft used.

The ni-cad battery has a very distinct advantage in that its internal resistance is very low. Its output voltage, therefore remain almost constant

until it is nearly totally discharged. The low resistance also allows high charging rates without damage. The ni-cad cell has positive plates

made from powdered nickel which is fused, or sintered to a porous nickel mesh. The mesh is then impregnated with nickel hydroxide. The

negative plates are of the same construction but are impregnated with cadmium hydroxide.

Separators of nylon and cellophane, in the form of a continuous strip wound between the plates, keeps the plates from touching each other.

Cellophane is used because it has low electrical resistivity and also acts a gas barrier preventing oxygen, given off at the positive plates during

overcharge, from passing to the negative plates. If the oxygen were allowed to reach the negative plates it would combine with active

cadmium, reduce cell voltage and produce heat as a result of chemical reaction. The electrolyte is an alkaline solution of potassium hydroxide

and distilled or de-ionized water with a specific gravity of 1.24 to 1.30.The specific gravity of the electrolyte does not change during charge or

discharge so it cannot be used to indicate the state of charge. The electrolyte does not play an active part in the chemical reaction and is used

only to provide a path of current flow.

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During charging of the cell an exchange of ions takes place. Oxygen is removed from the negative plates and added to the positive plates, the

electrolyte acting as an ionized conductor. The positive plates are, therefore brought to a higher state of oxidation. The electrolyte is forced out

to both plates during charging so that the electrolyte level in the cell rises. The electrolyte level is, therefore only checked and any water added

when the cell is fully charged. Towards the end of the charging process and during overcharging, gassing occurs as result of electrolysis. This

only reduces the water content of the electrolyte.

During discharge the chemical reaction is reversed. The positive plates gradually lose oxygen to become less oxidized and the negative plates

regain oxygen and change to cadmium hydroxide. The plate absorb electrolyte so that the level in the cell falls but it should always cover the

top of the plates.

The discharge and charging cycle of a ni-cad cell produces high temperature which, if not correctly monitored can break down the cellophane

gas barrier. This creates a short circuit allowing current flow to increase. More heat is produced, causing further break down. The condition is

aggravated by the internal resistance of the cell falling as the temperature rises. These factors all contribute to a process known as “thermal

runaway” which ultimately results in the destruction of the cell.

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FIGURE 41: Alkaline Battery FIGURE 42: Nickel Cadmium Battery

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FIGURE 43: Nickel Cadmium battery connections

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3.5.5.9 Alkaline Battery Inspection

The schedule servicing usually based on flying hours, annual and periodic inspection.

General guideline laid down by the manufacturer must be followed:

1) Inspect the battery case

2) Inspect the vent system for proper airflow

3) Inspect the cells and clean as needed

4) inspect the cell connectors for corrosion, cracks and overheating

5) Inspect the cell caps

6) Check the cell electrolyte for correct level

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3.5.5.10 Battery Charging

It should be remembered that adding the active ingredient to the electrolyte of a discharged battery does not recharge the battery. Adding the

active ingredient only increases the specific gravity of the electrolyte and does not converts the plates back to active materials, and so does

not bring the battery back to a charged condition. A charging current must be passed through the battery to recharge it.

Batteries are usually charged in battery shops. Each shop will have specific charging procedures for the types of batteries to be charged.

Two types of charging

1. Constant voltage charging

2. Constant current charging

1. Constant Voltage Charging

The charger supplies a constant voltage to a battery and allow current to charge as the battery become charged. If the battery is nearly

discharged it will offer very little opposition to the electron flowing into the battery. As the battery becomes charged, resistance increases thus

current will slowly diminishing.

On aircraft, the battery charged with the constant voltage charging. If more than one battery put on charge, the battery must be connected in

parallel.

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2. Constant Current Charging

The charger supplies a consistent current to a battery. The charging equipment monitors current flow and varies the applied voltage in order to

charge the battery. When charging more than one battery, batteries are to be connected in series. A constant current charging requires close

supervision to avoid over charging.

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3.5.6 Thermocouples

A thermocouple is a sensor for measuring temperature; it consists of two dissimilar metals, joined together at one end.

When the junction of the two metals is heated or cooled a voltage is produced that can be correlated back to the temperature.

The thermocouple alloys are commonly available as wire.

In 1821 a German physicist named See beck discovered the thermoelectric effect. Thermocouples make use of this so-called Peltier-Seebeck

effect. Thermocouples produce an output voltage which depends on the temperature difference between the junctions of two dissimilar metal

wires and it measure the temperature difference between two points, not absolute temperature

3.5.6.1 System Operation

Refer to Figure 45

The thermoelectric voltage produced depends on:

Material used

Temperature difference between hot and cold junction

Each hot junction is a pair of dissimilar metallic electrical conductors If two dissimilar metals are joined together a contact potential, which is

independent of any external electric supply, will appear at the junction. In a thermocouple two dissimilar metals are joined at both ends to form

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a hot junction and a cold junction. In the simplest arrangement the thermocouple would be connected directly to the meter, the meter terminals

being the cold junction in an aircraft, however the hot junction is in the engine and the meter indicator on the flight deck.

FIGURE 45: Thermocouple

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If the thermocouple cold junction were to be connected to the meter by copper wires, as shown in figure 45, the potential at the cold junction

would be as if point ‘A’ and ‘B’ were joined together (provided that A and B were at the same temperature). This would still allow the meter to

read the difference between V1 and V2.

If however, the hot and cold junctions were relatively close together, the temperature difference between them would not be so great as if they

were apart. The thermocouple EMF would therefore, be reduced and in Figure 45, there would be a problem of fluctuations in the readings.

If the cold junction was in the meter itself there would be a greater temperature difference and hence a greater EMF and also less fluctuations.

To achieve this, the connecting leads from the thermocouple to the meter must be of the same materials as the thermocouples or at least

have the same thermoelectric characteristic. They are called extension leads if they are of the same material and compensating leads if they

are of the same characteristic.

The small EMF generated by the thermocouple is not only dependent upon the temperature but also upon the metals employed.

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The measuring junction: (often referred to as the "hot" junction) is that which is exposed to measured temperature.

The reference junction: Other junction which is kept at a known temperature; this is often referred to as the "cold" junction.

The term thermocouple referred to the complete system for producing thermal voltages

Refer to Figure 46

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FIGURE 46: Thermocouple Principle

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3.5.6.2 Types of Thermocouple

Surface contact

Designed to measure temperature of a solid component

Used as the temperature-sensing element of air-cooled-engine cylinder-head temperature-indicating systems

Immersion type

Designed for the measurement of gases, liquid (e.g. oil temperature).

Used as the sensing element of turbine-engine gas temperature-indicating systems.

Copper-Constantan (T Curve)

The Copper-Constantan thermocouple, with a positive copper wire and a negative Constantan wire is recommended for use in mildly oxidizing

and reducing atmospheres up to 400ºC. They are suitable for applications where moisture is present. This alloy is recommended for low

temperature work since the homogeneity of the component wires can be maintained better than other base metal wires. Therefore, errors due

to the non-homogeneity of wires in zones of temperature gradients are greatly reduced.

Chromel-Alumel (K Curve)

The Chromel-Alumel thermocouple, with a positive Chromel wire and a negative Alumel wire, is recommended for use in clean oxidizing

atmospheres. The operating range for this alloy is 1260ºC for the largest wire sizes. Smaller wires should operate in correspondingly lower

temperatures.

Refer to Figure 47

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FIGURE 47: Copper-constantan (T Curve) / Chromel-Alumel (K Curve)

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3.5.7 Photocells

Photovoltaic cell, also known as a solar cell and photocell It is a device that converts a visible light, infrared and ultra violet directly into a

voltage. Since the current from a photocell can easily be used to operate switches or relays, it is often used in light-actuated counters,

automatic door openers, and intrusion alarms. Photocells in such devices are popularly known as electric eyes.

Photo-emission:

The application of light causes the emission of electron from a prepared surface, the construction of which is shown in Figure 48A. With the

positive of a supply connected to the anode of the cell and the negative to the cathode, the current in the circuit will depend upon the amount

of light falling on the device: no light, no current; high intensity light, high current.

When the cell is used in an aircraft smoke detector, a projector lamp shines abeam of light past the detector cell. If no light reaches the cell, no

current flows in the cell’s external circuit and no warning is given.

When smoke appears in the detection chamber, the projection lamp beam is refracted onto the detector cell by the smoke particles. The cell

conducts activating the smoke warning circuit. This shown in Figure 48B Proprietary of




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Photo-voltaic:

The application of lights causes the production of a voltage. It can be used to produce electrical energy for a variety of purposes. If a large

number of cells are connected together to form a solar panel the power generated is limited only by number of cells employed.

The silicon solar cell consists of a water of silicon which has been doped to make it a semiconductor. A thin layer of boron is then diffused into

it. The wafer is reinforced with metal and provided with electrical contacts to enable it to be connected to other cells

Photon light penetrating an atom of the cell forces electrons in the atom into the conduction band. This produces a voltage across the cell

which can be used to drive a current around an externally connected circuit.

They are many uses of the solar cell, from the operation of light meters in cameras to powering calculators and satellites in space.

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Schematic symbol for a photovoltaic cell

The device is a flat semiconductor P - N junction. The assembly is made transparent - light can fall directly on the P-type silicon.

The metal ribbing, forming the positive electrode, is interconnected by means of tiny wires. The negative electrode is a metal backing, placed

in contact with the N-type silicon.

Most solar cells provide about 1 watt and 0.5 Volt.

3.5.7.1 Construction of Photo-cells

Two semiconductor materials are sandwiched together. Electrical energy is produced when light shines on the cell

The power capacity of a photocell is very small. It reacts to light-intensity variations in an extremely short time.

This characteristic makes the photocell very useful in detecting or accurately controlling a great number of operations.

The photoelectric cell, or some form of the photoelectric principle, is used in:

television cameras

automatic manufacturing process controls

door openers

burglar alarms, and so forth.

Refer to Figure 48C

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FIGURE 48: Operation of Photo-CellsProprietary of


PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS DIRECT CURRENT (DC) CIRCUITS (DCAM 3.6 L2)


3.6 DIRECT CURRENT (DC) ELECTRICAL CIRCUITS (EASE Ref 3.6) Level 2

3.6.1 Introduction

A direct current (DC) electrical circuit consists of a source of DC electricity with a conducting wire going from one of the source terminals to a

set of electrical devices and then back to the other terminal, in a complete circuit. A DC circuit is necessary for DC electricity to exist. DC

circuits may be in series, parallel or a combination. Understanding DC circuits is important for learning about the more complex AC circuits,

like those used in homes.

3.6.1.1 Simple circuit

If you take a continuous source of DC electricity, such as a battery, and connect conducting wires from the positive and negative poles of the

battery to an electrical device such as a light bulb, you have formed an electric circuit (Figure 49).

In other words, the electricity flows in a loop from one end of the battery (or source of electricity) to the other end in a circuit. The concept of

electric circuits is the basis for our use of electricity. One nice feature of an electrical circuit is that you can install a switch in the circuit to turn

the power on or off when you want.

Note: Although electrons move from a negative (-) area toward the positive (+), the convention was established that electricity is designation

as moving from (+) to (-).

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3.6.1.2 Power source, Voltage, current and resistance

A DC circuit requires a source of power. Typically, a battery is used to provide continuous DC electricity. A DC generator is another source of

energy. Alternating current (AC) electricity can be modified through a rectifier or adapter to create DC electricity. The common adapter used

for some of your small DC-powered devices will transform 11OV AC house current into 12V DC current for your device.

The electricity moving through a wire or other conductor consists of its voltage (V), current (I) and resistance (R). The voltage or potential

energy of a source of electricity is measured in Volts. The current of amount of electrons flowing through the wire is measured in Amperes or

Amps. The resistance or electrical friction is measured in Ohms.

3.6.1.3 Conductors

The wire and electrical devices must be able to conduct electricity. Metal such as copper is a good conductor of electricity and has a low

resistance. The tungsten filament in a light bulb conducts electricity, but it has high resistance that causes it to heat up and glow.\

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3.6.1.4 Series DC circuit

In an electrical circuit, several electrical devices such as light bulbs can be placed in a line or in series in the circuit between the positive and

negative poles of the battery. This is called a series circuit (Figure 50). One problem with such an arrangement is if one light bulb burns out,

then it acts like a switch and turns off the whole circuit.

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3.6.1.5 Schematic

Every device in a DC circuit, whether a light bulb or electrical motor can be represented by an electrical resistance or resistor. Usually, when

drawing a circuit diagram or schematic, you use certain symbols for the battery and resistors. The circuit elements are connected end-to-end

(Figure 51). With this configuration, the current through each element is the same, but the voltage drop across each element is different.

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3.6.1.6 Parallel DC circuit

Devices can also be arranged in a parallel configuration, such that if any bulbs go out, the circuit is still intact. Not only is a parallel circuit

useful for holiday lighting, the electrical wiring in homes is also in parallel. In this way lights and appliances can be turned on and off at will.

Otherwise if you turned one light off or one burned out, all the other lights in the house would go off too (Figure 52&53).

If either light bulb would go out, the other would still shine. You could add other bulbs or even appliances such as electric motors in parallel to

this circuit, and they would remain independent of each other. You could also replace a bulb with a series circuit of bulbs or add bulbs or

devices in series between parallel items. There are many combinations possible.

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Quiz to check your understanding

1. Why do they call it a DC circuit?

a) The electricity flows from the source around and back to the source in a circuit

b) Because most have a circuit breaker installed

c) To warn people of possible shocks

2. What happens when a light burns out in a series circuit?

a) The other lights remain lit

b) The voltage increases dramatically

c) The circuit is broken and all lights go out

3. How could you turn off a parallel circuit?

a) You can't turn off a parallel circuit

b) Put a switch before the parallel configuration, like near the battery

c) Unscrew one light bulb

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RV

I =

3.6.2 Ohm’s Law

Ohm's law states that, in an electrical circuit, the current passing through a conductor, from one terminal point on the conductor to another

terminal point on the conductor, is directly proportional to the potential difference (i.e. voltage drop or voltage) across the two terminal points

and inversely proportional to the resistance of the conductor between the two terminal point. For real devices (resistors, in particular), this law

is usually valid over a large range of values of current and voltage, but exceeding certain limitations may result in losing simple direct

proportionality (e.g. temperature effects). In mathematical terms, this is written as:

Where I is the current, V is the potential difference, and R is a constant called the resistance. The potential difference is also known as the

voltage drop, and is sometimes denoted by E or U instead of V. The SI unit of current is the ampere; that of potential difference is the volt; and

that of resistance is the ohm, equal to one volt per ampere.

The law was named after the physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage, and

current passing through, simple electrical circuits containing various lengths of wire, and presented a slightly more complex equation than the

above equation to explain his experimental results. The equation above could not exist until the ohm, a unit of resistance, was defined (1861,

1864).

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Figure 54: A voltage source, V, drives an electric current, I, through resistor, R, the three quantities obeying Ohm’s law: V = IR

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3.6.2.1 Using equation

The importance of Ohm's Law is that if you know the value to two of the variables in the equation, you can then determine the third. You can

measure any of the parameters with a voltmeter. Most voltmeters or multi-meters measure voltage, current and resistance for both AC and

DC. Here is an easy way to remember how to solve for any part of the equation. To use this "solving circle," in the Figure 55, cover the letter

you don't know. The remaining letters give the equation for determining the unknown quantity.

Here are the standard units of measurement for electrical current, voltage, and resistance:

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Ohm's Law is a very simple and useful tool for analysing electric circuits. It is used so often in the study of electricity and electronics that it needs to

be committed to memory by the serious student. For those who are not yet comfortable with algebra, there's a trick to remembering how to solve for

anyone quantity, given the other two. First, arrange the letters E, I, and R in a triangle like this:

If you know the value E and I, and wish to determine R, just eliminate R from the picture and see what's left:

If you know the value E and R, and wish to determine I, eliminate I and see what's left:

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Lastly, if you know the value I and R, and wish to determine E, eliminate E and see what's left:

Find voltage

If you know the value of current and resistance, you can find voltage from V = I * R. For example, if the current I = 0.2A and the resistance

R = 1000 ohms, then

V = 0.2A * 1000 ΩΩΩΩ = 200V

Find current

If you know the value of voltage and resistance, you can use algebra to change the equation to I =V / R to find the current. For example, if

V = 110V and R = 22000 ohms, then

1= 110V / 22000 ΩΩΩΩ = 0.005A

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Find resistance

If you know the value of voltage and current, you can use algebra to change the equation to R =V / I to find the resistance. If V = 220V and

I = 5A, then

R = 220V / 5A = 44 Ω

Example 1:

An emf source of 6.0V is connected to a purely resistive lamp and a current of 2.0 amperes flows. All the wires are resistance free. What is the

resistance of the lamp? (Figure 56)

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Hints:

1. Where in the circuit does the gain in potential energy occur?

2. Where in the circuit does the loss of potential energy occur?

3. What is Ohm's Law?

Solution:

The gain of potential energy occurs as a charge passes through the battery, that is, it gains a potential of E=6.0V. No energy is lost to the

wires, since they are assumed to be resistance-free. By conservation of energy, the potential that was gained (i.e. E=V=6.0V) must be lost in

the resistor.

So, by Ohm's Law:

V=I R

R=V/I = 3.0

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Example 2:

Suppose we have a battery that is 1.5 Volts, and we attach a resistance of 10 Ohms between its terminals (as shown in the

figure below). What is the value of the current that will flow through the resistance? (Figure 57)

Solution:

I = E/R

I = 1.5 V /10

= 0.15 A

= 150 mA (milliamps

Figure 57: Diagram of the circuit in this problem

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RIE↑↑

=

↑

↓= RIE

3.6.2.2 An analogy for Ohm's Law

Ohm's Law also makes intuitive sense if you apply it to the water-and-pipe analogy. If we have a water pump that exerts pressure (voltage) to

push water around a "circuit" (current) through a restriction (resistance), we can model how the three variables interrelate. If the resistance to

water flow stays the same and the pump pressure increases, the flow rate must also increase.

Pressure = increase Voltage = increase

Flow rate = increase Current = increase

Resistance = same Resistance = Same

If the pressure stays the same and the resistance increases (making it more difficult for the water to flow), then the flow rate must decrease:

Pressure = same Voltage = same

Flow rate = decrease Current =decrease

Resistance = increase Resistance = increase

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↓↓= RIE

If the flow rate were to stay the same while the resistance to flow decreased, the required pressure from the pump would necessarily

decrease:

Pressure = decrease Voltage = decrease

Flow rate = same Current = same

Resistance = decrease Resistance = decrease

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Figure 58 summarizes the relationship between voltage, resistance, and current. This chart can predict the effect of changes in voltage and

resistance or it can predict the cause of changes in current. In addition, to showing what happens to current if voltage or resistance changes,

the chart also tells you the most likely result if both voltage and resistance change. If the voltage increases (Column 2), the current increases

(Column 1) provided the resistance stays the same (Column 3). If the voltage decreases (Column 2), the current decreases (Column 1)

provided the resistance stays the same (Column 3).

Example:

Solving the three columns mathematically, if 12 volts /4 ohms = 3 amps then increase the voltage to 14 volts/4 ohms = 3.5 amps, an increase

in current with the resistance staying at 4 ohms. Decrease the voltage to 10 volts, 10 volts/4 ohms = 2.5 amps or a decrease in current. In both

cases, the resistance stays the same.

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Figure 58: Relationship between voltage, resistance, and current

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3.6.3 Kirchhoff's Voltage and Current Law

Kirchhoff's voltage and current laws basically state that voltage or current in a circuit must be accounted for - it cannot just 'disappear'. The

laws are as follows:

3.6.3.1 Kirchhoff's Current Law

Kirchhoff's Current Law, also known as Kirchhoff's Junction Law and Kirchhoff's First Law, defines the way that electrical current is distributed

when it crosses through a junction - a point where three or more conductors meet. Specifically, the law states that:

The algebraic sum of current into any junction is zero.

Since current is the flow of electrons through a conductor, it cannot build up at a junction, meaning that current is conserved: what comes in

must come out. When performing calculations, current flowing into and out of the junction typically has opposite signs. This allows Kirchhoff's

Current Law to be restated as:

The sum of current into a junction equals the sum of current out of the junction.

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|

3.6.3.2 Kirchhoff's Current Law in action

In figure 59, a junction of four conductors (i.e. wires) is shown. The currents i2 and i3 are flowing into the junction, while i1and i4 flow out of it. In

other words the sum of all currents entering a junction must equal the sum of those leaving it. In this example, Kirchhoff's Junction Rule yields

the following equation:

i2 + i3 = i1 + i4 or -i1 + i2 +i3 – i4 =0

Note: Currents towards point designated as positive, those away from point negative.

Figure 59: A diagram of Kirchhoff’s Law

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3.6.3.3 Kirchhoff's Voltage Law

Kirchhoff's Voltage Law describes the distribution of voltage within a loop, or closed conducting path, of an electrical circuit. Specifically,

Kirchhoff's Voltage Law states that:

The algebraic sum of the voltage (potential differences) in any loop must equal zero.

The voltage differences include those associated with electromagnetic fields (emfs) and resistive elements, such as resistors, power sources

(i.e. batteries) or devices (i.e., lamps, televisions, blenders, etc.) plugged into the circuit. Kirchhoff's Voltage Law comes about because the

electrostatic field within an electric circuit is a conservative force field. As you go around a loop, when you arrive at the starting point has the

same potential as it did when you began, so any increases and decreases along the loop has to be cancelled out for a total change of O. If it

didn't, then the potential at the start/end point would have two different values.

Kirchhoff's Voltage Law states that 'in travelling round any closed mesh (section) of a network (circuit), the algebraic sum of the emfs

(voltages) acting in the mesh is equal to the algebraic sum of the IR voltage drops for the individual resistance in the mesh.' In other words the

sum of all voltage sources must equal the sum of all voltages dropped across resistances in the circuit, or part of circuit as shown in Figure

60:

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Figure 60: Kirchhoff’s Voltage Law

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3.6.3.4 Positive and Negative Signs in Kirchhoff's Voltage Law

Using the Voltage Rule requires some sign conventions, which aren't necessarily as clear as those in the Current Rule. You choose a direction

(clockwise or counter-clockwise) to go along the loop. When travelling from positive to negative (+ to -) in an emf (power source) the voltage

drops, so the value is negative. When going from negative to positive (- to +) the voltage goes up, so the value is positive.

When crossing a resistor, the voltage change is determined by the formula I *R, where I is the value of the current and R is the resistance of

the resistor. Crossing in the same direction as the current means the voltage goes down, so its value is negative. When crossing a resistor in

the direction opposite the current, the voltage value is positive (the voltage is increasing).

Example 1:

Often, we may only know the value of current flowing through a part of the circuit, and we wish to calculate the voltage drop across that portion

of the circuit. Suppose we know that a current of 2 Amperes is flowing through a resistance of 2.5 Ohms, and we would like to determine the

voltage across the resistor (Figure 61). Proprietary of




Solution:

Voltage across the resistor

= 2 A x 2.5 Q = 5 V

In this case, the voltage we are calculating is not at a single point, relative to ground. Rather, the two points in question are either end of the

resistor, as shown in the schematic here. Notice that the voltage indicated by the meter is actually 5 volts. This indicates a drop.

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The current enters the resistor on the left and exits on the right. When the electrons exit the resistor, they have less energy-lower potential.

There is always a voltage drop across a resistor. The side of the resistor where the current enters is the positive side (the side with the higher

voltage). If we reverse the leads on the meter, we see that the sign of the voltage changes to positive (Figure 62).

3.6.4 Significance of the internal resistance of a supply

All electrical components have internal resistance. In batteries it is mainly due to the resistance of the electrolyte, in electrical generators it is

mainly due to the machine windings, and brushes. The voltage across the open-circuited terminals of a supply is equal to the emf. When the

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load is connected to the supply, the load currents flow through the internal resistance of the supply and causes an internal resistance volts

drop. With the reference to the Figure 63 the on-load terminal voltage V is equal to the emf minus the internal resistance volts drop. So:

V = E - Ir

This means that a certain amount of the emf at the cell is not available to drive the current round the circuit because it is 'lost' inside the

battery. Where:

V = Terminal Voltage I = Current

E = emf r = Internal Resistance

Figure 63: Internal Resistance

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If the battery was 1.5V and had an internal resistance of 1Ω and was supplying a lamp which took O.3A then the internal volt drop would be:

0.3 A x 1ΩΩΩΩ = 0.3 V

So the terminal voltage would be:

1.5V - 0.3V = 1.2V

When we put a voltmeter across the battery that is what we would measure. We cannot measure the internal volts drop.

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NOTES

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS RESISTANCE /RESISTOR (DCAM 3.7 L1 & 2)


3.7 RESISTANCE AND RESISTOR (EASA Ref: 3.7) Level 1 and 2

3.7.1 Fundamentals

3.7.1.1 (a) Resistance and affecting factors

The resistor is one of the most diverse and easiest of all the electrical components you will find in your average radio or TV set. This is

because it has been around for many years and plays such a vital role that it will continue to in many new shapes and sizes to come. A

resistor is a two-terminal electrical or electronic component that resists an electric current by producing a voltage drop between its terminals in

accordance with Ohm's law. The symbol for a resistor is shown in the Figure 64(a) (upper: American symbol, lower: European symbol). As

you can see, resistor symbols can be shown either horizontally or vertically (Figure 64(b)).

Figure 64: Resistor symbols

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The SI unit for measuring resistance is the Ohm (the Greek letterΩ). A component has a resistance of 1 Ω if a voltage of 1 volt across the

component results in a current of 1 ampere, or amp, which is equivalent to a flow of one coulomb of electrical charge (approximately 6.241506

x 1018 electrons) per second. The multiples kilo ohm (1 kΩ = 1000Ω) and mega ohm (1 MΩ = 106 Ω) are also commonly used. For example,

120 000 Ω is represented as 120k, while 1 200 000 Ω is represented as 1M2. The dot is generally omitted as it can easily be lost in the

printing process. In some circuit diagrams, a value such as 8 or 120 represents a resistance in ohms. Another common practice is to use the

letter E for resistance. For example, 120E (120R) stands for 120 , 1E2 stands for 1R2 etc.

In an ideal resistor, the resistance remains constant regardless of the applied voltage or current through the device or the rate of change of the

current. Whereas real resistors cannot attain this goal, they are designed to present little variation in electrical resistance when subjected to

these changes, or to changing temperature and other environmental factors.

A resistor has a maximum working voltage and current above which the resistance may change (drastically, in some cases) or the resistor

may be physically damaged (overheat or burn up, for instance). Although some resistors have specified voltage and current ratings, most are

rated with a maximum power which is determined by the physical size. Common power ratings for carbon composition and metal-film resistors

are 1/8 watt, 1/4 watt, and 1/2 watt. Metal-film and carbon film resistors are more stable than carbon resistors against temperature changes

and age. Larger resistors are able to dissipate more heat because of their larger surface area. Wire-wound and resistors embedded in sand

(ceramic) are used when a high power rating is required.

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3.7.1.2 (a) Variables Effecting Electrical Resistance

The flow of charge through wires is often compared to the flow of water through pipes. The resistance to the flow of charge in an electric circuit

is analogous to the frictional effects between water and the pipe surfaces as well as the resistance offered by obstacles which are present in

its path. It is this resistance which hinders the water flow and reduces both its flow rate and its drift speed. Like the resistance to water flow,

the total amount of resistance to charge flow within a wire of an electric circuit is affected by some clearly identifiable variables.

First, the total length of the wires will affect the amount of resistance. The longer the wire, there will be more resistance. There is a direct

relationship between the amount of resistance encountered by charge and the length of wire it must traverse. After all, if resistance occurs as

the result of collisions between charge carriers and the atoms of the wire, then there is likely to be more collisions in a longer wire. More

collisions mean more resistance.

Second, the cross-sectional area of the wires will affect the amount of resistance. Wider wires have a greater cross-sectional area. Water will

flow through a wider pipe at a higher rate than it will flow through a narrow pipe; this can be attributed to the lower amount of resistance which

is present in the wider pipe. In the same manner, the wider the wire, there will be less resistance to the flow of electric charge. When all other

variables are the same, charge will flow at higher rates through wider wires with greater cross-sectional areas than through thinner wires.

A third variable which is known to affect the resistance to charge flow is the material that a wire is made of. Not all materials are created equal

in terms of their conductive ability. Some materials are better conductors than others and offer less resistance to the flow of charge. Silver is

one of the best conductors, but is never used in wires of household circuits due to its cost. Copper and aluminium are among the least

expensive materials with suitable conducting ability to permit their use in wires of household circuits.

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The conducting ability of a material is often indicated by its resistivity. The resistivity of a material is dependent upon the material's electronic

structure and its temperature. For most (but not all) materials, resistivity increases with increasing temperature. Figure 65 lists resistivity

values for various materials at temperatures of 20 degrees Celsius.

Figure 65: The resistivity of a material

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As seen in the Figure 65, there is a broad range of resistivity values for various materials. Those materials with lower resistivities offer less

resistance to the flow of charge; they are better conductors. The materials shown in the last five rows of the above table have such high

resistivity that they would not even be considered to be conductors.

The last major factor influencing the resistance of a conductor is temperature. Although some substances, such as carbon, show a decrease

in resistance as the ambient (surrounding) temperature increases, most materials used as conductors increase in resistance as temperature

increases. The resistance of a few alloys, such as constantan and manganin, change very little as the temperature changes. The amount of

increase in the resistance of a 1-ohm sample of a conductor per degree rise in temperature above 0°C, the assumed standard, is called the

temperature coefficient of resistance. The temperature coefficient of resistance must be considered where there is an appreciable change in

temperature of a conductor during operation.

3.7.1.3 (b) Positive and negative temperature coefficient conductance

The resistance of pure metals, such as silver, copper, and aluminium, increases as the temperature increases. They are said to have a

positive temperature coefficient. The resistance of insulators and semi-conductors and thermistors decreases with an increase in temperature

and are to said to have a negative temperature coefficient. However, the resistance of some alloys, such as constantan and manganin, show

very little resistance change over their working temperature range.

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Al

R ρ=

3.7.2 (a) Specific resistance

Specific resistance, or resistivity, is the resistance in ohms offered by a unit volume (the circular-mil/foot or the centimetre cube) of a

substance to the flow of electric current. Resistivity is the reciprocal of conductivity. A substance that has a high resistivity will have a low

conductivity, and vice versa. Thus, the specific resistance of a substance is the resistance of a unit volume of that substance.

The resistance of a conductor of a uniform cross section varies directly as the product of the length and the specific resistance of the

conductor, and inversely as the cross-sectional area of the conductor. Therefore, you can calculate the resistance of a conductor if you know

the length, cross-sectional area, and specific resistance of the substance. Expressed as an equation, the "R" (resistance in ohms) of a

conductor is:

Where:

= (Greek rho) the specific

resistance in ohms circular mil/foot

L = length in feet

A = the cross-sectional area in

circular mils.

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Conductor ampacity rating is a crude assessment of resistance based on the potential for current to create a fire hazard. However, we may

come across situations where the voltage drop created by wire resistance in a circuit poses concerns other than fire avoidance. For instance,

we may be designing a circuit where voltage across a component is critical, and must not fall below a certain limit. If this is the case, the

voltage drops resulting from wire resistance may cause an engineering problem while being well within safe (fire) limits of ampacity.

If the load in the Figure 66 will not tolerate less than 220 volts, given a source voltage of 230 volts, then we'd better be sure that the wiring

doesn't drop more than 10 volts along the way. Counting both the supply and return conductors of this circuit, this leaves a maximum tolerable

drop of 5 volts along the length of each wire. Using Ohm's Law (R=E/I), we can determine the maximum allowable resistance for each piece of

wire.

Figure 66

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Al

R ρ=

We know that the wire length is 2300 feet for each piece of wire, but how do we determine the amount of resistance for a specific size and

length of wire? To do that, we need another formula:

This formula relates the resistance of a conductor with its specific resistance (the Greek letter "rho" (p), which looks similar to a lower-case

letter "p"), its length ("l"), and its cross-sectional area ("A"). Notice that with the length variable on the top of the fraction, the resistance value

increases as the length increases (analogy: it is more difficult to force liquid through a long pipe than a short one), and decreases as cross-

sectional area increases (analogy: liquid flows easier through a fat pipe than through a skinny one).

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Specific resistance is a constant for the type of conductor material being calculated. The specific resistances of several conductive materials

can be found in the Figure 67. We find copper near the bottom of the table, second only to silver in having low specific resistance (good

conductivity).

Figure 67: The specific resistances of several conductive materials

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Notice that the figures for specific resistance in the above table are given in the very strange unit of "ohms-cmil/ft" (Ω-cmil/ft). This unit

indicates what units we are expected to use in the resistance formula (R=pl/A). In this case, these figures for specific resistance are intended

to be used when length is measured in feet and cross-sectional area is measured in circular mils.

The metric unit for specific resistance is the ohm-meter (Ω-m), or ohm-centimetre (Ω-cm), with 1.66243 x 10-9 Ω-meters per Ωcmil/ft

(1.66243 x 10-7 Ω-cm per Ω-cmil/ft). In the Ω-cm column of the table, the figures are actually scaled as µΩ-cm due to their very small

magnitudes. For example, iron is listed as 9.61 µcm, which could be represented as 9.61 x 10-6 Ω-cm. When using the unit of Ω-meter for

specific resistance in the R=pl/A formula, the length needs to be in meters and the area in square meters. When using the unit of Ω-centimetre

(Ω-cm) in the same formula, the length needs to be in centimetres and the area in square centimetres.

All these units for specific resistance are valid for any material (Ω-cmil/ft, Ω-m, or Ω-cm). One might prefer to use Ω-cmil/ft, however, when

dealing with round wire where the cross-sectional area is already known in circular mils. Conversely, when dealing with odd-shaped bus bar or

custom bus bar cut out of metal stock, where only the linear dimensions of length, width, and height are known, the specific resistance units of

Ω-meter or Ω-cm may be more appropriate.

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Going back to our example circuit, we were looking for a wire that had 0.2 or less of resistance over a length of 2300 feet. Assuming that

we're going to use copper wire (the most common type of electrical wire manufactured), we can set up our formula as such:

Algebraically solving for A, we get a value of 116,035 circular mils. Referencing our solid wire size table, we find that "double nought" (2/0)

wire with 133,100 cmils is adequate, whereas the next lower size, "single-nought" (1/0), at 105,500 cmils is too small. Bear in mind that our

circuit current is a modest 25 amps. According to our ampacity table for copper wire in free air, 14 gauge wires would have sufficed (as far as

not starting a fire is concerned). However, from the standpoint of voltage drop, 14 gauge wires would have been very unacceptable.

Let's see what 14 gauge wire would have done to our power circuit's performance. Looking at our wire size table, we find that 14 gauge wires

have a cross-sectional area of 4,107 circular mils. If we're still using copper as a wire material, then our specific resistance will still be

10.09 Ω-cmil/ft:

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Remember that this is 5.651 Ω per 2300 feet of 14-gauge copper wire, and that we have two runs of 2300 feet in the entire circuit, so each

wire piece in the circuit has 5.651 Ω of resistance (Figure 68).

Figure 68

Our total circuit wire resistance is two times 5.651, or 11.301Ω. Unfortunately, this is far too much resistance to allow 25 amps of current with

a source voltage of 230 volts. Even if our load resistance was 0Ω, our wiring resistance of 11.301 Ω would restrict the circuit current to a mere

20.352 amps! As you can see, a "small" amount of wire resistance can make a big difference in circuit performance, especially in power

circuits where the currents are much higher than typically encountered in electronic circuits. Let's do an example resistance problem for a

piece of custom-cut bus bar. Suppose we have a piece of solid aluminium bar, 4 centimetres wide by 3 centimetres tall by 125 centimetres

long, and we wish to figure the end-to-end resistance along the long dimension (125 cm). First, we would need to determine the cross-

sectional area of the bar:

Area = Width x Height

A = (4 cm) (3 cm)

A = 12cm2

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We also need to know the specific resistance of aluminium, in the unit proper for this application (Ω-cm). From our table of specific

resistances, we see that this is 2.65 x 10-6 -cm. Setting up our R=pl/A formula, we have:

As you can see, the sheer thickness of a bus bar makes for very low resistances compared to that of standard wire sizes, even when using a

material with a greater specific resistance. The procedure for determining bus bar resistance is not fundamentally different than for

determining round wire resistance. We just need to make sure that cross-sectional area is calculated properly and that all the units correspond

to each other as they should.

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NOTES

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3.7.3 ( a ) Resistor identification

3.7.3.1 ( a ) Resistor colour code

Resistance value is marked on the resistor body. The first three bands provide the value of the resistor in ohms and the fourth band indicates

the tolerance. Tolerance values of 5%, 2%, and 1% are most commonly available.

Resistors manufactured for military use may also include a fifth band which indicates component failure rate (reliability). Figure 69 shows the

colors used to identify resistor values.

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Marking the resistance with five bands is used for resistors with tolerance of 2%, 1% and other high-accuracy resistors. First three bands

determine the first three digits, fourth is the multiplier and fifth represent the tolerance. For SMD (Surface Mounted Device) the available space

on the resistor is very small. 5% resistors use a 3 digit code, while 1% resistors use a 4 digit code (Figure 70). For some electrical circuits, the

resistor tolerance is not important and it is not specified. In that case, resistors with 5% tolerance can be used. However, devices which

require resistors to have a certain amount of accuracy need a specified tolerance. BS 1852 (British Standard 1852) Coding for resistor values

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Figure 70: (a) Four-band resistor (b) Five-band resistor (c) Cylindrical SMD resistor (d) Flat SMD resistor

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The letter R is used for Ohms and K for Kilo ohms M for Mega ohms and placed where the decimal point would go. At the end is a letter that

represents tolerance where M=20%, K=10%, J=5%, G=2%, and F=1% D=.5% C=.25% B=.1% (Figure 71).

Figure 71: BS 1852 (British Standard 1852)

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3.7.3.2 (a) Wattage ratings

If the flow of current through a resistor increases, it heats up, and if the temperature exceeds a certain critical value, it can be damaged. The

wattage rating of a resistor is the power it can dissipate over a long period of time. Wattage rating is not identified on small resistors. Figure

72 shows the size and wattage rating.

Figure 72: Resistor Dimensions

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Most commonly used resistors in electronic circuits have a wattage rating of 1/2W or 1/4W. There are smaller resistors (1/8W and 1/16W) and

higher (1W, 2W, 5W, etc). In place of a single resistor with specified dissipation, another one with the same resistance and higher rating may

be used, but its larger dimensions increase the space taken on a printed circuit board as well as the added cost. Power (in watts) can be

calculated according to one of the following formulae:

Where V represents resistor voltage in Volts, I is the current flowing through the resistor in Amps and R is the resistance of resistor in Ohms.

For example, if the voltage across an 820 Ω resistor is 12V, the wattage dissipated by the resistors is:

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A 1/4W resistor can be used. In many cases, it is not easy to determine the current or voltage across a resistor. In this case the wattage

dissipated by the resistor is determined for the "worst" case. We should assume the highest possible voltage across a resistor, i.e., the full

voltage of the power supply (battery, etc). If we mark this voltage as VB, the lowest dissipation is:

For example, if VB=9V, the dissipation of a 220 Ω resistor is:

A 0.5W or higher wattage resistor should be used.

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3.7.4 (a ) Resistors in series, parallel and series parallel combination

Below are some of the most basic and most abundant resistor patterns you will see in the electronics field. You will see these patterns in many

circuits for two main reasons and the first being that it may be difficult and/or expensive to create a resistive level with just one resistor. The

other reason being that in many circuits a component such as the variable resistor will be in parallel with a capacitor or an inductor to produce

such circuits as bass and tone control for radios. The possibilities are endless and you will see these same circuits many times in the field of

electronics. There are basically three different types of circuits that the resistor can be in:

1. Series

2. Parallel

3. Series parallel combination

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7.4.1 (a) Resistors in series

The current through resistors in series stays the same, but the voltage across each resistor can be different. The sum of the potential

differences (voltage) is equal to the total voltage. The basic idea of a "series" connection is that components are connected end-to-end in a

line to form a single path for electrons to flow (Figure 73).

Figure 73: Resistors in series

In general, the equivalent resistance of resistors connected in series is the sum of their resistances (add up all the resistor values). That is,

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Example:

The current flowing in a circuit containing four resistors connected in series is I = 1.0 A. The potential drops across the first, second and third

resistors are, respectively: V1 = 5 V, V2= 8 V and V3 = 7 V. The equivalent resistance of the circuit is R = 30 (Figure 74). Find the total

voltage supplied by the battery and also current, voltage drop, and resistance of each resistor in the circuit.

Figure 74: Example Problem: Resistors in series

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Hints

1. How are resistors related when connected in series?

2. What is true about potential drops of resistors when connected in series?

3. You will need to use Ohm's Law.

Solution:

First, let's label the diagram with the information given in the question.

Because the resistors are connected in series, then the same current flows through each one. Using the Ohm's Law, we can find the

resistances of the first, second and third resistors.

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Now, using the equivalent resistance, we can find the resistance in the fourth resistor. This is a series circuit, so the equivalent resistance is

the sum of the individual resistances.

The current flowing through the fourth resistor is also 1=1.0A. Using Ohm's Law again, we find the voltage across this resistor.

The total voltage supplied by the battery must equal to the total voltage drop across the circuit (this is known as Kirchhoff's Voltage Law). So,

we must sum up the voltage drops across the resistors.

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3.7.4.2 (a) Resistors in parallel

Resistors can be connected such that they branch out from a single point (known as a node), and join up again somewhere else in the circuit.

This is known as a parallel connection. Each of the three resistors in Figure 75 is another path for current to travel between points A and B.

There are many paths for electrons to flow, but only one voltage across all components. Resistors in a parallel configuration each have the

same potential difference (voltage). Note that the node does not have to physically be a single point; as long as the current has several

alternate paths to follow, then that part of the circuit is considered to be parallel. Figure 75(a) and 75(b) are identical circuits, but with different

appearances.

Figure 75: Resistors in parallel

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To find their total equivalent resistance (Req):

The parallel property can be represented in equations by two vertical lines "II" (as in geometry) to simplify equations. For two resistors:

Total parallel resistance is less than anyone of the individual branch resistances because parallel resistors resist less together than they would

separately.

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Example:

In the following schematic diagram (Figure 76), find the total current, I.

Hints

1. You will need Ohm's Law.

2. How are resistors related when connected in parallel?

3. What is the potential drop across each resistor?

4. How does current behave in parallel branches?

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Solution:

We know the total potential of this circuit, ε =12.0 V

So, between points A and B, the potential must drop 12.0V. Also, the potential drop across branches of a circuit is equal. That is,

We can use Ohm's Law to find the current across each resistor.

Therefore,

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Recall that the currents through branches of a parallel circuit add to give the total current. That is, the total current 'splits up' so that part of the

total current travels down each branch. Because of conservation of charge, the sum of the currents in each branch must equal the amount

going into the branch. (This is Kirchhoff's Current Law.) So, adding up the three currents, we get:

So, the total current is I =12.0A.

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3.7.4.3 (a) Resistors in Series Parallel Combinations

A resistor network that is a combination of parallel and series can sometimes be broken up into smaller parts that are either one or the other.

For instance,

Figure 77: Resistors in Series Parallel Combinations

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Here, we will combine series circuits and parallel circuits. No new equations will be learned here. We can imagine a branch in a parallel circuit,

but which contains two resistors in series. Example in Figure 78(a) is between points A and B.

78: Combination Circuit 1

In this situation, we could calculate the equivalent resistance of branch AS using our rules for series circuits. So,

RAB=R 1 + R 2

Now, we can replace the two resistors with a single, equivalent resistor with no effective change to the circuit. As can be seen in Figure 78(b),

the circuit is now a parallel circuit, with resistors RAB and R3 in parallel. This circuit can be solved using the same rules as any other parallel

circuit. Another combination circuit can occur with parallel circuits connected in series. Figure 79(a) shows a typical example of two parallel

circuits (AB and CD) connected in series with another resistor, R3.

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Parts (b) and (c), the resistors in the parallel circuit AB and CD can be replaced by an equivalent resistance. Again, we will use the

equivalence rule for resistors connected in parallel. This gives:

So, the equivalent resistance between points A and B is RAB. Similarly, we can replace the parallel circuit containing R4 and R5 (between

points C and D) with its equivalent resistance, RCD. Now, you can see that we have simplified Circuit 2 to one which contains resistors

connected in series only. That is, this circuit now contains RAB, R3, and RCD in series. The equivalent resistance for this circuit would be found

using:

Figure 79: Combination Circuit 2

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Analysis technique

The goal of series-parallel resistor circuit analysis is to be able to determine all voltage drops, currents, and power dissipations in a circuit. The

general strategy to accomplish this goal is as follows:

• Step 1: Assess which resistors in a circuit are connected together in simple series or simple parallel.

• Step 2: Re-draw the circuit, replacing each of those series or parallel resistor combinations identified in step 1 with a single, equivalent-value

resistor. If using a table to manage variables, make a new table column for each resistance equivalent.

• Step 3: Repeat steps 1 and 2 until the entire circuit is reduced to one equivalent resistor.

• Step 4: Calculate total current from total voltage and total resistance (I=E/R).

• Step 5: Taking total voltage and total current values go back to last step in the circuit reduction process and insert those values where

applicable.

• Step 6: From known resistances and total voltage / total current values from step 5, use Ohm's Law to calculate unknown values (voltage or

current) (E=IR or I=E/R).

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• Step 7: Repeat steps 5 and 6 until all values for voltage and current are known in the original circuit configuration.

Essentially, you will proceed step-by-step from the simplified version of the circuit back into its original, complex form, plugging in values of

voltage and current where appropriate until all values of voltage and current are known.

• Step 8: Calculate power dissipations from known voltage, current, and/or resistance values.

Example 1:

Find the total resistance in Figure 80

FIGURE 80: Combination Circuit 3

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Hints

1. Which resistors are in parallel and which are in series?

2. Is this circuit composed of small groups of parallel resistors, all connected in series? Or is it composed of groups of series

resistors, connected in parallel?

Solution:

This circuit is composed of 3 'elements' connected in series: the group of parallel resistors between A and B, the single resistor R3, and the

group of parallel resistors between C and D. First, we will find the equivalent resistance between A and B. Here, we have two resistors, R1 and

R2, connected in parallel. Using the formula for resistors connected in parallel we can find the equivalent resistance between points A and B.

Let's call this equivalent resistance RAB.

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Now, we'll find the equivalent resistance between C and D, and will call it RCD. Using the equation from above for resistors connected in

parallel,

Replacing the two parallel sections with their equivalent resistances, and redrawing the circuit, we get the circuit in Figure 81. We see that

there are three resistances connected in series: RAB, R3, and RCD.

Figure 81: Combination Circuit 3, Simplified

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Using the formula for resistors in series, we can find the equivalent resistance of the circuit.

R=RAB + R3 + RCD

R=2.857 + 0.889 + 3.0

R=6.7Ω

So the equivalent resistance of this circuit is R =6.7Ω.

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Example 2:

Figure 82 shows part of a circuit. It consists of resistors combined in both parallel and series configurations. Find the equivalent resistance.

Hints

1. What is the equivalent resistance for resistors in parallel? in series?

Solution:

In this partial circuit, there are three main branches, branch AB, branch CD, and branch EF. As you can see, branch AB contains two resistors

in series, R1 and R2. Branch CD has just one resistor, R3. Finally, there are two resistors in branch EF. Let's look at branch AB first. We will

simplify this branch by finding the equivalent resistance between A and B. Note that R1 is connected in series with R2.

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Using the equation for resistors in series we can find RAB.

Now, in branch CD there is only one resistor, so this branch cannot be simplified further. In branch EF, however, there are two resistors,

connected in series with one another. Using the equation for resistors in series, we can find the equivalent resistance in branch EF, REF.

We can redraw circuit 4 using RAB , R3, and REF, as seen in Figure 83. This circuit has been simplified to a parallel circuit, with three

resistances in parallel.

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Using the formula for resistors connected in parallel we can find the equivalent resistance of these branches.

3.7.5 (b) Fixed resistors

In an electrical circuit, some objects may need a lesser amount of current than the input value. In such cases, fixed resistors are used to

reduce the flow of current. They are placed in such a way that a higher voltage must first pass through them before it flows further. The value

of the resistance is fixed and does not change with change in the applied voltage or current flowing through it. The resistance value is

measured in ohms and the value ranges from a few milliohms to about a gigaohm. Resistors are universally used in all electrical circuits of

devices like TVs, radios, refrigerators, machines, microelectronic semiconductor devices, regulators, etc. Proprietary of




3.7.6 (b) Tolerance and limitations

A fixed resistor has a resisting material in the centre and conducting material at the end. Resistance is proportional to the length of the resistor

and to the material's resistivity and inversely proportional to its cross-sectional area. The resistor will be damaged if it is exposed to a voltage

greater than its maximum working value. The equation to determine the voltage V through a resistor of resistance R ohms with a current I in

amperes is V= IR.

When a designer chooses a resistor, certain factors must be taken into account. These are tolerance, power rating, and stability. Due to mass

production of resistors their exact value cannot be guaranteed and the tolerance specifies the maximum and minimum value of resistance the

resistor will have e.g., 200Ω ± 10%. This will have a resistance value from 180Ω to 220Ω. All resistors have a power rating (in watts) which

indicates the maximum power that can be dissipated without the temperature rise being such that damage occurs to the resistor. If the current

through the resistor is exceeded the resistor will overheat and burn out. In electronic circuits typical ratings are 1/4W, 1/2W, 1W, and 2W. The

greater the physical size, the greater it's rating.

3.7.7 (b) Stability

The stability of a resistor is its ability to maintain its resistance value over a period of time within a working circuit. This can be an important

factor in some electronic circuits.

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3.7.8 (b) Methods of construction of Fixed Resistors

3.7.8.1 (b) Types of fixed resistors: Low power resistors

The carbon film resistor is composed of a resistive material like graphite that is then cut into blocks or wrapped, or grafted in a desired way.

For example, the length of the resistive material will determine how much resistance will there be while the width of the resistive material will

determine what kind of power it can handle, the wider it is the more power it can handle. The different types of carbon film resistors can be

seen in Figure 84. There are some three distinct types of carbon film resistors which as follows:

• The standard film resistor (A) - a circular resistor with two pins extending from opposite sides or the barrel- shaped resistor.

• The chip resistor (B) - this type of resistor was introduced in the late 80's to accommodate for the ever shrinking computer components

where there can be up to 6 layers per circuit board.

• The network resistor (C) - this type of resistor comes in (SIPP) form and can contain up to 12 resistors in a compact space that cannot

compare.

Typical tolerance is ± 5% from a few ohms to 10MΩ. Ratings from 0.125W to 1W with very good stability

Figure 84: Low power resistors

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3.7.8.2 (b) Types of fixed resistors: High power resistors

The most common wire wound resistor is composed up by a fairly resistive wire wrapped around a ceramic cylinder and typically has a power

range from 5 to 50 watts and is most often found in power supplies and amplifiers. It is common to find these components heat up to levels

that burns to the touch and is the reason why they are made up of ceramic, a fire resistant material. The schematic symbol is the same as the

carbon film resistor so it is also quite easy to remember.

Figure 85: High power resistors

The wire wound resistors have low tolerance and high stability, and any resistor over 1W will be of the wire wound type. The wire is in-home,

constantan or managing wound on a former and given a protective coating. They have resistance values from 1Ω to 25kΩ and can operate up

to 10-20W.

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3.7.9 (b) Variable resistors

Resistors can also be shown to have varying rather than fixed resistances. This might be for the purpose of describing an actual physical

device designed for the purpose of providing an adjustable resistance, or to show some component that just happens to have an unstable

resistance. In fact, any time you see a component symbol drawn with a diagonal arrow through it, then that component has a variable rather

than a fixed value.

The variable resistor is a very important component that is found in many electrical appliances for such things as tone and bass controls as

well as volume. This is due to the fact that resistors can be joined together with other components to form filters for a desired levels. They can

also be found in computer monitors for color or positioning as well as the dimming switch for your lamps. This is done through digital to

analogue and analogue to digital circuits, one great advantage to this is that you are able to turn a knob instead of typing a value in every time

you want to change the tint or brightness. The variable resistor is a resistor whose value can be adjusted by turning a shaft or sliding a control.

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NOTES

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3.7.9.1 (b) Variable Resistors - Construction

Variable resistors consist of a resistance track with connections at both ends and a wiper that moves along the track as you turn the spindle

(Figure 86). The track may be made from carbon, cermets (ceramic and metal mixture) or a coil of wire (for low resistances). The track is

usually rotary but straight track versions, usually called sliders, are also available.

Variable resistors may be used as a rheostat with two connections (the wiper and just one end of the track) or as a potentiometer with all three

connections in use. Miniature versions called presets are made for setting up circuits that will not require further adjustment. Variable resistors

are often called potentiometers in books and catalogues. Some variable resistor are designed to be mounted directly on the circuit board, but

most are for mounting through a hole drilled in the case containing the circuit with stranded wire connecting their terminals to the circuit board.

Variable resistors can be inexpensive single-turn types or multi-turn types with a helical element. Some variable resistors can be fitted with a

mechanical display to count the turns. Variable resistors can sometimes be unreliable, because the wire or metal can corrode or wear. Some

modern variable resistors use plastic materials that do not corrode and have better wear characteristics.

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Rheostat

This is the simplest way of using a variable resistor. Two terminals are used: one connected to an end of the track, the other to the moveable

wiper. Turning the spindle changes the resistance between the two terminals from zero up to the maximum resistance. Rheostats are often

used to vary current, for example to control the brightness of a lamp or the rate at which a capacitor charges. If the rheostat is mounted on a

printed circuit board you may find that all three terminals are connected. However, one of them will be linked to the wiper terminal. This

improves the mechanical strength of the mounting but it serves no function electrically. The term rheostat is usually reserved for higher-

powered devices, above about 1/2 watt.

Potentiometer

Variable resistors used as potentiometers have all three terminals connected. This arrangement is normally used to vary voltage, for example

to set the switching point of a circuit with a sensor, or control the volume (loudness) in an amplifier circuit. If the terminals at the ends of the

track are connected across the power supply then the wiper terminal will provide a voltage that can be varied from zero up to the maximum of

the supply.

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Presets

These are miniature versions of the standard variable resistor. They are designed to be mounted directly onto the circuit board and adjusted

only when the circuit is built. Some example is to set the frequency of an alarm tone or the sensitivity of a light-sensitive circuit. A small

screwdriver or similar tool is required to adjust presets. Presets are much cheaper than standard variable resistors so they are sometimes

used in projects where a standard variable resistor would normally be used. Multiturn presets are used where very precise adjustments must

be made. The screw must be turned many times (10+) to move the slider from one end of the track to the other, giving very fine control.

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3.7.9.2 (b) Construction of potentiometers

By means of construction, potentiometer can be divided into 2 groups: coated and coiled. With coated potentiometers, (Figure 88), insulator

body is coated with a resistive material. There is an elastic, conductive slider moving across the resistive layer, increasing the resistance

between slider and one end of pot, while decreasing the resistance between slider and the other end of the pot.

Coiled potentiometers are made of conductor wires coiled around the insulator body. There is an elastic, conductive slider moving across the

wire, increasing the resistance between slider and one end of the pot, while decreasing the resistance between slider and the other the end of

pot.

Coated pots are much more common variants. With these, resistance can be linear, logarithmic, inverse-logarithmic or other function

depending upon the angle or position of the slider. The most common are linear and logarithmic potentiometers, and the most common

applications are radio-receivers, audio amplifiers, and similar devices where pots are used for adjusting the volume, tone, balance, etc. Coiled

potentiometers are used in devices that require increased accuracy and constancy of attributes. They feature higher dissipation than coated

pots, and are therefore a necessity in high current circuits.

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Potentiometer's resistance commonly of E6 series, most frequently used multipliers including 1, 2.2 and 4.7. Standard tolerance values

include 30%, 20%, 10% (and 5% for coiled pots). Potentiometers come in many different shapes and sizes, with wattage ranging from 1/4W

(coated pots for volume control in amps, etc) to tens of Watts (for regulating high currents). Several different pots are shown in the Figure 89

along with the symbol of a potentiometer.

Figure 89: Potentiometers

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Uppermost models represent the so called stereo potentiometer. These are actually two pots in one casing, with sliders mounted on shared

axis, so they move simultaneously. These are used in stereophonic amps for simultaneous regulation of both LF channels, etc. Lower left is

the so called ruler potentiometer, with a slider moving across straight line, not in circle as with other pots. Lower right is coiled pot with wattage

of 20W, commonly used as rheostat (for regulating current while charging accumulator and similar).

For circuits that demand very accurate voltage and current value, trimmer potentiometers (or just trimmers) are used. These are small

potentiometers with slider that is adjusted via screw (unlike other pots where adjustments are made via push-button mounted upon the axis

which slider is connected to). Trimmer potentiometers also come in many different shapes and sizes, with wattage ranging from 0.1W to 0.5W.

Figure 90 shows several different trimmers, along with the symbol for this element.

Figure 90: Trimmer potentiometers

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Resistance adjustments are made via screw. Exception is the trimmer from the lower right corner, which can be also adjusted via plastic axis.

Particularly fine adjusting can be achieved with the trimmer in plastic rectangular casing (lower middle). Its slider is moved via special

transmission system, so that several full turns of the wheel are required to move slider from one end to the other.

3.7.10. (a) Operation and use of potentiometers and rheostats

Potentiometers (also called pots) are variable resistors which have three terminals, used as voltage regulators in electronic circuits.

Potentiometers are most commonly used in amps, radio and TV receivers, cassette players and similar devices. They are used for adjusting

volume, tone, balance, etc. A rheostat is a variable resistor used to vary the amount of current flowing in a circuit.

Potentiometers find their most sophisticated application as voltage dividers, where shaft position determines a specific voltage division ratio.

However, there are applications where we don't necessarily need a variable voltage divider, but merely a variable resistor: a two-terminal

device. Technically, a variable resistor is known as a rheostat, but potentiometers can be made to function as rheostats quite easily. In its

simplest configuration, a potentiometer may be used as a rheostat by simply using the wiper terminal and one of the other terminals, the third

terminal left unconnected and unused (Figure 91).

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Moving the potentiometer control to the direction where the wiper' is closest to the other used terminal results in a lower resistance. The

direction of motion required increasing or decreasing in resistance may be changed by using a different set of terminals (Figure 92).

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Be careful, though, that you don't use the two outer terminals, as this will result in no change in resistance as the potentiometer shaft is turned.

In other words, it will no longer function as a variable resistance (Figure 93).

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Build the circuit as shown in the schematic and illustration, using just two terminals on the potentiometer, and see how motor speed may be

controlled by adjusting shaft position. Experiment with different terminal connections on the potentiometer, noting the changes in motor speed

control. If your potentiometer has a high resistance (as measured between the two outer terminals), the motor might not move at all until the

wiper is brought very close to the connected outer terminal.

As you can see, motor speed may be made variable using a series-connected rheostat to change total circuit resistance and limit total current.

This simple method of motor speed control, however, is inefficient, as it results in substantial amounts of power being dissipated (wasted) by

the rheostat. A much more efficient means of motor control relies on fast "pulsing" of power to the motor, using a high-speed switching device

such as a transistor. A similar method of power control is used in household light "dimmer" switches. Unfortunately, these techniques are

much too sophisticated to explore at this point in the experiments. When a potentiometer is used as a rheostat, the "unused" terminal is often

connected to the wiper terminal (Figure 94).

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At first, this seems rather pointless, as it has no impact on resistance control. You may verify this fact for yourself by inserting another wire in

your circuit and comparing motor behavior before and after the change (Figure 95).

If the potentiometer is in good working order, this additional wire makes no difference whatsoever. However, if the wiper ever loses contact

with the resistive strip inside the potentiometer, this connection ensures the circuit does not completely open: that there will still be a resistive

path for current through the motor. In some applications, this may be an important. Old potentiometers tend to suffer from intermittent losses

of contact between the wiper and the resistive strip, and if a circuit cannot tolerate the complete loss of continuity (infinite resistance) created

by this condition, that "extra" wire provides a measure of protection by maintaining circuit continuity.

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You may simulate such a wiper contact "failure" by disconnecting the potentiometer's middle terminal from the terminal strip, measuring

voltage across the motor to ensure there is still power getting to it, however small (Figure 96).

It would have been valid to measure circuit current instead of motor voltage to verify a completed circuit, but this is a safer method because it

does not involve breaking the circuit to insert an ammeter in series. Whenever an ammeter is used, there is risk of causing a short circuit by

connecting it across a substantial voltage source, possibly resulting in instrument damage or personal injury. Voltmeters lack this inherent

safety risk, and so whenever a voltage measurement may be made instead of a current measurement to verify the same thing, it is the wiser

choice.

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3.7.11 (b) Thermistors

A thermistor is a temperature-sensing element or 'thermally sensitive resistors' or temperature-dependent resistor composed of sintered

semiconductor material that exhibits a large change in resistance proportional to a small change in temperature. There are two kinds,

classified according to the sign of their temperature coefficients:

• A Positive Temperature Coefficient (PTC) resistor is a resistor with a positive temperature coefficient. When the temperature raises the

resistance of the PTC increases. PTCs are often found in televisions in series with the demagnetizing coil where they are used to

provide a short-duration current burst through the coil when the TV is turned on. One specialized version of a PTC is the polyswitch that

acts as a self-repairing fuse.

• A Negative Temperature Coefficient (NTC) resistor is also a temperature-dependent resistor, but with a negative temperature

coefficient. When the temperature raise the resistance of the NTC drops. NTCs are often used in simple temperature detectors and

measuring instruments.

Most thermistors decrease their resistance with an increase in temperature (negative temperature coefficient). They are made in either rod,

disc or bead form, and are made of oxides of nickel, manganese, copper, cobalt and other materials. They are used extensively on aircraft as

temperature sensors in heating, air conditioning and battery systems. There are some thermistors that have a positive temperature coefficient.

The material used for their construction is barium titanate; they may be used in circuits to limit current due to excessive temperature rise. Proprietary of




3.7.11.1 Benefits of Using Thermistors

Accuracy

Thermistors are one of the most accurate types of temperature sensors. However thermistors are fairly limited in their temperature range,

working only over a nominal range of O0C to 1000C.

Stability

Finished thermistors are chemically stable and not significantly affected by aging.

3.7.12 (b) Voltage dependent resistors

Sometimes known as varistors, these are devices whose resistance reduces as the applied voltage is increased. They are manufactured from

silicon carbide. Applications include transient voltage suppression, voltage stabilization and switch contact protection e.g. it is connected

across the component to be protected and draws only a small current at its normal operating voltage. However, should the voltage increase,

(i.e. a surge) its resistance reduces, and it absorbs some of the energy in the surge by diverting current through itself.

The most common type of varistor is the Metal Oxide Varistor (MOV). This contains a ceramic mass of zinc oxide grains, in a matrix of other

metal oxides (such as small amounts of bismuth, cobalt, manganese) sandwiched between two metal plates (the electrodes).

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The boundary between each grain and its neighbor forms a diode junction, which allows current to flow in only one direction. A metal oxide

varistor (MOV) is a special type of resistor that changes its resistance with rise in voltage: a very high resistance at low voltage (below the

trigger voltage) and very low resistance at high voltage (above the trigger voltage). It acts as a" switch. It is usually used for short circuit

protection in power strips or lightning bolt "arrestors" on street power poles, or as a "snubber" in inductive circuits.

3.7.13 (b) Construction of Wheatstone bridge

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3.7.13.1 (a) Operation of Wheatstone bridge

The resistive bridge is also known as Wheatstone bridge. A basic Wheatstone bridge circuit contains four resistances (two voltage dividers,

both fed by the same input.), a constant voltage input, and a voltage gage, as illustrated in Figure 97. The circuit output is taken from both

voltage divider outputs. In its classic form, a galvanometer (a very sensitive dc current meter) is connected between the output terminals, and

is used to monitor the current flowing from one voltage divider to the other.

Consider the current flow from A to D (you could think of it as fluid flow in a set of pipelines) and assume that all the resistors are the same

value then the same amount of current will flow down arm ABD as in the arm ACD. The voltage at B will be the same as at C (there will be the

same volts drop across R1 as R2) and the voltmeter will show zero. In this condition the bridge is said balanced.

A volts drop is sometimes expressed as an IR drop (V = I x R).

As the voltage drop across R3 must equal the voltage drop across R4.

Dividing one equation by the other:

So 'at balance' this ratio of resistance is true and no current flows in either direction through the galvanometer. If one of the resistors changes

even a little bit in value, the bridge will become unbalance and current will flow through the galvanometer. Thus, the galvanometer becomes a

very sensitive indicator of the balance condition.

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Using the Wheatstone bridge

In its basic application a dc voltage (E or V) is applied to the Wheatstone bridge and a galvanometer (G) is used to monitor the balance

condition. The values of R1 and R3 are precisely known, but do not have to be identical. R2 is a calibrated variable resistance, whose current

value may be read from a dial or scale. An unknown resistor, Rx, is connected as the fourth side of the circuit, and power is applied. R2 is

adjusted until the galvanometer (G) reads zero current.

This circuit is most sensitive when all four resistors have similar resistance values. However, the circuit works quite well in any event. If R2 can

be varied over a 10:1 resistance range and R1 is of a similar value, we can switch decade values of R3 into and out of the circuit according to

the range of value we expect from Rx. Using this method, we can accurately measure any value of Rx by moving one multiple-position switch

and adjusting one precision potentiometer. If the bridge is used for temperature control systems e.g. windscreen heating then one of the

resistors is placed inside the screen next to the heater.

3.7.13.2 (b) Applications of the Wheatstone bridge

Bridge circuits are widely used for the measurement of resistance, capacitance, and inductance. Sir Charles Wheatstone invented many uses

himself, and others have been developed, along with many variations, since that time. One very common application in industry today is to

monitor sensor devices such as strain gauges. Such devices change their internal resistance according to the specific level of strain (or

pressure, temperature, etc.), and serve as the unknown resistor Rx. However, instead of trying to constantly adjust R2 to balance the circuit,

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the galvanometer is replaced by a circuit that can be calibrated to record the degree of imbalance in the bridge as the value of strain or other

condition being applied to the sensor.

A second application is used by electrical power distributors to accurately locate breaks in a power line. The method is fast and accurate, and

does not require a large number of field technicians. Other applications abound in electronic circuits. It also can be used as:

• Temperature measurement - acting as temperature control device for heated windscreen for example.

• Measuring strain - fitted to landing gear for the accurate measurement of aircraft weight and C of G position for example.

• Measuring electrical values - use in measuring instruments.

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NOTES

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS POWER (DCAM 3.8 L2)


3.8 POWER (EASA 3.8) Level 2

3.8.1 Power and Energy

An important part in the study of electricity is the proper use of the correct terminology.

The statement 'the voltage through a circuit is so many volts' is not correct. Voltage does not pass through a circuit. Voltage or PD exists

between two points and therefore the correct statement is 'the voltage across a circuit' or 'the voltage between two points in a circuit'.

Likewise, the statement 'the current across a circuit is so many amperes' is not correct. Current does not exist across two points; it flows

through the wires and through the circuit. It should be said 'the current through the circuit' or 'the current through the resistor'.

Just as it is important to use the terms 'voltage' and 'current' correctly, it is also important to use the terms 'energy' and 'power' according to

their technical meaning.

3.8.2 Energy

Energy is defined as the capability to do work. Energy has different forms. 'Electrical energy' is one form, because electricity is capable of

performing work. But it is necessary to use some kind of electrical components to convert electrical energy into some other forms of energy to

accomplish work.

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For example, an electric motor is used to exert a vertical force on an elevator through a distance. Other examples of energy are heat and light.

One of the first types of energy was mechanical energy. Mechanical energy exists in two forms:

• potential energy and

• Kinetic energy.

Refer to Figure 98

Figure 98: Potential Energy

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Potential energy is the energy that a body has by virtue of its position. It took a certain amount of work to get the box on the table. A vertical

force had to be exerted through a distance to accomplish this.

Once the box is resting in the table, it is capable of doing work simply because of its position. In other words, it has potential energy. Refer to

Figure 99. If the box is knocked off the table, it will fall and strike the ground with an impact. It is supposed there is a nail resting under the box

where it strikes. If the box is heavy enough, it can actually push the nail into a wooden floor. Since this requires a force through a distance, the

box is capable of doing work.

Although the box resting on the table has potential energy, it will do no work until this potential energy is converted into some other forms.

Figure 99: Kinetic Energy

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As the box is moving through space it has energy by virtue of its motion. This is called kinetic energy. Both kinetic and potential energy are

forms of energy which represents the capability to do work.

When energy is converted into work, some of it may be lost in the form of heat. The energy and the amount of work done are equivalent;

the heat losses are neglected.

Electrical energy expressed in watt-seconds (Ws) or watt-hours (Wh) is found by multiplying the voltage times the current times the time.

Electrical energy = Volts · Ampere · time

W = U ·I· t

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3.8.3 Power Formula

Power is the rate at which work is done or the rate at which energy is being used. Whenever the term power is used it should be noticed that

there is a certain amount of time involved.

The amount of energy in an electric circuit is obtained by multiplying the voltage times the current times the time. The amount of electric power

is equal to the amount of energy, per unit of time. The word 'per' means to divide.

The two t's cancel and the equation for power becomes:

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Now three formulas are available to calculate power:

P = U.I

P = I 2 R

P = U2

R

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3.8.4 Maximum Power Transfer

Maximum power is transferred from the source of electric power to the load when the internal resistance of the source has the same

resistance as the load.

i.e. when: Ri = RLoad

This is known as resistance matching and is of importance in radio and electronic circuits, where a high internal resistance power source

exists. Resistance matching is not considered when loads to the mains or secondary batteries are connected because the internal resistance

is so low that the battery or mains would be overloaded. This is the basic equiation for electric power, when the voltage is in volts and the

current is in amperes, the power is given in watts.

From Ohm's Law it is known that:

If these equations are used in conjunction with the power equation, two furthermore definitions for power are obtained:

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Figure 100: Maximum Power Transfer

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS CAPACITANCE / CAPACITOR (DCAM 3.9 L2)


3.9 CAPACITANCE AND CAPACITOR (EASA Ref. 3.9) Level 2

3.9.1 Operation and Function of a capacitor

Capacitance is the property of an electric conductor that characterizes its ability to store an electric charge. An electronic device called a

capacitor is designed to provide capacitance in an electric circuit by providing a means for storing energy in an electric field between two

conducting bodies. Capacitors are used in many ways in electronic circuit such as barriers to direct currents, storing memory in a computer

chip, storing a charge for an electronic flash camera, or adjusting a tuned circuit such as in a radio.

Description of a Capacitor

Capacitors are short term charge-stores. A capacitor in its simplest form consists of two conducting plates separated by an insulating layer

called a dielectric (Figure 101). When a capacitor is connected in a circuit across a voltage source, the voltage forces electron onto the

surface of one plate and pulls electrons off the surface of the other plate resulting in a potential difference between the plates. Capacitors are

charged and discharged as needed by its application. Capacitors differ in size and arrangements of plates and the type of dielectric materials

used. Paper, ceramic, air, mica, and electrolytic materials can be used, depending on the type of dielectric needed. The capacitance of a

capacitor may be fixed or adjustable (as in a radio tuner).

The purpose of capacitor is to store electrical energy by electrostatic stress in the dielectric.

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It is experimentally found that in the presence of an earthed plate B, plate A is capable of withholding more charge than when B is not there.

When such a capacitor is connected to a battery, then there is a momentary flow of electrons from A to B. As negatively charged electrons are

withdrawn from A, it becomes positive and as these electron collect on B, it becomes negative. Hence, a potential difference is established

between plates A and B.

Figure 101: A capacitor essentially consists of two conducting surfaces separated by a layer of an insulating medium called

dielectric

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When electric charge accumulates on the plates, an electric field is created in the region between the plates that is proportional to the amount

of accumulated charge. This electric field creates a potential difference, V = E·d between the plates of this simple parallel-plate capacitor

(Figure 102). Capacitors also allow AC current to flow and blocks DC current.

Figure 103: Capacitor Symbols

The symbol for a capacitor is shown in Figure 103.

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FIGURE 104: Air Tank Analogy for a Capacitor Proprietary of




Dielectric Materials

The dielectric material in a capacitor prevents the flow of current between its plates. It also serves as a medium to support the electrostatic

force of a charged capacitor. A variety of materials are used for dielectrics as shown in the Figure 105.

Dielectric materials are rated based upon their ability to support electrostatic forces in terms of a number called a dielectric constant. The

ability of the dielectric to support electrostatic forces is directly proportional to the dielectric constant. A vacuum is the standard by which other

dielectrics are rated. The dielectric constant of a vacuum is 1. You can see from the chart that there is very little difference in the dielectric

constant of a vacuum and air. Therefore, air is often referred to as having a dielectric constant of 1.

Figure 105: Dielectric Materials

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Capacitance

If we pump electrons onto the negative plate, electrons are repelled from the negative plate. Since positives do not move, a positive charge is

induced. The higher the potential difference, the more charge is crowded onto the negative plate and the more electrons repelled from the

positive plate. Therefore charge is stored. The plates have a certain capacitance. Capacitance is defined as:

The charge required to cause unit potential difference in a conductor.

Capacitance is measured in units called farads (F), which is named after Michael Faraday (1791-1867). The definition is:

1 Farad is the capacitance of a conductor, which has potential difference of 1 volt when it carries a charge of 1 coulomb. A one farad capacitor

stores one coulomb (a unit of charge (Q) equal to 6.28 X1 018 electrons) of charge when a potential of 1 volt is applied across the terminals of

the capacitor.

The capacitance of a capacitor is proportional to the quantity of charge that can be stored in it for each volt difference in potential between its

plates. Mathematically this relationship is written as:

[Q - Quantity of stored electrical charge in coulombs (C); C - capacitance in farads (F); V - potential difference in volts (V)]

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Therefore, stored electric charge can be calculated using the formula:

Charge (Q) = Capacitance (C) x Voltage (V)

The difference in potential or voltage of the capacitor can be calculated using the formula:

A large capacitance means that more charge can be stored. Capacitance is measured in farads symbol F. However 1F is very large, so

prefixes (multipliers) are used to show the smaller values:

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Question:

Define the term "farad."

What is the mathematical relationship between a farad, a microfarad, and a Pico farad?

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Parallel Plate Capacitor

The capacitance of flat, parallel metallic plates of area A and separation d is given by the expression where:

k = relative permittivity of the dielectric material between the plates. k=1 for free space, k>1 for all media, approximately =1 for air.

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Capacitance of Parallel Plates

The electric field between two large parallel plates is given by:

The voltage difference between the two plates can be expressed in terms of the work done on a positive test charge q when it moves from the

positive to the negative plate.

It then follows from the definition of capacitance that:

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Stored energy

As opposite charges accumulate on the plates of a capacitor due to the separation of charge, a voltage develops across the capacitor owing

to the electric field of these charges. Ever-increasing work must be done against this ever-increasing electric field as more charge is

separated. The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish the voltage across

the capacitor, and therefore the electric field. The energy stored is given by:

Where V is the voltage across the capacitor.

The maximum energy that can be (safely) stored in a particular capacitor is limited by the maximum electric field that the dielectric can

withstand before it breaks down. Therefore, all capacitors made with the same dielectric have about the same maximum energy density

(joules of energy per cubic meter).

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Example:

1. What is the energy held by a 50 000 µ F capacitor charged to 12.0 V?

E = ½ CV2

E = ½ X 50 000 x 10-6 F x (12.0 V)2

=3.6 J

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3.9.2 Factors affecting capacitance

The value of capacitance of a capacitor depends on three factors:

• The area of the plates.

• The distance between the plates.

• The dielectric constant of the material between the plates.

Plate area affects the value of capacitance in the same manner that the size of a container affects the amount of water that can be held by the

container. A capacitor with the large plate area can store more charges than a capacitor with a small plate area. Simply stated, "the larger the

plate area, the larger the capacitance". The second factor affecting capacitance is the distance between the plates. Electrostatic lines of force

are strongest when the charged particles that create them are close together. When the charged particles are moved further apart, the lines of

force weaken, and the ability to store a charge decreases.

The third factor affecting capacitance is the dielectric constant of the insulating material between the plates of a capacitor. The various

insulating materials used as the dielectric in a capacitor differ in their ability to respond to (pass) electrostatic lines of force. A dielectric

material, or insulator, is rated as to its ability to respond to electrostatic lines of force in terms of a figure called the dielectric constant. A

dielectric material with a high dielectric constant is a better insulator than a dielectric material with a low dielectric constant. Dielectric

constants for some common materials are given in the Figure 106

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Figure 106: Dielectric constants for some common materials

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Notice the dielectric constant for a vacuum. Since a vacuum is the standard of reference, it is assigned a constant of one. The dielectric

constants of all materials are compared to that of a vacuum. Since the dielectric constant of air has been determined to be approximately the

same as that of a vacuum, the dielectric constant of air is also considered to be equal to one. The formula used to compute the value of

capacitance is

C = 0.2249 (KA) Where, C = capacitance in picofarads

d A = area of one plate in sq inches

d = distance between the plates in inches

K = dielectric constant of the insulating material

0.2249 = a constant resulting from conversion from Metric to English units

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Figure 107: Factors Affecting Capacitance

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Example:

Find the capacitance of a parallel plate capacitor with paraffin paper as the dielectric.

By examining the above formula you can see that capacitance varies directly as the dielectric constant and the area of the capacitor plates,

and inversely as the distance between the plates.

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Question:

1. State three factors that affect the capacitance of a capacitor.

2. A parallel plate capacitor has the following values: K = 81, d = .025 inches, A = 6 square inches. What is the capacitance of the capacitor?

(4372 pF)

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Voltage Rating of Capacitors

In selecting or substituting a capacitor for use, consideration must be given to:

1. the value of capacitance desired

2. the amount of voltage to be applied across the capacitor

If the voltage applied across the capacitor is too great, the dielectric will break down and arcing will occur between the capacitor plates. When

this happens the capacitor becomes a short circuit and the flow of direct current through it can cause damage to other electronic parts. Each

capacitor has a voltage rating (a working voltage) that should not be exceeded.

The working voltage of the capacitor is the maximum voltage that can be steadily applied without danger of breaking down the dielectric. The

working voltage depends on the type of material used as the dielectric and on the thickness of the dialectic. (A high-voltage capacitor that has

a thick dielectric must have a relatively large plate area in order to have the same capacitance as a similar low-voltage capacitor having a thin

dielectric.) The working voltage also depends on the applied frequency because the losses, and the resultant heating effect, increase as the

frequency increases.

A capacitor with a voltage rating of 500 volts dc cannot be safely subjected to an alternating voltage or a pulsating direct voltage having an

effective value of 500 volts. Since an alternating voltage of 500 volts (rms) has a peak value of 707 volts, a capacitor to which it is applied

should have a working voltage of at least 750 volts. In practice, a capacitor should be selected so that its working voltage is at least 50 percent

greater than the highest effective voltage to be applied to it.

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Capacitor Losses

Power loss in a capacitor may be attributed to dielectric hysteresis and dielectric leakage. Dielectric hysteresis may be defined as an effect in

a dielectric material similar to the hysteresis found in a magnetic material. It is the result of changes in orientation of electron orbits in the

dielectric because of the rapid reversals of the polarity of the line voltage. The amount of power loss due to dielectric hysteresis depends upon

the type of dielectric used. A vacuum dielectric has the smallest power loss.

Dielectric leakage occurs in a capacitor as the result of leakage current through the dielectric. Normally it is assumed that the dielectric will

effectively prevent the flow of current through the capacitor. Although the resistance of the dielectric is extremely high, a minute amount of

current does flow. Ordinarily this current is so small that for all practical purposes it is ignored. However, if the leakage through the dielectric is

abnormally high, there will be a rapid loss of charge and an overheating of the capacitor.

The power loss of a capacitor is determined by loss in the dielectric. If the loss is negligible and the capacitor returns the total charge to the

circuit, it is considered to be a perfect capacitor with a power loss of zero.

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Question:

1. Name two types of power losses associated with a capacitor.

2. Define the term "working voltage" of a capacitor. What should be the working voltage of a capacitor in a circuit that is operating at 600

volts?

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3.9.3 Capacitor types, Construction, and Function

There are many types of capacitor but they can be split into two groups, polarized (electrolytic) and unpolarised (non electrolytic). Each group

has its own circuit symbol. We won't worry at the moment what these terms mean, other than to say:

• Electrolytic capacitors hold much more charge;

• Electrolytic capacitors have to be connected with the correct polarity otherwise they can explode.

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3.9.3.1 Polarized capacitors (large values, 1pF +)

1. Electrolytic capacitors

Electrolytic capacitors are polarized components, meaning that they have positive and negative connector. They must be connected the

correct way round, at least one of their leads will be marked + or -. Positive connector has to be connected to the node with a high voltage

than the node for connecting the negative connector. If done otherwise, electrolytic capacitor could be permanently damaged due to

electrolysis and eventually destroyed. Explosion may also occur if capacitor is connected to voltage that exceeds its working voltage. Working

voltage is printed on capacitor body. They are not damaged by heat when soldering.

Electrolytic capacitors represent the special type of capacitors with fixed capacity value. Thanks to the special construction, they can have

exceptionally high capacity, ranging from one to several thousand µF. They are most frequently used in transformers for leveling the voltage,

in various filters, etc. There are two designs of electrolytic capacitors; axial where the leads are attached to each end (220µF in picture) and

radial where both leads are at the same end (10µF in picture). Radial capacitors tend to be a little smaller and they stand upright on the circuit

board (Figure 108).

It is easy to find the value of electrolytic capacitors because they are clearly printed with their capacitance and voltage rating. The voltage

rating can be quite low (6V for example) and it should always be checked when selecting an electrolytic capacitor. It the project parts list does

not specify a voltage; choose a capacitor with a rating which is greater than the project's power supply voltage. 25V is a sensible minimum for

most battery circuits.

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2. Tantalum Bead Capacitors

Tantalum capacitors represent a special type of electrolytic capacitors. Tantalum bead capacitors are polarized and have low voltage ratings

like electrolytic capacitors. They are expensive but very small, so they are used where a large capacitance is needed in a small size. Modern

tantalum bead capacitors are printed with their capacitance, voltage and polarity in full. However older ones use a color-code system which

has two stripes (for the two digits) and a spot of color for the number of zeros to give the value in µF.

The standard color code is used, but for the spot, grey is used to mean x 0.01 and white means x 0.1 so that values of less than 10µF can be

shown. A third color stripe near the leads shows the voltage (yellow 6.3V, black 10V, green 16V, blue 20V, grey 25V, white 30V, pink 35V).

The positive (+) lead is to the right when the spot is facing you: 'when the spot is in sight, the positive is to the right'.

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3.9.3.2 Unpolarised capacitors (small values, up to 1pF)

Small value capacitors are unpolarised and may be connected either way round. They are not damaged by heat when soldering, except for

one unusual type (polystyrene). They have high voltage ratings of at least 50V, usually 250V or so. It can be difficult to find the values of these

small capacitors because there are many types of them and several different labeling systems. Many small value capacitors have their value

printed but without a multiplier, so you need to use experience to work out what the multiplier should be.

For example 0.1 means 0.1µF = 100nF. Sometimes the multiplier is used in place of the decimal point. For example: 4n7 means 4.7nF.

Figure 110: Examples of Unpolarised capacitors and Circuit Symbol

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1. Polystyrene Capacitors

This type is rarely used now. Their value (in pF) is normally printed without units. Polystyrene capacitors can be damaged by heat when

soldering (it melts the polystyrene) so you should use a heat sink (such as a crocodile clip). Clip the heat sink to the lead between the

capacitor and the joint.

Figure 111: Polystyrene Capacitors

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Real capacitor values (the E3 and E6 series)

You may have noticed that capacitors are not available with every possible value, for example 22µF and 47µF are readily available, but 25µF

and 50µF are not. Imagine that you decided to make capacitors every 1OµF giving 10, 20, 30, 40, and 50 and so on. That seems fine, but

what happens when you reach 1000? It would be pointless to make 1000, 1010, 1020, and 1030 and so on because for these values 10 is a

very small difference, too small to be noticeable in most circuits and capacitors cannot be made with that accuracy. To produce a sensible

range of capacitor values you need to increase the size of the 'step' as the value increases. The standard capacitor values are based on this

idea and they form a series that follows the same pattern for every multiple of ten.

The E3 series (3 values for each multiple of ten): 10, 22, 47, then it continues 100, 220, 470, 1000, 2200,4700,10000 etc.

"Notice how the step size increases as the value increases (values roughly double each time)."

The E6 series (6 values for each multiple of ten): 10,15,22,33,47, 68,etc then it continues 100,150,220,330,470,680,1000 etc.

Notice how this is the E3 series with an extra value in the gaps. The E3 series is the one most frequently used for capacitors because many

types cannot be made with very accurate values.

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Mica Capacitor

Plates are formed by depositing a silver film on mica or using interleaved sheets of metal foil (aluminium). Stability is high but tolerance is low

(± 1%). Working voltage is high and leakage current is low. Values range from 0.01µF to 10,000 pF.

Figure 112: Mica Capacitor

Ceramic Capacitor

These come in many forms e.g. disc, rod or plate, shaped with the ceramic as the dielectric. Small capacitance types range from 1pF to 1µF,

with a high working voltage (up to a few thousand volts). Other types may use a ceramic compound (barium titanate), which has a very high

dielectric constant so gives a very high capacitance for a small physical size. Stability and tolerance are poor.

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Variable capacitors

There are two major types of capacitors: fixed and variable. The fixed capacitor has a specific value of capacitance. A variable capacitor

allows for a range of capacitance. Variable capacitors are designed so that capacitance can be changed through a mechanical means such as

adjusting a screw or turning a shaft.

Variable capacitors are mostly used in radio tuning circuits and they are sometimes called 'tuning capacitors'. They have very small

capacitance values, typically between 100pF and 500pF (100pF = 0.0001µF). Variable capacitors are manufactured in various shapes and

sizes, but common feature for all of them is a set of immobile, interconnected aluminium plates called stator, and another set of plates,

connected to a common axis, called rotor.

In axis rotating, rotor plates get in between stator plates, thus increasing capacity of the device. Naturally, these capacitors are constructed in

such a way that rotor and stator plates are placed consecutively. Insulator (dielectric) between the plates is a thin layers of air, hence the

name variable capacitor with air dielectric. When setting these capacitors, special attention should be paid not to band metal plates, in order to

prevent short-circuiting of rotor and stator and ruining the capacitor (Figure 113(a) upper).

These are actually two capacitors with air dielectric whose rotors share the common axis, so that axis rotation changes the capacities of both

capacitors. These two-fold capacitors are used in radio receivers: larger one is used in the input circuit, and the smaller one in the local

oscillator. The photo shows symbol for such capacitors. Contour line points to the fact that the rotors are mechanically and electrically

interconnected. If one part of variable capacitor should be connected to the mass, which is often the case, then it is rotor(s).

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Figure 113(a) below shows a typical variable capacitor. It has two sets of plates. One set is called the rotor and the other the stator. The rotor

is usually connected to a knob outside the capacitor. The two sets of plates are close together but not touching. Air is the dielectric in a

variable capacitor. As the knob is turned, the sets of plates become more or less meshed, increasing or decreasing the distance between the

plates. As the plates become more meshed, capacitance increases. As the plates become less meshed, capacitance decreases.

Beside the capacitors with air dielectric, there are also variable capacitors with solid insulator. With these, thin insulator foil occupies the space

between stator and rotor, while capacitor itself is contained in a plastic casing. These capacitors are much more resistant to mechanical

damage and quakes, which makes them very convenient for portable electronic devices. One such one-fold capacitor is shown on the Figure

113(b). Many variable capacitors have very short spindles which are not suitable for the standard knobs used for variable resistors and rotary

switches. It would be wise to check that a suitable knob is available before ordering a variable capacitor.

Variable capacitors are not readily available in amateur conditions, but can be obtained from worn out radio receivers, for example (these

capacitors are usually Japanese in origin). One such capacitor, used in portable radio receivers with AM area only, is shown on the Figure

113(c). The' plastic casing contains four capacitors, two variacs and two trimmers, connected according to the scheme from the upper left

corner. Connecting the pins according to the lower scheme gets us a one fold variable capacitor with capacity ranging from 12pF to 218pF.

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Figure 113: Variable Capacitors

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Preset or Trimmer Capacitors

Variable capacitors are not normally used in timing circuits because their capacitance is too small to be practical and the range of values

available is very limited. Instead timing circuits use a fixed capacitor and a variable resistor if it is necessary to vary the time period.

The most common devices containing variable capacitors are the radio receivers, where these are used for frequency tuning. Semi-variable or

trimmer capacitors are miniature variable capacitors, with capacity ranging from several pF to several tens of pFs. These are used for fine-

tuning in the radio receivers, radio transmitters, oscillators, etc. They are designed to be mounted directly onto the circuit board and adjusted

only when the circuit is built. A small screwdriver or similar tool is required to adjust trimmers. The process of adjusting them requires patience

because the presence of your hand and the tool will slightly change the capacitance of the circuit in the region of the trimmer.

Trimmer capacitors are only available with very small capacitances, normally less than 100pF. It is impossible to reduce their capacitance to

zero, so they are usually specified by their minimum and maximum values, for example 2-10pF. Three trimmers, along with their symbol, are

shown on the Figure 114.

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FIGURE 114: Trimmer Capacitors and Circuit Symbol

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3.9.4 Capacitor Color Coding

Marking the block-capacitors

Commonly, capacitors are marked by a number representing the capacity value printed on the capacitor. Beside this value, number

representing the maximal capacitor working voltage is mandatory, and sometimes tolerance, temperature coefficient and some other values

are printed too. If, for example, capacitor mark in the scheme reads 5nF/40V, it means that capacitor with 5nF capacity value is used and that

its maximal working voltage is 40V. Any other 5nF capacitor with higher maximal working voltage can be used instead, but they are as a rule

larger and more expensive.

Sometimes, especially with capacitors of low capacity values, capacity may be represented with colors, similar to four-ring system used for

resistors (Figure 115(a)). The first two colors (A and B) represent the first two digits, third color (C) is the multiplier, fourth color (D) is the

tolerance, and the fifth color (E) is the working voltage. The color codes currently in use are the Joint Army-Navy (JAN) code and the Radio

Manufacturers' Association (RMA) code.

With disk-ceramic capacitors (Figure 115(b)) and tubular capacitors (Figure 115(c) working voltage is not specified, because these are used

in circuits with low or no DC voltage. If tubular capacitor does have five color rings on it, then the first color represents the temperature

coefficient, while the other four specify its capacity value in the previously described way. Proprietary of




Figure 115: Marking the Capacity Using Colours

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Example: Figure 116

Ignore the 4th band (tolerance) and 5th band (voltage rating).

(a) (b)

Figure: 116

(a) Brown, black, orange means 1OOOOpF = 1OnF = 0.01µF.

(b) Note that there are no gaps between the colors bands, so 2 identical bands actually appear as a wide band.

Wide red, yellow means 220nF = 0.22µF.

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NOTES

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A mica capacitor, it should be noted, may be marked with either three dots or six dots. Both the three-dot and the six-dot codes are similar, but

the six-dot code contains more information about electrical ratings of the capacitor, such as working voltage and temperature coefficient. The

capacitor shown in Figure117 represents either a mica capacitor or a moulded paper capacitor. To determine the type and value of the

capacitor, hold the capacitor so that the three arrows point left to right (>). The first dot at the base of the arrow sequence (the left-most dot)

represents the capacitor type. This dot is black, white, silver, or the same color as the capacitor body.

Mica is represented by a black or white dot and paper by a silver dot or dot having the same color as the body of the capacitor. The two dots

to the immediate right of the type dot indicate the first and second digits of the capacitance value. The dot at the bottom right represents the

multiplier to be used. The multiplier represents picofarads. The dot in the bottom centre indicates the tolerance value of the capacitor.

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Figure 117: 6 dot colour code for mica and moulded paper capacitors

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Notice that this type of mica capacitor differs from the one shown in Figure 117; in that the arrow is solid instead of broken. This type of mica

capacitor is read in the same manner as the one shown in Figure 118, with one exception: the first dot indicates the first digit.

(Note: Because this type of capacitor is always type dot mica)

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Figure 118: Mica capacitor color code.-3 dots

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Example:

Read the capacitor color code on the mica capacitor (Figure 119).

Figure 119

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Solution:

1) Hold the capacitor so the arrows point left to right.

2) Read the first dot.

3) Read the first digit dot.

4) Read the second digit dot and apply it to the first digit.

5) Read the multiplier dot and multiply the first two digits by multiplier (Remember that the multiplier is in picofarads).

6) Lastly, read the tolerance dot.

According to the above coding, the capacitor is a mica capacitor whose capacitance is 1200 pF with a tolerance of ±6%

The Figure 120 shows how capacity of miniature tantalum electrolytic capacitors is marked by colors. The first two colors represent the first

two digits and have the same values as with resistors. The third color represents the multiplier, which the first two digits should be multiplied

by, to get the capacity value expressed in µF. The fourth color represents the maximal working voltage value.

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One important note on the working voltage: capacitor voltage mustn't exceed the maximal working voltage as capacitor may get destroyed. In

case when the voltage between nodes where the capacitor is about to be connected is unknown, the "worst" case should be considered.

There is the possibility that, due to malfunction of some other component, voltage on capacitor equals the power supply voltage. If, for

example, the power supply is 12V battery, then the maximal working voltage of used capacitors should exceed 12V, for security's sake.

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Figure 120: Marking the tantalum electrolytic capacitors

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Capacitor Number Code

A number code is often used on small capacitors where printing is difficult:

• The 1st number is the 1st digit,

• The 2nd number is the 2nd digit,

• The 3rd number is the number of zeros to give the capacitance in pF.

• Ignore any letters - they just indicate tolerance and voltage rating.

For example: 102 means 1OOOpF = 1nF (not 102pF)

For example: 472J means 4700pF =4.7nF (J means 5% tolerance).

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Question:

Examine the three capacitors shown below. What is the capacitance of each?

Answer:

(1) 26 mF or 260,000 pF

(2) 630 pF

(3) 9600 pF. Proprietary of




3.9.5 Calculations of capacitance and voltage in series circuits and parallel circuits

3.9.5.1 Capacitor in Series

The overall effect of connecting capacitors in series is to move the plates of the capacitors further apart. This is shown in Figure 121. Notice

that the junction between C1 and C2 has both a negative and a positive charge. This causes the junction to be essentially neutral. The total

capacitance of the circuit is developed between the left plate of C1 and the right plate of C2. Because these plates are farther apart, the total

value of the capacitance in the circuit is decreased.

FIGURE 121: Capacitors in series

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The current through capacitors in series stays the same, but the voltage across each capacitor can be different. The sum of the potential

differences (voltage) is equal to the total voltage. Solving for the total capacitance (CT) of capacitors connected in series is similar to solving

for the total resistance (RT) of resistors connected in parallel. Note the similarity between the formulas for RT and CT:

If the circuit contains more than two capacitors, use the above formula. If the circuit contains only two capacitors, use the below formula:

Note: All values for CT, C1, C2, and C3... C n should be in farads. It should be evident from the above formulas that the total capacitance of

capacitors in series is less than the capacitance of any of the individual capacitors.

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Example 1:

Determine the total capacitance of a series circuit containing three capacitors whose values are 0.01µF, 0.25 µF, and 50,000 pF, respectively.

Solution:

The total capacitance of 0.008µF is slightly smaller than the smallest capacitor (0.01µF).

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Example 2:

What is the total capacitance of a circuit that contains two capacitors (10 µF and 0.1 µF) wired together in series?

CT = C1 C2

C1 + C2

CT = 10 X 0.1 µ F

10 + 0.1

CT = 1 µF

10.1

CT = 0.099µF or 0.1µF

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3.9.5.2 Capacitors in Parallel

When capacitors are connected in parallel, one plate of each capacitor is connected directly to one terminal of the source, while the other

plate of each capacitor is connected to the other terminal of the source.

Figure 122 shows all the negative plates of the capacitors connected together, and all the positive plates connected together. CT, therefore,

appears as a capacitor with a plate area equal to the sum of all the individual plate areas. As previously mentioned, capacitance is a direct

function of plate area. Connecting capacitors in parallel effectively increases plate area and thereby increases total capacitance.

Figure 122: Parallel Capacitive Circuit

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The total capacitance of the circuit may by calculated using the formula:

CT = Cl + C2 + C3+........ Cn

Where all capacitances are in the same units. Capacitors in a parallel configuration each have the same potential difference (voltage). For

capacitors connected in parallel the total capacitance is the sum of all the individual capacitances.

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Example 1:

Determine the total capacitance in a parallel capacitive circuit containing three capacitors whose values are 0.03µF, 2.0 µF, and 0.25 µF,

respectively.

Given:

C1 = 0.03.uF

C2 =2.uF

C3 = 0.25.uF

Solution:

CT = C1 + C2 + C3

CT = 0.03uF + 2.0µF + 0.25uF

CT = 2.28uF

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Example 2:

What is the total capacitance of a circuit in which four capacitors (10µF, 21µF, 0.1µF and 2µF) are connected in parallel?

CT = C1+C2+C3+C4

CT = 10uF+21uF+O.luF+2uF

CT = 33.1.uF

The reason for putting capacitors in parallel is to increase the total amount of charge stored. In other words, increasing the capacitance also

increases the amount of energy that can be stored. Its expression is:

In parallel the effective area of the combined capacitor has increased, increasing the overall capacitance. While in series, the distance

between the plates has effectively been increased, reducing the overall capacitance. In practice capacitors will be placed in series as a means

of economically obtaining very high voltage capacitors, for example for smoothing ripples in a high voltage power supply. Three "600 volt

maximum" capacitors in series will increase their overall working voltage to 1800 volts.

This is of course offset by the capacitance obtained being only one third of the value of the capacitors used. This can be countered by

connecting 3 of these series set-ups in parallel, resulting in a 3x3 matrix of capacitors with the same overall capacitance as an individual

capacitor but operable under three times the voltage. In this application, a large resistor would be connected across each capacitor to ensure

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that the total voltage is divided equally across each capacitor and also to discharge the capacitors for safety when the equipment is not in use.

Another application is for use of polarized capacitors in alternating current circuits; the capacitors are connected in series, in reverse polarity,

so that at any given time one of the capacitors is not conducting.

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NOTES

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3.9.6 Exponential charge and discharge of a capacitor

3.9.6.1 Charging a Capacitor

In order to better understand the action of a capacitor in conjunction with other components, the charge and discharge actions of a purely

capacitive circuit are analyzed first. For ease of explanation, the capacitor and voltage source shown in Figure 124 are assumed to be perfect

(no internal resistance), although this is impossible in practice.

In Figure 124(A), an uncharged capacitor is shown connected to a four-position switch. With the switch in position 1 the circuit is open and no

voltage is applied to the capacitor. Initially each plate of the capacitor is a neutral body and until a difference of potential is impressed across

the capacitor, no electrostatic field can exist between the plates.

To charge the capacitor, the switch must be thrown to position 2, which places the capacitor across the terminals of the battery. Under the

assumed perfect conditions, the capacitor would reach full charge instantaneously. However, the charging action is spread out over a period

of time in the following discussion so that a step-by-step analysis can be made.

At the instant the switch is thrown to position 2 (Figure 124(B)), a displacement of electrons occurs simultaneously in all parts of the circuit.

This electron displacement is directed away from the negative terminal and toward the positive terminal of the source (the battery). A brief

surge of current will flow as the capacitor charges.

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Figure 124: Charging a Capacitor

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If it were possible to analyze the motion of the individual electrons in this surge of charging current, the following action would be observed.

See Figure 125

At the instant the switch is closed, the positive terminal of the battery extracts an electron from the bottom conductor. The negative terminal of

the battery forces an electron into the top conductor. At this same instant an electron is forced into the top plate of the capacitor and another is

pulled from the bottom plate. Thus, in every part of the circuit a clockwise displacement of electrons occurs simultaneously.

As electrons accumulate on the top plate of the capacitor and others depart from the bottom plate, a difference of potential develops across

the capacitor. Each electron forced onto the top plate makes that plate more negative, while each electron removed from the bottom causes

the bottom plate to become more positive. Notice that the polarity of the voltage that builds up across the capacitor is such as to oppose the

source voltage. The source voltage (emf) forces current around the circuit of Figure 125 in a clockwise direction.

The emf developed across the capacitor, however, has a tendency to force the current in a counter clockwise direction, opposing the source

emf. As the capacitor continues to charge, the voltage across the capacitor rises until it is equal to the source voltage. Once the capacitor

voltage equals the source voltage, the two voltages balance one another and current ceases to flow in the circuit.

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Figure 125: Electron motion during charge.

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In studying the charging process of a capacitor, you must be aware that no current flows through the capacitor. The material between the

plates of the capacitor must be an insulator. However, to an observer stationed at the source or along one of the circuit conductors, the action

has all the appearances of a true flow of current, even though the insulating material between the plates of the capacitor prevents the current

from having a complete path. The current that appears to flow through a capacitor is called displacement current.

When a capacitor is fully charged and the source voltage is equaled by the counter electromotive force (cemf) across the capacitor, the

electrostatic field between the plates of the capacitor is maximum. Since the electrostatic field is maximum the energy stored in the dielectric is

also maximum.

If the switch is now opened as shown in Figure 126(A), the electrons on the upper plate are isolated. The electrons on the top plate are

attracted to the charged bottom plate. Because the dielectric is an insulator, the electrons cannot cross the dielectric to the bottom plate. The

electrostatic field will effectively trap the charges on both plates and the capacitor will remain charged indefinitely. You should note at this point

that the insulating dielectric material in a practical capacitor is not perfect and small leakage current will flow through the dielectric. This

current will eventually dissipate the charge. However, a high quality capacitor may hold its charge for a month or more.

Review briefly, when a capacitor is connected across a voltage source, a surge of charging current flows. This charging current develops a

cemf across the capacitor which opposes the applied voltage. When the capacitor is fully charged, the cemf is equal to the applied voltage and

charging current ceases. At full charge, the electrostatic field between the plates is at maximum intensity and the energy stored in the

dielectric is at maximum. If the charged capacitor is disconnected from the source, the charge will be retained for some period of time. The

length of time the charge is retained depends on the amount of leakage current present. Since electrical energy is stored in the capacitor, a

charged capacitor can act as a source emf.

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3.9.6.2 Discharging a Capacitor

To discharge a capacitor, the charges on the two plates must be neutralized. This is accomplished by providing a conducting path between

the two plates as shown in Figure 126(B). With the switch in position (4) the excess electrons on the negative plate can flow to the positive

plate and neutralize its charge. When the capacitor is discharged, the distorted orbits of the electrons in the dielectric return to their normal

positions and the stored energy is returned to the circuit. It is important for you to note that a capacitor does not consume power. The energy

the capacitor draws from the source is recovered when the capacitor is discharged.

Figure 126: Discharging a Capacitor

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Question

1. State what happens to the electrons in a capacitor circuit when:

The capacitor is charging

The capacitor is discharging.

2. A 5000 µF capacitor is charged to 12.0 V and discharged through a 2000Ω resistor.

(a) What is the time constant?

(b) What is the voltage after 13 s?

(c) What is the half-life of the decay?

(d) How long would it take the capacitor to discharge to 2.0 V?

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NOTES

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3.9.7 RC Time constants

The time require to charge a capacitor to 63 percent (actually 63.2 percent) of full charge or to discharge it to 37 percent (actually 36.8

percent) of its initial voltage is known as the TIME CONSTANT (TC) of the circuit. The charge and discharge curves of a capacitor are shown

in Figure 127.

Figure 127: RC time constant

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The value of the time constant in seconds is equal to the product of the circuit resistance in ohms and the circuit capacitance in farads. The

value of one time constant is expressed mathematically as t = RC. Some forms of this formula used in calculating RC time constants are:

Question:

What is the RC time constant of a series RC circuit that contains a 12-megohm resistor and a 12-microfarad capacitor?

t = R (mégohms) x C (microfarads)

t= 12 x 106x 12 x10-6

t =144 seconds

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As a capacitor becomes charged, the current flow decreases because the voltage developed by the capacitor increases over time and

opposes the source voltage. Therefore, the rate of charge of a capacitor is reduced over time. The amount time required to charge and

discharge a capacitor is a very important factor in the design of electronic circuits. Resistors are often used in combination with capacitors in

order to control the charge and discharge time necessary for the intended application. Resistance directly affects the time required to charge a

capacitor. As resistance increases, it takes more time to charge a capacitor. The amount of time for the capacitor to become fully charged in a

resistive-capacitive (RC) circuit depends on the values of the capacitor and resistor.

Figure 128 shows the rate of charge of a capacitor in a RC circuit. Note that the rate of charge greatly decreases over time. The latter part of

its charging time is many times longer than the first part. In fact, a capacitor reaches 63.2% of its charge in one fifth of the time it takes to

become fully charged. Because of this, capacitors in actual applications are generally not fully charged. Capacitors in circuits are generally

charged to just 63.2% of full capacity. The time required for a capacitor to charge to 63.2% of its full capacity is referred as its RC (resistive-

capacitive) time constant.

A large time constant means the capacitor charges slowly. Note that the time constant is a property of the circuit containing the capacitance

and resistance; it is not a property of a capacitor alone.

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Figure 128: The Rate of Charge of a Capacitor in a RC Circuit

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The time constant is the time taken for the charging (or discharging) current (I) to fall to 1/e of its initial value (lo). 'e' is the base of natural

logarithms, an important number in mathematics (likeπ). e = 2.71828 (to 6 significant figures) so we can roughly say that the time constant is

the time taken for the current to fall to 1/3 of its initial value.

After each time constant the current falls by 1/e (about 1/3). After 5 time constants (5RC) the current has fallen to less than 1% of its initial

value and we can reasonably say that the capacitor is fully charged, but in fact the capacitor takes for ever to charge fully. Figure 129 shows

how the voltage (V) increases as the capacitor charges. At first the voltage changes rapidly because the current is large; but as the current

decreases, the charge builds up more slowly and the voltage increases more slowly. After 5 time constants (5RC) the capacitor is almost fully

charged with its voltage almost equal to the supply voltage. We can reasonably say that the capacitor is fully charged after 5RC, although

really charging continues for ever (or until the circuit is changed).

Figure 129 (graph) shows how the current (I) decreases as the capacitor discharges. The initial current (lo) is determined by the initial voltage

across the capacitor (Va) and resistance (R):

Initial current,

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Figure 129: Graphs showing the current and voltage for a capacitor charging (time constant = RC)

Note that the current graphs are the same shape for both charging and discharging a capacitor. This type of graph is an example of

exponential decay.

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Figure 130 (graph) shows how the voltage (V) decreases as the capacitor discharges. At first the current is large because the voltage is large,

so charge is lost quickly and the voltage decreases rapidly. As charge is lost the voltage is reduced making the current smaller so the rate of

discharging becomes progressively slower.

After 5 time constants (5RC) the voltage across the capacitor is almost zero and we can reasonably say that the capacitor is fully discharged,

although really discharging continues for ever (or until the circuit is changed).

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Figure 130: Graphs showing the current and voltage for a capacitor discharging (time constant = RC)

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3.9.8 Testing of capacitors

An analogue multimeter or digital multimeter set to high resistance range can be used to test a capacitor.

(1) Non-polarized Types - If the resistance is less than about 1M it is allowing current from the battery in the multimeter to 'pass' so it is

leaking and is faulty.

Note -- there may be an initial short burst of current as the capacitor charges up.

(2) Polarized Types - For the dielectric to form in these types a positive voltage must be applied to the positive side of the capacitor

(marked + or a groove). In most analogue multimeters the terminal marked - (black) is the positive of the internal

battery when selected to the ohms setting.

For digital meters the manufacturer’s instructions will have to be consulted. When the capacitor is first connected

to the multimeter its resistance is low but rises as the dielectric forms, otherwise the capacitor is faulty.

Capacitor is extensively used in electronic circuit as well as high energy ignition unit and strobe light systems.

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NOTES

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EASA PART 66 CAT B1.1 MODULE 3 ELECTRICAL FUNDAMENTALS MAGNETISM (EASA 3.10 L2)


3.10 MAGNETISM (EASA Ref 3.10) Level 2

3.10.1 (a) Theory of magnetism

Introduction

There is a close relationship between electricity and magnetism. Not only can an electric current generate magnetic effects, but also a

movement of a magnet can generate electrical effects.

Electromagnets can be constructed which may to be used to convert electrical energy into mechanical energy.

The movement of a magnet causes an electric current to be set up in a conductor. So it is used to convert mechanical energy into electrical

energy.

The most common method of converting mechanical energy into electrical energy is by the use of magnetism in a generator. In an electric

motor electrical energy is converted into mechanical energy by the use of magnetism.

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EASA PART 66 CAT B1.1 MODULE 3 ELECTRICAL FUNDAMENTALS MAGNETISM (EASA 3.10 L2)


3.10.2 (a) Properties of a magnet

The Nature of Magnetism

Magnetism is a property that is associated with an electric charge in motion. An electron, of course, is such a charge. As an electron moves

about the nucleus of an atom in an orbital path, it also spins on its own axis. This spinning motion, in effect, causes each electron to be a tiny

magnet.

The polarity of the magnetic field that is generated by a spinning electron is determined by the direction of the spin. In most materials, the

number of electrons spinning in one direction approximately equals the number of those spinning in the opposite direction. As a result, for all

practical purposes, the materials are magnetically neutral and do not exhibit external magnetic characteristics.

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS MAGNETISM (DCAM 3.10 L2)


3.10.3 (a) Action of magnet suspended in the Earth's magnetic field

Refer to Figure 131.

If freely suspended, a natural magnet comes to rest pointing in a north-south direction.

Figure 131: Magnets in Earth Magnetic Field

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This is because the earth itself is a large natural magnet with a north pole and a south pole, and the magnetism or magnetic force of attraction

pulls the magnet into a magnetic north-south line.

The magnetic field or 'lines of force' between north and south poles are invisible. Thus a magnet is a piece of material which has a magnetic

field surrounding it. Such magnets are also called permanent magnets. Refer to Figure 132.

Figure 132: Magnets Field and Poles of the Earth

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Modern permanent magnets are made of steel. They exist in many different shapes, for example, compass needles, bars, rods, horseshoes

and rings.

FIGURE 133: Shapes of Magnets

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3.10.3.1 (a) Magnetic Poles

The two ends of a magnet have different characters. One end is called a 'south-seeking pole', while the other is called a 'north seeking pole'.

As described before a bar magnet will align it self in a north south direction if the freedom of movements are allowed. The ends of a magnet

are usually referred to simply as the north and the south poles. The north pole of a magnet is defined as that end which points towards the

north pole of the earth. The south pole of a magnet points towards the south pole of the earth. Refer to Figure 134.

FIGURE 134: Magnetic Poles

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3.10.3.2 (a) Magnetic Attraction and Repulsion

When two magnets are placed close together, according to how they are placed they will either attract or repel each other.

Refer to Figure 135

FIGURE 135: Magnetic Attraction

The north pole of one magnet will tend to draw towards itself to the south pole of an adjacent magnet and vice versa. It can be seen by means

of the iron filings that magnetic lines from a north pole are drawn into an adjoining south pole.

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Refer to Figure 136

Two north poles or two south poles close together will tend to push away from one another. The iron filings show that the magnetic lines from

two adjoining north poles or south poles are forced apart. The content or the last two paragraphs can be summed up by saying that, in

common with the charges in atomic particles:

• unlike poles attract

• like poles repel.

FIGURE 136: Magnetic Repulsion Proprietary of




3.10.3.3 (a) Magnetic Field and Direction


The area immediately surrounding a magnet, in which magnetic attraction occurs, is said to contain a magnetic field. A magnetic field, in the

form of lines of force, can be mapped out on a sheet of paper by using some iron filings (Figure 137, detail a).

The magnetic lines of force travel outside from and to the poles of the magnet in the direction north to south or more correctly, from the north-

seeking pole to the south-seeking pole. Inside the magnet the lines of force travel from the South Pole towards the North Pole (Figure 137,

detail b).

FIGURE 137: Magnetic Field and Direction

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3.10.4 (a) Magnetization and demagnetization

Natural magnet is a certain type of iron or lodestone that has the property of attracting and picking up pieces of iron and steel.


If a piece of soft iron is placed near to one end of a magnet, the iron becomes slightly magnetized. This process is called induction, meaning

that magnetism has been led into the iron, or induced. If the soft iron is stroked a number of times in one direction with the end of the magnet,

the iron becomes even more strongly magnetized.

FIGURE 138: Magnetization by Induction

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Another method to magnetize a material is to place the material (steel bar) in a current carrying solenoid. The polarity of the magnet can be

found by applying right hand grasp rule.

For demagnetizing, it is necessary to remove the alignment of the molecular magnets. There are three different methods of achieving that:

a) by heat

b) by mechanical force – dropping or hammering

c) by an altering magnetic field – using alternating current

Place the magnet inside a solenoid which is carrying alternating current. While the current is still flowing the magnet is withdrawn slowly to a

distance of several meters in an E – W direction. Refer Figure 139

The magnet is held in an E – W direction so that it will not have any residual magnetism due to the earth magnetic field.

This method of demagnetizing is sometimes called de –Gaussing. Proprietary of




FIGURE 139: Demagnetization

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3.10.5 (a) Magnetic shielding

It is necessary to isolate equipment from the effect of magnetic fields. To protect the equipment from errors due to a magnetic field, shielding

is required.


Where magnetic flux would be undesirable (e.g. in the vicinity of a watch) a magnetic screen of iron is used. This has the effect of

concentrating the flux within itself so that it does not penetrate the surrounding air space. The soft iron magnetic flux concentrating effect is

called permeability, i.e. soft iron has a high permeability and air has a low permeability

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FIGURE 140: Magnetic Screen

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3.10.6 (a) Various types of magnetic material

3.10.6.1 (a) Magnetic Materials

It is useful to know about magnetism which types of materials are magnetic, i.e. which materials are attracted to a magnet and which are not.

In general there are three different kinds of materials related to the study of magnetism. A magnet can be used to lift a pair of scissors, nails,

tacks and needles. Those materials which attracted to a magnet are called magnetic materials. Another name for them is ferromagnetic

materials. These materials are iron, nickel and cobalt. A magnet cannot pick up a piece of wood or paper. These materials are called

nonmagnetic. Another name for them is paramagnetic materials.

There is a third class of materials, called diamagnetic, that act in a very unusual way near a strong magnet. Instead of being attracted to a

magnet as are magnetic materials, or indifferent to the magnet as are nonmagnetic materials, diamagnetic materials actually move away from

a magnetic field. So far, diamagnetism has not been put to any large practical use because the effect is relatively small. It would take a very

strong magnet to move diamagnetic materials with any noticeable force. If pieces of iron become magnetized by a loadstone they are called

artificial magnets.

Some of the artificial magnets are able to retain their magnetism for long periods of time, while others lose their magnetism quickly. The ones

that lose their magnetism quickly are called temporary magnets, while the ones that can retain their magnetism over a long period of time are

called permanent magnets.

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There are applications in electricity in which a material is need to become magnetized for a short period of time, and there are also

applications where permanent magnets are wanted. Soft iron is a material that is used for making temporary magnets. This name is very

misleading. There is nothing soft about the iron. Instead, the name comes from the fact that it cannot retain a magnetic field for any period of

time. Refer to Figure 141.

FIGURE 141: Magnetic Material

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Magnetic materials are divided into ferromagnetic materials and non-magnetic materials.

Ferromagnetic materials are materials such as iron, cobalt and nickel. Most of their alloys which can be magnetized have a high flux

concentrating power. Iron for example has a flux-multiplying factor µ of about 5000.

Non-magnetic materials are those that have no flux-multiplying factor. Its permeability (µ) is around one. Non-magnetic materials are copper,

aluminium, water and air. Air is a standard and has a permeability of one.

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3.10.7 (a) Electromagnets Construction

3.10.7.1 (a) Application of Electromagnets

A typical application of an electromagnet is the relay or solenoid. When a current (control current) is fed to an electromagnet the lever-like

armature is attracted. Depending on the construction this closes the contact (normally-open contact) and an external circuit is closed (Figure

142, detail a) or this opens the contact (normally-closed contact) and an external circuit is interrupted (Figure 142, detail b).

FIGURE 142: Construction of Relay

When the control circuit is interrupted the armature returns to its initial position through a restoring force of a spring.

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In the circuit diagrams of electric equipment it is necessary to identify individual relays and their contacts by a system of numbering. Therefore

they are usually annotated as shown in Figure 143. Furthermore the relay number (RL 2) and the denominator (3) that documents the number

of contacts associated with the relay is shown.

Figure 143: Circuit Symbol of a Relay

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3.10.7.2 (a) Principles of operation

Figure 144: Various Symbols of Relays As Used In Circuit Diagrams.

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By the use of a relay it is possible to prevent excessive voltage drop across long length of cable. The electrical equipment can be switched

ON/OFF from a remote point by the use of a relay. When the switch at the remote point is switched ON relay RL 2 becomes energized and

contact RL 2/1 closes thereby connecting the equipment to the supply. There is now only a small voltage drop in the connecting cable. The

current taken by the relay is small.

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Figure 145: Remote Switching using a Relay

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Refer to Figure 146

With a relay, a heavier current can be switched ON or OFF by a weak control current, sometimes over long distances. In this connection

distinction is made between fields of application, e.g. heavy and light-current relays or according to the duty, e.g. protective, indicating, power

and telegraph relays.

FIGURE 146: Heavy Working Current switched by a Relay

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3.10.8 (a) Hand clasp rules to determine: magnetic field around current carrying conductor

3.10.8.1 (a) the Magnetic Effect of Current

Whenever a current flows through a conductor a magnetic field is developed. There are two methods for determining the field direction. Refer

to Figure 147

FIGURE 147: Magnetic Field around a Conductor

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Figure 148 shows the 'right hand rule', whereby the thumb points into the current direction through a conductor and the other fingers point

into the magnetic field direction

FIGURE 148: Right Hand Rule

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Figure 149 shows the 'corkscrew rule'. When the current flows into the paper the magnetic field is clockwise. When the current direction is

out of the paper the magnetic field is counter-clockwise

FIGURE 149: Corkscrew Rule

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3.10.8.2 (a) Direction of Current within a Wire

The direction of the current within a wire is indicated as follows:

• an arrow indicates direction of current flow

• the cross represents tail of arrow pointing into the page

• the dot represents head of arrow pointing out of the page.

FIGURE 150: Direction of Current

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3.10.8.3 (a) The Magnetic Field of a Coil

A coil carrying a current is surrounded by a magnetic field like a permanent magnet. One end of the coil acts like a south pole the opposite

pole acts like a north pole.

By reversing the current direction in the coil its magnetic poles are interchanged. If a conductor is straight piece of wire a weak magnetic field

of little practical use is developed around the wire. Although the magnetic flux has direction the conductor has no north or South Pole.

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By changing the shape of the conductor its magnetic properties can be greatly improved. Figure151 shows a view of a short piece of wire

twisted into a loop. Simply forming the loop improves the magnetic characteristics in three ways:

• brings the flux lines together

• concentrate the flux lines at the centre

• creates north and south pole.

FIGURE 151: North and South Pole of a Coil

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Refer to Figure 152

The north pole of an electromagnet can be determined by the use of the 'right hand grasp rule'. The fingers of the right hand comprehend the

coil and point into the current direction. The thumb points to north.

The flux density of an electromagnet depends on the current in the coil, the number of turns and the core material, if arranged within the coil.

Iron within a coil concentrates the flux and therefore increases the strength of the magnet. The iron core makes the magnetic force stronger,

so that heavy loads can be carried. Comparison of coils with different numbers of turns shows that with a higher number of turns a smaller

current is sufficient to hold a load of equal weight.

As well as its high load bearing capacity the electromagnet has the further advantage, in comparison with a permanent magnet, that this

capacity can be varied within wide limits by varying the supply current.

FIGURE 152: North-South Direction of a Coil

3.10.8.4 (a) Magnetic Circuit

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The flux lines or lines of force surrounding a permanent magnet or a current carrying solenoid are all continuous or completely closed. The

magnetic circuit is formed by the closed path of magnetic flux. One of the simplest forms of magnetic circuit is shown in Figure 153 where part

of the magnetic circuit is in the iron and part is in the air gap.

FIGURE 153: Magnetic Circuit Proprietary of




3.10.9 (b) Magnetic Terms

3.10.9.1 (b) Magneto motive force

The magneto motive force (mmf) of a magnet is that force which tends to produce a magnetic field. The c.g.s system unit of magneto motive

force is the gilberts, which is represented by the symbol F. One Gilbert is equal to that magnitude of force required to establish a flux of one

Maxwell in a flux path or magnetic circuit having a reluctance of one unit.

The SI unit of mmf is the ampere-turns mmf = I x N A-t

3.10.9.2 (b) the Magnetic Field Strength

The magnetic field strength (symbol H) is the intensity of the magnetic force that sets up the magnetic flux density (symbol B) in an

electromagnet (magnetic circuit). It can be compared with the EMF that forces a current (I) through an electric circuit.

The magnetic field strength is determined as: H = IN A-t/m

l Proprietary of




3.10.9.3 (b) Magnetic Flux and Flux Density

Magnetic Flux

The lines of force within magnetic fields form a magnetic flux (symbol φ - Greek letter phi), a term which indicates that what issues or flows out

from a magnet. The SI unit of magnetic flux is Weber. The cgs unit is Maxwell.

Flux Density

The more powerful the magnet the greater is the amount of flux which it generates. For some applications it is the concentration of flux or flux

density (symbol B) which is important, rather than the total amount of flux generated by the magnet.

Flux density is equal to magnetic flux per unit area, B =/A Tesla or Weber/m2

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3.10.9.4 (b) Permeability

Permeability or flux-multiplying factor (symbolµ) is a measure of how easily a magnetic flux can be set up in a material. Air and most materials

(including most metals) have a multiplying factor of approximately one. Iron placed in a magnetic field causes the lines of flux to concentrate in

it. In doing so the iron itself becomes magnetized. The iron generates 'flux lines'· of its own so more 'lines' are added to the original flux. Thus

the presence of iron increases the flux density. Refer to Figure 154

µ = µo µr = B/H

Where,

µ - Absolute permeability

µo - Permeability of Free Space = 4 x 10-7

µr - Relative permeability

B - Flux densityFigure 154: Effect of Iron in a Magnetic Field

H - Field strength (Magnetizing force)

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3.10.9.5 (b) Hysteresis loop

Hysteresis

The B-H curve shows the magnetic characteristics of a material when the magnetic field strength is increased to eventual saturation. If the

magnetizing force is removed some magnetism may remain with the material. This effect is known as 'hysteresis'. Hysteresis then is the lag of

flux density (B) behind the magnetic field strength (H).

Refer to Figure 155

If the magnetic field strength is increased from zero in a positive direction the flux density B rises as in a normal B-H curve

On reducing the magnetizing force H to zero again the flux density B does not follow its original path to zero but follows the path QR. When

the material has first reached saturation the flux density at R is called the remanence or residual magnetism. If the material has not reached

saturation the flux density at R is called remnant flux density.

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Figure 155: Remanence or residual Magnetism

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3.10.9.6 (b) Retentivity

Retentivity is a measure of the magnetism retained by a material over a long period of time. Retentivity must not be confused with remnant

since in some materials remnant is quickly reduced to zero under normal conditions.

3.10.9.7 (b) Coercive force

As shown in Figure 156, a negative value of magnetizing force H must be applied to reduce the flux density B to zero (S). The actual value of

negative magnetizing force H necessary to do this is known as the 'coercive force'. If the material has first reached saturation this value is

termed the 'coercivity' of the material.

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FIGURE 156: Coercive Force

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3.10.9.8 (b) Reluctance

Reluctance is the opposition to magnetic flux and therefore the opposite or reciprocal of permeability. Reluctance can be compared to

resistance in an electric circuit. A material has a permeability of 2700 (µ =2700) and a reluctance of:

1 = 1 = 0.00037 A-t/Weber

µ 2700

3.10.9.9 (b) Saturation points

Refer to Figure 157

If the negative value of magnetizing force is increased past flux density B zero the material will eventually reach saturation T.

This relationship shows that for a permanent magnet, a material with a high coercivity is required, i.e. the force required to 'remove' the

magnetism must be very large.

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FIGURE 157: Negative Saturation

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3.10.9.10 (b) Eddy currents

As a magnetic field expands and collapses about the windings of an iron-core transformer, its flux lines cut across both the turns of the

windings and the core. As a result, voltages are induced within the core itself. These voltages, in turn, establish currents called eddy currents

that move through the core in circular paths.

3.10.10 (b) Protection for care and storage of magnets

Refer to Figure 158

If a permanent magnet is left for a long period without a keeper, or means of completing the magnetic path for the flux, its magnetic strength

will soon decrease.

To prevent this, bar magnets are stored in pairs with their opposite poles adjacent, with small pieces of soft iron called keepers placed across

their ends. The keepers become strong induced magnets keeping the magnetic domains in line via the closed loop of the magnets and

keepers.

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FIGURE 158: Magnet with Keepers

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3.10.11 (b) Magnetic Field Strength/Flux Density Curve (B-H Curve)

Refer to Figure 159

If a circuit is set up as shown in Figure 159 the current can be varied by moving the rheostat slider. Adjusting the current, changes the

magnetic field strength (H) because:

H = I N Amperes.turns/meter

L

The formula shows that the number of turns and the length of the magnetic circuit are fixed values. Only the current is variable.

Increasing the magnetic field strength (H) increases the flux density (B) because flux density (B) is proportional to:

• magnetic field strength (H)

• permeability (µ) of the magnetic circuit or core multiplying factor.)

Therefore B = µ . H

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FIGURE 159: Current Control of a Coil

FIGURE 160: B-H Curve for Air

The B-H curve for air is therefore linear (a straight line) because the permeability of air is one.

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Refer to Figure 161

Figure 161 shows a typical ferromagnetic B-H curve. Increasing H from 0 to 1 results in a small increase of B due mostly to H in air. The

ferromagnetic material has little effect; therefore the permeability of the ferromagnetic material is very low here.

Increasing H further from 1to 2 results in a large increase of B because the ferromagnetic material itself magnetizes, multiplying that increase

of B due to H in air. The ferromagnetic material has a great effect on the increase of B. Therefore the permeability of the ferromagnetic

material rapidly increases to a large value.

Increasing H still further from 2 to 3 results in a small increase of B in fact the slope of the graph (rate of increase) is about the same as from 0

to 1. This is because the ferromagnetic material is fully magnetized so there are no more flux multiplying effects and the increase of B is due

only to the air.

The ferromagnetic material has therefore reached saturation point, the material cannot be magnetized any further and the permeability

decreases to a very low value.

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FIGURE 161: B-H Curve for a typical Ferromagnetic Material

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Refer to Figure 162

The flux density B always lags behind the magnetic field strength H because of the inertia required to change the magnetism in the material.

Figure 162: Hysteresis Loop of Magnetic Material

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3.10.12 (b) Characteristics of Ferromagnetic Materials

Ferromagnetic materials are classed as soft or hard magnetic materials. Soft and hard refer to how easily they magnetize and not whether

they are mechanically hard or soft.

FIGURE 163: Hysteresis Loop of Ferromagnetic Materials

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Hard Magnetic Material

A high magnetic field strength (H) is required to saturate a hard magnetic material and a high value of coercivity is required to remove the

remanence of the magnet (residual magnetism). A hard magnetic material has therefore a good retentivity, making it a good permanent

magnet.

Because a high magnetic field strength H is necessary to magnetize a hard material, the area of the loop is large and therefore the energy (H

is proportional to current) to complete a full cycle or loop, is large. A hard material has therefore large hysteresis losses proportional to the

hysteresis loop area and frequency of the magnet field strength H. A typical hard magnetic material is 'Alnico' used for permanent magnets.

'Alnico' alloys consist of aluminium, cobalt, nickel and iron.

Soft magnetic Materials

A low magnetic field strength (H) is required to saturate a soft magnetic material and a low value of coercivity is required to remove the

remanence of the magnet (residual magnetism). A soft magnetic material has therefore a low retentivity making it unsuitable for use as a

permanent magnet.

Because a low magnetic field strength is necessary to magnetize a soft material the area of the loop is small and the energy required to

complete a full cycle or loop is small.

A soft material usually has a low hysteresis loss and high permeability values make it suitable for use when the magnetic field strength is

alternating (AC current) driving the flux density through a complete hysteresis loop as in AC electric motors, generators and transformers.

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Steel alloys such as permalloy or stalloy are suitable for AC use. For DC applications soft iron is used. Soft iron has a high permeability but

also a relative high hysteresis loss.

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Refer to Figure 164

As most of the core materials used in electronic equipment is ferromagnetic it is important to compare the various characteristics exhibited by

the most common used materials. The main characteristics of ferromagnetic materials can be ascertained by a study of their hysteresis loops

as shown in Figure 164.

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Figure 164: Hysteresis Loop of Ferromagnetic Materials

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS INDUCTANCE / INDUCTOR (DCAM 3.11 L2)


3.11 INDUCTANCE/INDUCTOR (EASA Ref 3.11) Level 2

3.11.1 Electromagnetic Induction

Electrical energy is generated in a generator or transformer as a result of movement between a magnetic field and conductors.

3.11.2 Action of inducing a voltage in a conductor moving in a magnetic field

If a conductor is moved at right angles to a magnetic field this causes the free electrons in the conductor to concentrate at the right end side,

thus producing a lack of electrons at the left hand end of the conductor. The result is that a potential difference (PD) is developed between the

two ends of the conductor. This PD exists only while the conductor is cutting the magnetic flux lines of the magnet.

When the conductor moves out of the magnetic field the electrons return to their original position and the PD disappears. The PD also

disappears if the motion of the conductor is stopped in the magnetic field. Thus the conductor must move with respect to the field before a PD

is developed.

Motion or a rate of change is essential to electromagnetic induction. Some external force must be applied to cause the conductor to move

through the magnetic field. This mechanical force is converted into an electromotive force (EMF) by electromagnetic induction. Refer to

Figure 165

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Figure 165: Conductor Moving in a Magnetic Field

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3.11.3.1 Effect of the following on the magnitude of an induced voltage: magnetic field strength

Refer to Figure 166

Movement of a conductor in the same direction as the magnetic flux or movement of the magnetic flux in the same direction as the conductor

generates no rate of change in flux and therefore no EMF is induced in circuit 'B'.

FIGURE 166: No Induction of EMF

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3.11.3.2 Effect of the following on the magnitude of an induced voltage: rate of change of flux

Refer to Figure 167

Increasing the angle of the conductor from zero to ninety degrees increase the rate of change of flux. Therefore the induced EMF increases

from minimum at zero degrees to maximum at ninety degrees. Figure 167 shows that an amount of EMF is induced in circuit 'B' when the

switch in circuit 'A' is closed or opened.

FIGURE 167: Induction of a Value of EMF

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Rate of Change of Flux

The rate of change of flux and the magnitude of EMF induced in a conductor is determined by:

• the speed of the conductor moving through the field

• the length (proportional to number of turns) of the conductor in the field

• the strength of the magnetic field

• the angle between conductor and field.

Faraday's law summarizes these four points as follows:

When a conductor cuts or is cut by a magnetic flux there is induced an EMF in it, which is proportional to the rate at which the flux is cut.

The induced EMF corresponds to the rate of change of flux divided by rate of change of time (speed).

Furthermore the EMF corresponds to flux density (B) multiplied by length of conductor (I) and multiplied by the speed (V) of the conductor

through the field at ninety degrees.

Expressed in a formula is EMF =B. I. V

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Refer to Figure 168

Direction of an induced EMF (Lenz's Law)

The induced EMF in a closed circuit sets up a current in the conductor which creates its own magnetic field.

The conductor's magnetic field is:

• in front of the conductor's motion strengthened

• behind the conductor's motion weakened.

Figure 168: Conductor cutting a Magnetic Field

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Refer to Figure 169

The magnetic fields of parallel conductors carrying current interact with each other to either attract or repel.

The magnetic field direction around the conductors is determined using the right hand/corkscrew rule. The result is:

i. currents with same direction attract (Figure 169, detail a)

ii. Currents with opposite direction repel (Figure 169, detail b).

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(a)

(b)

FIGURE 169: Field of Parallel Conductors

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3.11.4 Force on a Current-carrying Conductor in a magnetic Field

Refer to Figure 170

When a current-carrying conductor is placed in a magnetic field an interaction of two fields happens. The current-carrying conductor's field is:

• strengthened on one side where the lines of force are all in the same direction

• weakened on the other side where the lines of force of the two fields oppose each other.

A mechanical force moves the conductor from the strengthened field to the weakened field. Electrical energy is therefore converted into

mechanical energy.

The direction of force can be determined as follows:

• the direction of the magnetic field (north to south) has to be noted

• the current direction in the conductor has to be determined

• the right hand / corkscrew rule should be used to determine the field direction of the conductor.

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FIGURE 170: Current-carrying Conductor in a Magnetic Field

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Refer to Figure 171

Another method of determining the direction of force is the left hand motor rule.

The magnetic flux is from north to south and the lines penetrate into the inside hand and tread out at the outside hand. The fingers point into

current direction and the thumb indicates the direction of force.

The magnitude of this force is proportional to:

• the flux density of the magnetic field between the poles

• the conductor current (proportional to the current-carrying conductor's flux density)

• the length of the current-carrying conductor in the magnetic field between the poles.

This can be expressed as:

Force = Flux Density. Current. Length.

F = B. I. I Proprietary of




Figure 171: Left Hand Motor Rule

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3.11.5 Lenz's Law

A mechanical force is therefore required in order to oppose the change of flux (or 'cutting' of the magnetic field) by two interacting fields. The

direction of the opposing force or drag of the conductor's magnetic field opposes the change of flux caused by the motion.

Lenz's law summarized this:

The induced current always opposes the motion or change generating it. In an open conductor circuit an EMF is induced but there is no

opposing force or drag because no current is flowing in the conductor to create a magnetic field.

Lenz's law can therefore be used to determine the direction of an induced current. Refer to Figure 172.

The direction of current can be determined as follows:

• the direction of conductor motion has to be noted

• the field direction of conductor has to be determined

• the right hand / corkscrew rule should be used in reverse to determine induced emf and current direction.

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FIGURE 172: Application of Lenz's Law

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3.11.6 Polarity determining rules

Refer to Figure 173

The right hand generator rule is another method of determining the direction of induced EMF/ current in a conductor moving in a magnetic

field. The magnetic flux is from north to south. The lines penetrate into the inside hand and tread out at the outside hand. The direction of

conductor movement is indicated by the thumb and the fingers point into current direction.

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FIGURE 173: Right Hand Generator Rule

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3.11.7 Back EMF and Inductance

Back EMF

As the current-carrying conductor moves through the magnetic field between the two poles of a magnet (main field) it 'cuts' the main field

magnetic lines of flux. The flux in the conductor changes or there is a rate of change of flux. Therefore an EMF is induced in the current-

carrying conductor which opposes the conductor current that causes the conductor to move in the first place. This EMF is called 'back EMF' (-

EMF) because it opposes the applied voltage and reduces the effective voltage driving the current through the conductor. The applied EMF is

always greater than the -EMF.

For the -EMF is also relevant:

- EMF =B·I· V

Inductance

Inductance is the opposition to a change of current or change of flux. Moving a bar magnet past a coil induced an EMF in the coil. The

resulting current's flux interacting with the bar magnet field causes a drag which is the opposition to a change of flux. The conductor therefore

has inductance.

Any circuit which has an EMF induced into it by a change of current through that circuit possesses self-inductance (L).

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When the current is changed in the loop the strength of magnetic lines of flux are also changed. This change of flux 'cuts' the loop itself

inducing a back EMF in the loop, which opposes the change of applied voltage. When the loop's applied voltage and current increases, a back

EMF in the loop is induced; this opposes the applied voltage increase. Likewise decreasing the loop's applied voltage and current induces a

back EMF in the loop, which opposes the applied voltage decrease.

In an inductance (inductive) circuit when current increases the circuit stores energy in the magnetic field. When current decreases the circuit

gives up energy from the magnetic field. Refer to Figure 174 The energy stored in a magnetic field depends on the inductance and the coil

current.

Energy = 1/2 L I2

FIGURE 174: Magnetic Lines of Flux around a Loop

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All conductors possess self-inductance. But a conductor wound into the form of a coil has a much greater inductance because the turns 'cut'

each other. A coil is therefore called an inductor.

The inductance (L) is measured in Henrys (H)

A circuit has an inductance of one Henry when a change of one ampere in one second causes an -EMF of one volt to be induced in the circuit.

Therefore is:

Inductance (L) = - EMF (V) = - EMF

Rate of change of current (A) di

Rate of change of time (s) dt

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NOTES

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3.11.8 Saturation Point

Refer to Figure 175. With increase of current in an iron cored coil, the inductance increases relatively linearly until saturation is reached.

Increase of current after saturation, results in rapidly decreasing of inductance.

When in a non-magnetic core (air, copper or aluminium) the current increases, the core does not saturate. Inductance therefore remains

constant, independent of coil current.

Inductance is proportional to the back EMF. Back EMF is proportional to the rate of change of flux or to the number of magnetic force which

'cut' the conductor. This 'cutting' depends on the following:

i. number of turns (N) squared (more turns, more 'cutting', and more induced back EMF)

ii. cross sectional area (A) of the core (the greater ' A’ is, the more flux 'cuts' the conductor)

iii. permeability (µ) (the greater 'µ' is, the more flux 'cuts' the conductor and the greater the induced back EMF)

iv. length (I) of the core (the less flux there is).

Therefore is the inductance (L) expressed as a formula:

L = N2. A· µµµµ (in Henrys H)

l

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FIGURE 175: Inductance of Cored Coils

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Refer to Figure 176

Inductances or inductors are represented in circuit diagrams as shown in Figure 176.

FIGURE 176: Inductor Symbols

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3.11.8.1 Time Constant

Refer to Figure 177

A change of current induces a back EMF in an inductive circuit which opposes the change of current. Thus current changes are delayed in an

inductive circuit.

When the switch is moved to position B as shown in Figure 177, detail a), a high rate of change of circuit current is observed as seen at the

slope of the graph at time t = 0 (Figure 177, detail b)

A high back EMF is induced in the inductor L which opposes the rate of change of current flow. That means at the instant of closing the switch

to position B:

• the time is nearly zero (t = 0)

• the rate of change of current is maximum

• the back EMF of the inductor is maximum and nearly equal to the applied voltage.

• the I R (voltage) drop across the resistor R is minimum.

The current flow increases at a certain rate determined by inductance (L) and resistance (R). When the current has risen to 63.2 % of its final

value the current has reached its 'time constant' value (t) as shown in Figure 177, detail b).

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The time constant (t) is announced in seconds and is calculated by:

L (Henrys)

t = R (Ohms)

At the time constant value of 1‘t the current is 63.2 % of the final current. Therefore the voltage drop across resistor R is 63.2 % of the applied

voltage. The back EMF is 36.8%.

The applied voltage V (100 %) =36.8 % + 63.2 %.

At five time constants the current has reached its approximate final value.

• back EMF of inductor is minimum

• rate of change of current is minimum

• current flow is maximum

• I· R (voltage) drop across the resistor R is maximum (applied voltage).

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(a) (b)

FIGURE 177: Inductive Circuit and Current Rise Time Proprietary of




Refer to Figure 178

When the switch is moved to position A (Figure 178, detail a) the opposite sequence of events to occur is caused. At the instant of opening

the switch:

• maximum rate of change of current occurs

• the back EMF of the inductor is maximum and tries to keep the current flowing.

The current flow decreases at a certain rate determined by inductance (L) and resistance (R). When the current has decreased 63.2 % the

current has reached its time constant value of 1t (Figure 178, detail b).

At the time constant value of 1t (t = L/R) the current is 36.8 % of its maximum value. Therefore the voltage drop across resistor R is 36.8 % of

the applied voltage. The inductor back EMF is also 36.8%. At five time constants t = 5. (L/R) the current is approximately zero. All of the

energy has been discharged through the resistor.

If there is no resistor for the current to discharge as shown in Figure 178, detail a) the rate of change of current is much greater than, when

the switch is closed. A much higher back EMF, many times the applied voltage could release all the stored inductive energy in a destructive

arc across the opening switch contacts or even break down the insulation. This high back EMF is also dangerous to servicing personal.

Closing a switch induced a back EMF not higher the applied voltage, but opening a switch can induce a dangerously high back EMF many

times the value of the applied voltage.

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FIGURE 178: Inductive Circuit and Current Decay Time

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Example:

A circuit has an inductance of 8 Henrys (H) and a resistance of 400 .

a What is the time constant of the circuit?

b What total time is required for the current to reach maximum?

a t = L/R

T= 8H

400 Q

t = 0.02 seconds

b Total time = 5. t

Total time = 5.x 0.02 seconds

Total time = 0.1 seconds

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NOTES

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3.11.8. 2 Inductance in Series and Parallel

Inductances in Series

Refer to Figure 179

Inductances in series are calculated like resistors in series because the total voltage UT is:

UT = U1 + U2 + U3

The total inductance LT is therefore:

LT = L 1 + L2 + L3

Example:

L1 = 1 H, L2 = 0.5 H, L3 = 0.3 H LT=?

LT = L 1 + L2 + L3

LT = 1 H + 0.5 H + 0.3 H LT =1.8H

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Figure 179: Inductance in Series

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LU

RU

l ==

33

22

11

LU

LU

LU ++

31

21

111

LLLLt

++=

Inductances in Parallel

Refer to Figure 180

Inductances in parallel are calculated like resistors in parallel because the total current IT is:

IT = I1 + I 2 + I 3

With Ohms law is:

Therefore is;

U is common for all inductances;

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FIGURE 180: Inductance in Parallel

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31

21

111

LLLLt

++=

HHHLt 41

11

211 ++=

HHHLt 41

44

421 ++=

HLt 471 =

Example;

L1 = 2H, L2 = 1H, L3 = 4H

LT =?

Solution;

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HLT 74=

LT = 0.57H

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3.11.9 Mutual Induction

Consider two coils as shown in Figure 181. When the switch is closed the current rises therefore the magnetic field is changing,

thus changing field in coil A ‘cuts’ coil B, inducing an emf into B. When the current reaches its steady DC value, there is no changing

flux, so no emf is induced.

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FIGURE 181: Mutual Induction

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Refer Figure 182,

When the switch is opened, the current starts to fall, there is a changing flux, and therefore an emf is induced. When the current falls to zero,

there is no magnetic and no induced emf.

The effect of changing current in one coil and the resultant change of flux inducing an emf into a coil close to the first coil is called MUTUAL

INDUCTION and the two coils are said to have mutual inductance.

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FIGURE 182: Mutual induction

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3.11.9.1 The effect the rate of change of primary current and mutual inductance has on induced emf .

If two circuits possess mutual inductance (M) of M henrys and there is a rate of change of current with respect to time (di/dt), the emf induced

in either circuit is:

E = M di/dt volts

Factors affecting Mutual Inductance

(a) The number of turns on the first coil and the second coil.

(b) The physical size of the coils

(c) The permeability of the coils.

(d) The position of the coils with respect to each other.

M = K L1 L 2

Where K is the coupling coefficient (between 0 and 1)

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3.11.10 Principle Uses of Inductors

(a) Tuning - blocking out noise, unwanted frequencies and reducing hum in radio broadcasting stations and equipment.

(b) DC filtering –when used as chokes in power supplies to remove hum and other types of fluctuation from the DC output.

(c) Filters – removing radio frequency (RF) interference.

(d) Small and compact transformers with 400Hz cycle frequency for aircraft.

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3.11.10.1 Types of Inductors

Inductors are classified by the type of core and the winding.

(a) Coupled inductors

The magnetic flux of one inductor is linked to another inductor .E.g. Transformers

(b) Multi layer inductors

The coil is wound in multiple layers with insulation between each layer. This provides very high inductance.

(c) Ceramic core inductors

This type of inductor has high linearity, low hysteresis and low distortion.

(d) Molded inductors

These are low value inductors used in printed circuit board

(e) Power inductors

(f) Wide band chokes

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3.11.10.2 Types of Cores

The number of turns in the winding and the core material determines the capacity of the inductor. Cores made of dielectric material like

ceramics, wood, paper, etc. provide small amounts of stored energy while cores made of ferrite substances have a much higher resistance

and the power that can be released is very high.

Major types of cores are:

Air core: These inductors do not have any metallic core. This type of core has the maximum linearity and the smallest distortion. But for large

values of inductance, longer coils are needed and the inductor size becomes very large.

Solid Ferrite cores: These types provide the maximum resistance but they are not stable at higher values of inductance and the magnetic

saturation is quickly reached. Ferrite materials are given designations like 33, 43, J/75, etc. Grade 33 is manganese zinc and used for the 1

KHz to 1 MHz range in loop stick antenna rods. Grade 43 nickel zinc has a high quality factor and is used as medium wave inductors in wide

band transformers. Grade 77 is used in wide band transformers, power converters, EMI and acoustic filters and is used in the 0.001 to 1MHz

band.

Powdered Ferrite cores: Powdered ferrite cores have greater linearity and distortion with predictable power curves. The core density is much

greater and can be controlled by the compaction process. The ferrite material is given different grades like 0, 1, 12, 13, 15, 26, and so on.

Grade 0 can be used for frequencies up to 200 MHz and the amount of inductance varies with the winding method. Grade 1 uses Carbonyl C

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and has good resistance, grade 12 is made of synthetic oxide, has a good quality factor and moderate stability in the range of 50 to 100 MHz,

grade 26 is made of iron that is reduced by hydrogen and is used in DC chokes and EMI filters.

Steel core: Cores made of iron nickel alloys are used when the requirements call for low resistance and high inductance. They are better then

air cores. While selecting steel cores, it is necessary to note the power rating, as denser cores avoid problems of magnetic saturation. By

using thin metal sheets that are suitably insulated, eddy currents are eliminated. Very thin air gaps need to be provided in the core to remove

non-linear effects.

Toroid cores: Toroidal inductors have donut shaped cores with close packed wire winding. Very thin sheets of ferrite or steel are held closely

together. Circular cross sections are the most efficient but square or rectangular sections are also used. Common types are Ferrite Toroid

Cores and Powdered Iron Toroid Cores.

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NOTES

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS DC MOTOR/GENERATOR (DCAM 3.12 L2)


3.12 DC MOTOR / GENERATOR THEORY (EASA Ref 3.12) Level 2

3.12.1 Basic Generator Theory

When a conductor ‘cuts’ a magnetic field an emf is induced into the conductor. Figure 183 shows a single coil which can be rotated between a

magnetic field, the ends of the coil are connected to slip rings, brushes bearing on the slip rings make the connection to the external circuit

(load)

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FIGURE 183: Generator Principle

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Figure 184 shows a section of the loop as it is rotated through 360° and the output waveform generated. The emf induced at 2, 3 and 4 is

opposite to that at 6, 7 and 8 i.e. this is an alternating emf and is therefore the basis of an ac generator.

The magnitude of the emf generated depends on

B = Flux Density in Tesla

l = length of the conductors in the field in meter

v = Velocity (speed) of the conductors in m/sec

E = Blv Volts

FIGURE 184: Production of a Sine Wave

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The direction of the induced emf can be found using Fleming’s Right Hand Rule. Figure 185 shows the thumb and first two fingers of the right

hand held mutually at right angles to each other.

First Finger - direction of magnetic field (N to S)

Second Finger - direction of current (conventional)

Thumb - direction of conductor movement

FIGURE 185: Fleming’s Right Hand Rule

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3.12.1.1 Basic DC Generator

Refer Figure 186

FIGURE 186: A Simple DC Generator

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3.12.1.2 Principle of DC Generator

Figure 187 (a) shows the two segments of the commutator approaching the point of maximum induced emf with the current flowing in the

load. Figure 187 (b) shows the segments approaching the point of zero emf and approaching the brushes at the point of change over from

one commentator segment to the next. Figure 187 (c) shows the changeover has occurred and the lower brush is now in contact with

segment 1 not to segment 2 as it was prior to changeover.

Conductor 1 (connected to segment 1) is now cutting the field in the opposite direction, so its emf is reversed to be the same as previously

induced in conductor 2. The current through the load remains the same in the same direction. The commutator ensures that whichever

conductor is passing the N pole is always connected to the negative end of the load and the conductor passing the S pole is connected to the

positive end of the load.

FIGURE 187: Principle of DC Generator

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Figure 188 shows the action of the commutator, note the changeover of the brush contact from one segment to another occurs at the induced

emf is zero i.e. at (a) and (c). Rotation is from ( a ) to ( b ) to ( c ) to ( d ) to ( a ) etc.

FIGURE 188: Action of the Commutator

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Figure 189 shows a graph of the output from a simple DC generator

FIGURE 189: Graph of Voltage and Current for a two segment DC Generator

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Figure 190 shows the effect of rotating many coils in a magnetic field

FIGURE 190: Multi segment DC Generator

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3.12.2 Construction and Components in a DC Generator

Generators used on aircraft may differ somewhat in design since they are made by various manufacturers. All however are of the same

general construction and operate similarly. The major parts or assemblies of a DC Generator are a field frame (yoke), a rotating armature, and

a brush assembly. The parts of a typical aircraft generator are shown in Figure 191

Figure 191: A typical aircraft Generator

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Field Frame

The field frame is also called yoke, which is the foundation or frame for the generator. The frame has two functions: it completes the magnetic

circuit between the poles and acts as a mechanical support for the other part of the generator.

In small generators, the frame is made of one piece of iron, but in large generators, it is usually made up of two parts bolted together. The

frame has high magnetic properties and, together with the pole pieces, forms the major part of the magnetic circuit.

FIGURE 192: A four-pole frame

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Armature

The rotating part of the generator consists of a shaft, iron core, the output windings (rotating loops or coils) and the commutator. The iron core

provides a low reluctance path between the field pole pieces, giving increased flux density, ensuring that the largest emf possible is induced in

the output windings. The core is laminated to reduce electromagnetic eddy currents. The output windings are wound in longitudinal slots in the

iron core, where they are wedged with insulating material to prevent them being thrown out due to centrifugal force.

The output voltage and maximum current that may be taken from a generator will depend to some extent on the method in which the coils of

the armature are connected to one another. There are two types in use, lap and wave windings. In a wave wound generator there are two

paths in parallel irrespective of the number of poles, each supplying half the total current output. Therefore only two brushes are required to

pick off the output. Wave wound generators produce a high voltage, low current output. While lap wound generators produce a low voltage

but high current output. Refer Figure 192

FIGURE 192: The Armature

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Commutator

This is located at the non-drive end of the armature. It consists of a number of copper segments mounted on, but insulated from, the shaft.

They are insulated from one another by strips of mica, which are usually 'undercut' to make their top surface slightly below the level of the

commutator segments.

Bushes and Brush Holders

The brush must be made of a material which has a low contact resistance, low specific resistance, low coefficient of friction and good

lubricating properties - graphite carbon has these properties. Some machines may have carbon brushes into which a lubricating ingredient

(molybdenum disulphide) has been added usually in the form of inserts (pegs) in the brushes. Other machines may have chemicals such as

barium fluoride added to form a film (darkish brown) on the commutator to provide the lubrication between the brush and commutator.

The brush holders are in effect metal boxes into which the brush is a good sliding fit, the necessary pressure being applied on the top of the

brush by a spring to maintain good contact between brush and commutator. Each brush holder is secured to a support ring sometimes called

a brush rocker; this allows limited angular movement of the brush-gear – allowing best contact with the commutator. Electrical connection to

the brush holder is via a "pigtail" usually of flexible copper braid moulded into the brush at manufacture, the brush holder then connects to the

main terminals of the generator.

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Field System

Except for very small machines the magnetic field is supplied by electromagnets arranged in such a way that the conductors pass under

North and south poles alternately; the number of poles is therefore always an even number. The intense magnetic field through which the

conductors pass is achieved by winding the magnet coils on cores of high permeability material ensuring the magnetic circuit has a low

reluctance.

The YOKE is the cylindrical frame of the machine and is an essential part of the magnetic circuit and must combine low reluctance with

structural strength. It is normally of cast or rolled steel.

The POLE PIECES form the cores of magnet coils and are bolted to the inside of the yoke. The pole pieces are laminated. The varying

magnetic field caused by movement of the rotor induces emfs into the pole faces which produce eddy currents lamination reduces eddy

currents and therefore local heating is minimized by laminating the pole pieces or in some cases just the pole tips.

The FIELD WINDINGS are pre-formed coils mounted on the pole pieces and, when current passes through, the polarity of the main poles is

alternately north and south.

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Bearings

The rotating armature is supported in ball or roller bearings. Normally a ball bearing is fitted at the drive end with a roller at the 'tail' end, this

permits longitudinal expansion of the shaft. Bearings are lubricated with high melting point grease or lubricating oil.

The ability to dissipate heat is one of the most important factors which limit the output of a generator. Heat is developed in the steel or iron of

the magnetic system due to flux changes and at the commutator and brush gear due to current flow. Cooling air is provided which may be ram

air from the air-flow via ducting to the generator or by an integral fan or a combination of both.

The generator drive system must have some method of disconnecting the generator in the event of seizure of the generator armature, so

between the generator and the gearbox will be a quill drive or wasted drive section This drive shaft has a smaller diameter section between

the spline drives which will act as a weak spot and shear should excessive torque be applied, e.g. if the generator armature seizes.

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NOTES

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3.12.2.1 Commutation

We are going to look at the effect of commutation in coil (1) in Figure 194. Prior to commutation the coil carries half the total armature current

in one direction (diagram a).

At the point of commutation, i.e. brush shorting the coil, the current collapses, this collapsing current produces a changing field which cuts the

coil and induces an emf (diagram b). As the coil leaves this shorted condition, (coil cutting flux in the other direction), the current should build

up to half total armature current in the reverse direction.

However this build up is opposed by the self induced emf (REACTANCE VOLTAGE) in the coil and current cannot build up fully so some of it

will go up to segment B and jump across the segment to the brush (diagram c).

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FIGURE 194: Commutation

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This REACTIVE SPARKING occurs at each point of commutation for every coil. This will cause brush wear, commutator wear and

considerable interference to the radio systems. One method of overcoming this problem is to use INTERPOLES (.Figure 195) Interpoles are

small poles located midway between the main poles, the interpole windings are connected in series with the armature and the interpole has

the same polarity as the next main pole ahead in the direction of rotation.

The poles are at the point of commutation and carry exactly the same current as the armature windings. As the armature coils approach the

point of commutation they come under the influence of the interpole which, attempts to induce an emf into them which is in opposition to the

emf already across the coil. The two opposite fluxes cancel, leaving no flux to collapse and no reactance voltage and therefore no reactive

sparking.

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FIGURE 195: Interpoles

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3.12.2.2 Armature Reaction

The main field of a DC generator is between the pole pieces as shown in Figure 196 (a). When the generator is supplying load, a magnetic

field is created by current flowing in the armature windings (b). The interaction of these two fields causes a resultant field which is distorted

and weakened to an extent dependent on the load (c). This interaction and resultant distortion of the main field is called ARMATURE

REACTION.

A line drawn vertically at a point midway between the poles is termed the Geometric Neutral Axis (GNA). A line joining the two points at which

no emf is induced in a coil is known as the Magnetic Neutral Axis (MNA).Ideally the MNA should be on the GNA.

As shown, armature reaction has caused the MNA to move in front of the GNA, and as the load varies so would the MNA, so brush position

would have to be continually adjusted, or if left as it was considerable arcing would take place. Another problem with armature reaction, as

shown in (c), is that the flux density at pole tip A is increased and that at pole tips B is reduced. As most machines have a magnetic circuit

working near saturation the overall effect is to reduce the magnetic field strength and a reduction in generated emf.

To overcome this problem COMPENSATING WINDINGS are used. These are windings let into slots in the pole faces lying parallel with the

armature windings. Refer Figure 196

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If the current is made to flow through the compensating windings in the opposite direction, and of the same value as the armature windings

then the two magnetic fields will neutralize each other and armature reaction will not exist. As the armature reaction is dependent on the value

of the load current then the compensating windings must vary with load current and are therefore in series with the armature.

To obtain true correction of armature reaction the interpoles may be wound with an extra number of turns to effectively eliminate the armature

reaction in the interpole region. So the GNA and MNA coincide at all times. When the generator is a wide speed range (2850rpm to l0,000rpm)

generator, the effects due to armature reaction and reactive sparking become more of a problem.

FIGURE 196: Compensating Winding

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3.12.3 Types of DC Generators

Generally, there are 3 types of DC generators known:

1. Series-wound DC generators

2. shunt-wound DC generators

3. shunt-series (or: compound) DC generators.

The various types mainly differ in the relationship of the field winding to the external circuit.

3.12.3.1 Series –wound DC Generator

The field winding of a series-wound generator is connected in series to the external circuit (called: the load). The field coils are composed of a

few turns of large wire. The strength of the magnetic field depends more on the current flow rather than on the number of turns in the coil.

Series-wound generators have very poor voltage-regulation capabilities under changing load, since the greater the current through the field

coils to the external circuit, the greater will be the induced electromotive force and the greater the terminal (or: output) voltage. Therefore,

when the load increases, the voltage increases as well; likewise, when the load decreases, the voltage decreases. Refer Figure 198

The output voltage of a series-wound generator may be controlled by a rheostat in parallel with the field windings, as shown in Figure 197,

detail a). Due to the poor regulation capabilities series-wound generators are not installed in aircraft

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FIGURE 197: Series-wound Generator, Schematic Diagram

FIGURE 198: Graph of Voltage against Load Current for Series wound DC Generator

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3.12.3.2 Shunt-wound DC Generator

A generator having a field winding connected in parallel to the external circuit is called a 'shunt-wound generator'. The field coils of such a

generator contain many turns of small wire. The magnetic strength is derived from the large number of turns rather than from the current

strength through the coils. When the armature is rotated, the conductors cut the weak magnetic flux due to the residual magnetism in the pole

pieces. This small emf induced in the armature windings will supply the field windings, increasing the flux and therefore the induced emf,

which again is fed to the field winding increasing the flux and generated emf further. Refer to Figure 199

This continues until a steady open circuit value is reached. When the load is applied the terminal voltage tends to fall due to IR drop in the

armature winding, this reduces field excitation and causes a further fall in terminal voltage. This reduction in voltage will be small over the

working range of the generator, but as the volts/ load characteristic shows it becomes greater the heavier the load demand. An important point

to note is that if the load is increased above the full load condition then, the voltage drops to zero. The falling voltage has to supply current to

the field (HIGH RESISTANCE) and load (LOW RESISTANCE). As more current is diverted to the load, the field strength falls, voltage falls and

the collapsing voltage can no longer sustain the load current and the voltage falls to zero.

This feature on the volts / load characteristic is known as ‘tuck under ‘or ‘turn under ‘Refer Figure 200. Shunt wound generator should be

allowed to build up to their correct voltage before the load is applied otherwise ‘turn under ‘ will occur and the generator will fail to excite.

This type of generator is the one most used on aircraft with DC as its main power source. The slight drop in generator voltage on load is

overcome with the use of a voltage regulator.

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FIGURE 199: Shunt-wound Generator, Schematic Diagram

FIGURE 200: Graph of Voltage against Load Current in a Shunt-wound DC Generator

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3.12.3.3 Compound wound Generator

A compound-wound (or: shunt-series) generator combines a series winding and a shunt winding in such a way that in the result the

advantages of both are added. The series-field coils are made of a relatively small number of turns of large copper conductor, either circular or

rectangular in cross-section. They are connected in series with the armature circuit. These coils are mounted to the same poles on which the

shunt-field coils are mounted. Therefore they produce a magneto-motive force which influences the main field flux of the generator. Refer

Figure 201

If the ampere-turns of the series field act into the same direction as those of the shunt field, the combined magnet motive force is equal to the

sum of the series and the shunt-field components. Load is added to a compound generator in the same way as to a shunt generator, i.e., by

increasing the number of parallel paths across the generator terminals. Thus, the decrease in total-load resistance with added load is

accompanied by an increase in armature-circuit and series-field circuit current.

The effect of the additive series field is that the field flux increases with increasing load. The extent of the increased field flux depends on the

degree of saturation of the field as determined by the shunt-field current. Thus, the terminal voltage of the generator may increase or decrease

with load, depending on the influence of the series-field coils. This influence is called 'degree of compounding'. Changes in terminal voltage

with increasing load depend upon the degree of compounding.

In a so-called flat-compound generator the 'no-load' and 'full-load' voltages are of the same value. In an under-compound generator the 'full-

load' voltage is less than the 'no-load' value. In an over-compound generator the 'full-load' voltage is higher than the 'no-load' value.

If the series field supplements the shunt field, the generator is said to be cumulative compounded (shown in Figure 201, detail b).

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If the series field opposes the shunt field, the generator is said to be 'differentially compounded' or may be called a 'differential generator'.

Compound-wound generators are usually designed to be over-compounded, i.e. varying degrees of compounding are possible by connecting

a variable shunt across the series field. Such a shunt is sometimes called a 'diverter'.

Compound-wound generators are used where voltage regulation is of primary importance.

FIGURE 201: Compound-wound Generator, Schematic Diagram

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3.12.3.4 Generator Ratings and Terms

Power Output

Generators are rated in power output. Since a generator is designed to operate at a specified voltage, the rating is usually given as the

number of amperes the generator can safely supply at its rated voltage. Generator rating and performance data are stamped on the name

plate attached to the generator. When replacing a generator, it is important to install a new one with the correct rating.

Direction of Rotation

The rotation of generators is termed 'clockwise' or 'counter clockwise', as seen from the driven end. Usually, the direction of rotation is

stamped on the data plate. If no direction is stamped on the plate the rotation may be marked by an arrow on the cover plate of the brush

housing. It is important to always install a generator with the correct direction of rotation; otherwise the polarity will be reversed.

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Speed of Rotation

The speed of an aircraft's engine varies from idle revolutions per minute (rpm) to take-off rpm. However, during the major portion of a flight, it

turns at a constant speed. The generator drive is usually geared to revolve the generator at a speed between 1.125 and 1.5 times of the

engine's crankshaft speed. Most aircraft generators begin to produce their normal voltage at approx. 1,500 rpm. This speed is called the

'coming-in' speed.

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Generator Terminals

On most large 24-V generators, the electrical connections to terminals are marked B, A and E. The positive armature lead in the generator

connects to the B terminal. The negative armature lead connects to the E terminal. The positive end of the shunt-field winding connects to

terminal A, and the opposite end connects to the negative terminal brush.

Terminal A receives current from the negative generator brush through the shunt-field winding. This current passes through the voltage

regulator and back to the armature through the positive brush. Load current leaving the armature through the negative brush and via the E

lead passes through the load before returning through the positive brush.

Refer to Figure 202

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FIGURE 202: Regulation of Generator Voltage by Field Rheostat

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3.12.4 Basic Motor Theory

A current carrying conductor has a magnetic field surrounding it. With the conventional current flowing away from the reader the field will be

clockwise- this is known as the corkscrew rule, Figure 203. With the current flowing towards the reader the field will be anticlockwise

When considering the magnetic field between the two poles pieces of a bar magnet with opposite polarity the field moves from north to south

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FIGURE 203: Magnetic Field around a Conductor

FIGURE 204: Magnetic Fields between two opposite Poles of a Magnet

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Refer Figure 205

When the current carrying conductor is placed within the magnetic field, the two fields cannot exist independently (conductor and poles)

Above the conductor, flux lines move in the same direction to cause a strong field above the conductor, the fields oppose each other below the

conductor and therefore are weak.

Magnetic lines of flux above the conductor are in tension and try to straighten, they also repel each other sideways so a force is created

forcing the conductor out of the magnetic field – in this case down. This is the principle of an electric motor

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FIGURE 205: Current carrying conductor in a Magnetic Field

The force on the conductor, F = B l I Newton’s

Where B = Flux Density in Tesla

l = length of conductor in Meters

I = current flowing in the conductor in Amperes

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3.12.4.1 Fleming’s Left Hand Rule

Refer Figure 206

Using the rule, it is possible to determine the direction of the current, force or field knowing any two of them.

The thumb, first finger and second of the left hand are placed mutually at right angles.

First finger - the Field direction (N to S)

Second finger - the Current direction

Thumb - the direction of Motion as a result of a force

.

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FIGURE 206: Fleming's Left Hand Rule

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3.12.4.2 Action of a Basic Electric Motor

Consider a coil connected via a commutator and brushes to a battery as shown in figure 207. Using Fleming's Left Hand Rule side A tends to

move upwards and side B downwards, giving a clockwise rotation of the loop.

FIGURE 207: A Simple DC Motor

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3.12.5 A Practical DC Motor

The construction of a dc motor is identical to that of a dc generator. However,the motor converts the electrical input into mechanical energy.

When a current flows through the large number of conductors on the armature, their fields interact with the main field system to give a turning

motion, with the commutator switching the supply at the point of commutation.

3.12.5.1 Back emf

As the armature conductors of a motor rotate in a magnetic field, they are therefore cutting this field and by Faraday's Law an emf will be

induced. By Lenz's Law this induced emf opposes the applied voltage and is called a BACK EMF. We have back emf (Es) pushing one way

and applied voltage (V) the other way, so it is the difference between these two which actually drives current through the armature circuit and

this difference may be known as the EFFECTIVE VOLTAGE or ARMATURE VOLTAGE.

For example, if the applied voltage is 28 volts dc and the back emf is 26 volts then the effective voltage is 2 volts.

EFFECTIVE VOLTS = APPLIED VOLTAGE - BACK EMF

IA RA = V – EB

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Assuming a 28 volt motor has a one ohm armature resistance then the initial current flow is:

V 28

IA = - = 1 = 28 A

R

When the motor is running the back emf is 26V, so the voltage that is available to drive current through the armature circuit is 2 volts.

IA = 2/1 = 2A

It is important you realise how back emf controls the current in a dc motor, and when the motor is running the back emf is very close to the

value of the applied voltage. On some earlier aircraft electrical starting systems, a resistance was introduced in series with the armature on

start, as the initial current would be too high (no back emf), but as the motor gathered speed the resistance was cut out, because the back emf

limited the current.

On most motors the starting current is not excessive and temporary in line resistances are not required.

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3.12.5.2 Torque

It can be shown that the force on each armature conductor and therefore the total ARMATURE TORQUE is directly proportional to the

magnetic field strength and armature current.

T x I a (N-m)

The whole of the armature torque is not available for doing useful work. Friction in the bearings, wind resistance of the armature or fan (if

fitted) causes some lost torque. So the output torque of a motor is:

OUTPUT TORQUE (SHAFT TORQUE) = ARMATURE TORQUE - LOST TORQUE

The torque loss will vary with speed.

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3.12.5.3 Power

The output power of a motor has two variables in its formula, torque and speed. P T x N. Therefore for a given power any increase in speed

can only be attained at the expense of torque and vice versa. A motor developing a given horsepower thus has alternative values of speed

and torque (ie it has a strong torque at low speed or low torque at high speed). If it is necessary to maintain the same speed with increased

torque, then the motor must develop increased power.

When a motor is run on no-load it speeds up until its torque balances the opposing torque of windage and friction and its speed will be a

maximum.When a mechanical load is placed on the drive shaft the motor will slow down until once again its torque balances the load torque.

3.12.5.4 Reactive Sparking and Armature Reaction

Armature reaction takes place in a motor for the same reasons as in a generator ie the main field is distorted by the armature field. However,

with reference to figure 208, note that the MNA moves backwards against the direction of fotation. Since back emf reduces armature current

to a fairly small figure, armature reaction is usually fairly small and many dc motors do not have any means of counteracting it.

In some motors, where a high standard of commutation is required compensating windings are fitted. As we saw with generators, interpoles

may be used to help control armature reaction, generally only large motors (high armature current) would be equipped with interpoles.

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Reactive sparking also occurs in motors. Collapse of current flowing into the coil at commutation, induces an emf trying to keep it

in the original direction and opposing build up in the reverse direction. Again back emf will keep the reactance emf down so some

motors will not be fitted with interpoles, however on larger motors interpoles would be fitted to provide correction for reactive

sparking. The polarity being the opposite to the next main pole ahead in the direction of rotation.

FIGURE 208: Armature Reaction in a DC Motor

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3.12.5.5 Speed control of a DC motor

The effect of the back emf is to make the dc motor a self regulating machine in which the speed and the armature current adjust themselves to

changing load condition.

Speed control may be obtained by controlling field current or armature current, i.e. by inserting variable resistors in the field or armature

circuits. Figure 209

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FIGURE 209: Speed Control of a Shunt wound DC Motor

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3.12.5.6 Reversal of Rotation of a DC Motor

To reverse the direction of a motor the direction of current through the armature OR through the field must be reversed. If the current through

Armature and field are both reversed the motor continues in the same direction.

To reverse the direction of rotation in a compound motor the same principle applies, that is to reverse the direction of current through the

armature OR both fields. On aircraft it is normal to reverse the direction of current through the armature by means of reversing relays.

An alternative method used to reverse the direction of a motor is to use two fields both wound on the same pole pieces but with one giving

opposite polarity to the other. Direction of rotation being determined by which field is selected.

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3.12.6 Types of DC Motors

Like generators, motors are classified according to the way the field system is connected to the armature, i.e.

Series

Shunt

Compound

For motors we use two characteristics to show the properties of the machine, the speed/ load characteristic and the torque/load characteristic.

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3.12.6.1 Series Motor

Previously we said that torque x Ia

In a series motor as the field () is connected in series with the armature then the Ia, as armature current is field current. So the TORQUE

Ia X Ia = 1a2

As can be seen from the characteristics graph the motor has a wide speed range, large starting torque, and high torque at low speed - ideal

characteristics for starting an aircraft engine.

The motor must be connected to a load permanently as the off-load speed will be dangerously high. As the field and armature turns are

different when speed increases, back emf rises and opposes armature current. This causes the field to be weakened which reduces the back

emf disproportionately and it cannot build up sufficiently to control the rise in speed, therefore speed increases and the sequence continues

causing excessive speed of the armature.

It should be noted on engine starter motors a small shunt winding is incorporated to limit this off load speed as the starter is disconnected from

the engine. Small series motors are used in dc actuators on aircraft which, of course, are permanently on-load. Proprietary of




FIGURE 210: Series Motor Characteristics Proprietary of




3.12.6.2 Shunt Motor

The field winding of a shunt motor is connected in parallel with the armature and is of fairly high resistance. This connection, as can be seen

by the characteristics shown in figure 211, produces different properties. The speed characteristic shows that from no-load to full-load the

speed reduction is very small and it can be considered to be a constant speed machine.

It is a self regulating machine in that when a new load is placed on the motor, the motor automatically adjusts its own effective voltage. The

following shows what happens when the load is increased:

• motor initially slows down

• the back emf falls

• armature or 'effective' voltage increases

• VSUPPLY - Vb emf

• armature current increases

• T x IA

• torque increases to match the new load torque and increase the speed to its original value

As the field is directly across the supply the field strength is practically constant. This means that the torque of a shunt motor is proportional to

armature current until approaching full load condition. The starting torque is small, due to slow build up of the field strength and the restricted

armature current.

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Shunt motors should therefore be started on light load or under no-load conditions. These motors would be used on applications that require

constant speed, e.g. early 28v dc aircraft, inverter drives, windscreen wipers and fuel pumps.

FIGURE 211: Shunt Motor Characteristics

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3.12.6.3 Compound Wound Motor

This motor has two windings wound on the pole pieces and the characteristics depend on whether the shunt or series predominates and

whether they are wound to assist one another (cumulative) or to oppose one another (differential).

Cumulative Compound Motor

The most common application of the compound motor on aircraft is the cumulative compound machine with a predominant shunt field winding.

The series winding enables a fairly high starting torque to be developed, allowing the motor to be started on reasonable load. The

characteristic graph shows that the motor speed drops on load, this is due to the series field increasing with increasing armature current.

This is an ideal characteristic for a motor supplying a load where the load torque is· proportional to speed, since the motor is virtually a

constant torque machine

.

This form of cumulative compound motor may be called a normal compound motor, and would be used on dc systems for inverter drives, and

dc aircraft for fuel pumps as well as heavy duty actuators. Another form of cumulative compound motor is the 'shunt limited' type. This has all

the characteristics of the series motor and therefore the main winding of the series motor with a minor shunt field connected across the

armature.

When used to start aircraft engines, high torque at low speed is required, but when the motor is disconnected from the engine, i.e. on no load,

a pure series motor would race away. The minor shunt winding limits this 'off load' speed while leaving the torque / speed characteristics

essentially that of a series motor.

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NOTES

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Differential Compound Motor

This is where the shunt and series field windings are wound to oppose one another. These tend to be mainly shunt wound machines with a

minor series winding, which gives a speed/load characteristic which is fairly constant but increases speed as the load becomes too great. The

torque on light loads is similar to a shunt motor as the characteristic graph shows, but if overloaded the series winding field strength will at

some point cancel the shunt winding.

There will be no torque the motor will stop even though taking excessive current. So it is important this motor is not overloaded. It also has a

problem on starting. The series field (low inductance) builds up before the shunt field and the motor starts in the reverse direction, this is

usually avoided by short circuiting the series winding on start.

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FIGURE 212: Compound Motor Characteristics

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3.12.7 Starter Generator

These are used on aircraft and offer a considerable weight saving over the system which has a starter motor and a generator. For starting

purposes the starter generator is supplied a dc current Once the engine has started the motor becomes a generator and supplies current the

other way to operate systems and charge batteries etc.

Typically it is a self excited compound wound machine which has compensating windings and interpole windings with an integral cooling fan

on the drive shaft. It is also cooled by ram air when the aircraft is airborne.

Located on the stator is a speed sensor, used to signal starter cut-off. It generally starts as a compound motor and then the shunt field is

weakened to allow it to become more of a series motor and therefore give the necessary torque and acceleration to the engine. Nearing self

sustaining speed the shunt field is brought fully back in.

At changeover the starter drive is disconnected and the driven machine now becomes a generator self exciting its own shunt field and when

the voltage is sufficient it will be connected to the bus-bar.

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FIGURE 213: Starter Generator Circuit

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS AC THEORY (DCAM 3.13 L1)


13 AC THEORY

3.13.1 Fundamentals

An electric current has been seen to be the drift of electric charge around a circuit in one direction. Such as current is called a ’direct current’,

such circuits are called ’direct current circuits’, or ’DC circuits’. There is however, widespread use of circuits in which the electric current is not

unidirectional, but is continually reversing. In these circuits in which the electric charge starts to move in one direction, then stops and restarts

to move in the opposite direction, only to stop and reverse.

Since the current flows in alternate directions, it is known as an ’alternating current’, and such currents are called ’alternating current circuits’

or simply ’AC circuits’.

3.13.2 AC Generation

Figure 214 shows the physical arrangement of a loop arranged to rotate in a magnetic field. The connections to the end of the loop, or coil,

have been made by sliding contacts known as ’slip rings’, so that any one terminal is always connected to the same side of the loop.

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FIGURE 214: Loop in a Magnetic Field

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Figure 215 shows a part of the loop at the instant when it has turned through an angle (Theta) from the reference point shown, midway

between the magnetic poles. The instantaneous velocity (V) of the loop, which will be tangential to the circle described by the rotating loop,

may be considered to have two components at right angles.

From the geometry it follows that the component of this velocity at right angles to the direction of the magnetic field is V x sin , while the

component of velocity parallel to the magnetic field is V x cos . The speed with which the loop cuts across the magnetic field will be V x sin

and this speed will determine the EMF induced in the loop at the instant considered.

The component of velocity V x cos , parallel to the magnetic field does not contribute to the ’cutting’ of any lines of magnetic flux.

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FIGURE 215: EMF Generation

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3.13.3 Waveform and Instantaneous Value

The loop as shown in Figure 216 is rotating at a constant speed, therefore its tangential velocity is always the same. It is the component of

this velocity which cuts across the magnetic field that determines the rate at which the loop cuts the magnetic flux and so determines the value

of induced EMF. It is this component of the loop velocity across the magnetic field that varies from instant to instant.

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FIGURE 216: Flux Cut by a Loop in a Magnetic Field

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The magnetic field between the poles is represented by a number of equal spaced parallel lines of force, and the loop is in various positions

as it moves round. Since the loop is assumed to be moving at a constant speed, and each point, shown numbered, represents 150

movements from the next point. The time taken for the loop to move from one point to the next will be the same in each case. The number of

lines of force ’cut’ by the loop in moving one point to the next, which represents the flux cut by the loop in the time taken, will then represent

the rate of cutting of flux; that is, the average EMF induced during this time.

As the loop moves from:

1 to 2, it cuts 0 lines,







8 to 9, it cuts 35 lines.

The time interval for each movement is the same and the flux cut during each movement in this time increases up to a maximum as the

average position of the loop reaches a point under the pole (7 to 8, 37 lines). The values of flux cut in equal times, are proportional to the

EMF induced in the loop.

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This can be plotted against average loop position in degrees. The instantaneous EMF (u) induced in the loop, i.e. the EMF at any point in the

360o rotation of the loop is given by the formula:

u = EMFmax x sin

When the loop has been round one revolution from any instantaneous position considered, it will be back again in the same position relative to

the magnetic field. It will have the same instantaneous velocity across the magnetic field, and so it will have induced in it at that instant, the

same EMF as when it was there before. This type of wave variation is known as SINUSOIDAL, so that the EMF induced in the loop is named

’sinusoidal’ alternating EMF. Refer Figure 217

FIGURE 217: Lines Cut against Loop Position

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Figure 218 shows the instantaneous loop EMF against values of the angle , for three complete revolutions of the loop.

In this diagram the scale for the angular position of the loop, as measured by the angle , goes beyond 360o. Each complete 360o represents

one complete revolution, so that 1.25 revolutions from zero is represented by an angle of 1.25 x 360o = 450o.

Alternating wave--forms other than sinusoidal wave-forms may be encountered in practice. However the sinusoidal wave-form has many

advantages over all other kinds for supply purposes, and a great deal of effort is made in electric supply systems to ensure a pure sinusoidal

wave-form for alternating voltages and currents.

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FIGURE 218: EMF against Loop Position Proprietary of




3.13.4 Sine Wave Characteristics

3.13.4.1 Peak Value

Figure 219 shows peak values that occur during an AC sine wave. Two peaks occur during one complete revolution of 3600. One peak occurs

during the positive part of the wave when its maximum height is reached.

This point represents the maximum positive value that occurs during the AC sine wave. A second peak value occurs during the negative part

of the wave, when the maximum height below the zero line is reached. This point is known as the negative peak value.

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FIGURE 219: Peak Value of a Sinusoidal Wave

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3.13.4.2 Peak--to--Peak Value

Figure 220 shows the peak--to--peak value of a sinusoidal wave. This value is measured between the point of maximum positive swing and

the point of maximum negative swing. The peak--to--peak value is therefore twice the peak value.

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FIGURE 220: Peak to Peak Value of a Sinusoidal Wave

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3.13.4.3 Root Mean Square Value

When a direct current flows through a resistor, a certain amount of power is dissipated by the resistor in a form of heat. A certain amount of

heat is also generated if an alternating current is allowed to flow through the same resistor. However, the heat generated by a DC of one

ampere will generate more heat than an AC current with a peak value of one ampere. The alternating current generates less heat because it

reaches its peak value of one ampere only once during each half wave.

The average value must, therefore, be lower than one ampere. Therefore an AC current with a higher peak value must be used to generate an

equivalent amount of heat. An alternating current that will generate the same amount of heat (in a specific resistor) as a direct current that has

a value of one ampere is considered to have an effective or rms value of one ampere.

The rate of dissipation of energy as heat in a resistor depends upon the SQUARE of the current or voltage:

P = I2 x R or P = U2

R.

Figure 221, (detail a) shows that the square of the sinusoidal current (I2) plotted against the time, generates a curve which is always above

the time axis (+ I2 = + I2; − I2 = +I2) and symmetrical about the halfway line. The energy dissipated over any time interval is proportional to the

shaded area beneath the curve. If the peaks of the I2 graph are imagined as being cut off half way up, they will fit exactly in the troughs as

shown in Figure 221, (detail b). This indicates that the height of the equivalent rectangle is exactly 50 A2 and the equivalent current can be

stated more accurately as 7.07 A (I2 = 50 A2, I = 50 A2 ,, I = 7.07 A). This heating effect of an alternating current is very important in AC theory

and is the value usually indicated by meters.

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FIGURE 221: Root Mean Square Value (rms)

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For example, when the statement is made that the alternating voltage available at the consumers supply terminals is 220 V, it is the effective

or rms value that is given.

Therefore the peak value is:

Peak value = rms value x 2

The factor 2 is to be seen as a given value.

Peak value = 220 V x 2

Peak value = 220 V x 1.414

Peak value = 311 V

That is, the heating effect resulting from applying this peak voltage across a resistance would be the same as that resulting from an

application of a steady DC voltage of 220 V, for the same length of time.

Since the effective value is less than the peak value for a sinusoidal wave-form, a 220 V sinusoidal supply will have instantaneous values

greater than 220 V for some parts of the cycle, and will have a peak value just over 311 V. Since it is calculated by finding the square root of

the average value of I2 or U2, the effective value is known as the root mean square or rms value.

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NOTES

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3.13.4.4 Period and Cycle

When a sinusoidal wave-form is analysed it is often necessary to know how much time is required to generate one complete cycle of the

wave-form.

Refer to Figure 222

The period is normally measured in seconds. Furthermore the period is often represented by the letter ’T’. If a generator generates one cycle

of output voltage in one second, the output sine wave has a period (T) of one second. If four cycles are generated in one second, the output

sine wave will have a period of one quarter of a second (T = 0.25 seconds).

The period is the time for one cycle, not the total time required to generate any given number of cycles.

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FIGURE 222: Period of a Sinusoidal Wave

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3.13.4.5 Frequency

Refer to Figure 223

Often it is necessary to know how rapidly an AC wave is changed its value. It is important to know how many cycles of the wave occur in a

given period of time. The number of cycles that occur in a specified period of time is the ’Frequency’ (f) of the wave.

Each time the armature (loop) of a simple generator completes one revolution, one cycle is generated. Therefore the frequency of an AC wave

is determined by the speed at which the armature rotates. As the speed of rotation increases, more cycles are generated in a given period of

time, thus causing the frequency to increase. The frequency (f) of a sinusoidal (sine) wave is expressed in terms of the number of cycles

generated per second.

For example, an armature (loop) that rotates one complete revolution each second generates one cycle of ac output voltage each second. The

AC voltage would therefore have a frequency (f) of one cycle per second. Although the frequency is the number of cycles generated each

second, it is expressed in HERTZ (abbreviated Hz).

A generator which generates an AC voltage that completes one cycle per second operates at a frequency (f) of one Hz. The term Hertz is the

unit for frequency. If the AC generator generates 30 cycles of AC output voltage each second, it operates at a frequency of 30 Hz. Likewise,

an output of 60 cycles per second would be expressed as 60 Hz.

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FIGURE 223: Frequency of a Sinusoidal Wave

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Refer to Figure 224

There is a definite relationship between the frequency and the period of a sine wave. When the period of a sine wave is equal to one second,

the frequency will be equal one Hz. If the period decreases to 0.5 seconds, or one half of its original value, the frequency would double, or

increase to 2 Hz. This is because exactly twice as many cycles would occur each second. Similarly if the period were doubled, the frequency

would be cut in half.

The relationship between frequency (f) and period (T) is therefore:

f = 1 / T

This equation states that the frequency (f) is equal to one divided by the period (T).

Furthermore, if the period is expressed in seconds, the frequency obtained will be in Hz. For example, when the period of a sine wave is equal

to 0.05 seconds, the frequency of the wave will be equal to:

f = 1 / T

f = 1 / 0.05 s

f = 20 Hz.

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A period of 0.05 seconds therefore corresponds to a frequency of 20 Hz. If the period was cut in half or reduced to 0.025 seconds, the

frequency would be:

f = 1 / T

f = 1 / 0.025 s

f = 40 Hz.

The result is that the frequency increases to 40 Hz, or double. The equation shows that f and T are inversely proportional. When one

increases the other decreases by a proportional amount and vice versa.

The equation f = 1 / T can also be transposed so that T can be determined when f is known:

T = 1 / f

For example, when f is 100 Hz, T can be determined as follows:

T = 1 / f

T = 1 / 100 Hz

T = 0.01 seconds.

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Frequencies that range from a few Hz to many millions of Hz are widely used in electronics. For example, the 220 V AC electric power that is

in common use has a frequency of 50 Hz. This 50 Hz voltage is used to operate lights and appliances.

In many electrical applications, the frequencies involved are much higher. These high frequencies are required to carry information or data.

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FIGURE 224: Period and Frequency

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Also the higher frequencies are easier to convert into electromagnetic (radio) waves which can be transmitted over long distances.

These higher frequencies cannot be generated by AC generator machines, since these devices rotate at a very high speed which would be

necessary. Instead they are generated by electronic circuits which do not require moving parts.

When frequencies are used that extend up to many millions of Hz, large numbers must be handled. These large numbers can be reduced to

manageable size by the use of various metric prefixes:

Prefix Symbol Value

Prefix Symbol Value

Kilo K 1000 (103)

Mega M 1000000 (106)

Giga G 1000000000 (109)

The prefixes can be placed before a word to change its meaning. For example, the prefix Kilo means 1000 and when it is placed before the

unit Hertz, the word ’Kilohertz’ which means 1000 Hz.

General 1000 Hz are expressed simple as 1Kilo--hertz, or the symbol K is used to represent Kilo and the symbol Hz to represent Hertz; the

quantity is expressed as 1KHz.

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In a similar manner the prefix Mega (M) is used to represent 1000000. Therefore 1000000 Hertz can be expressed as 1 Mega—hertz or 1

MHz. The prefix Giga (G) represents 1000000000.

Therefore 1000000000 Hertz can be expressed as 1 Giga--hertz or 1 GHz or 1000 MHz. Also a frequency of 10000 Hertz could be expressed

as 10KHz.

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Figure 225 shows the frequency band that is most commonly used. The frequencies between 15 Hz and 20 KHz are referred to as audio

frequencies. An AC voltage that has a frequency within this range will generate an audible tone to which the human ear will respond.

However the AC must be applied to device, such as a loudspeaker, which will convert it into sound waves that can be detected by the human

ear. The frequencies between 3 KHz and 300 GHz are referred to as radio frequencies (RF) since they are used extensively in radio

communications and radar systems.

The radio frequency band is subdivided into frequency ranges as follows:

• very--low frequency (VLF) – 3 KHz to 30 KHz

• low frequency (LF) -- 30 KHz to 300 KHz

• medium frequency (MF) -- 300 KHz to 3 MHz

• high frequency (HF) -- 3 MHz to 30 MHz

• very--high frequency (VHF) -- 30 MHz to 300 MHz

• ultra--high frequency (UHF) -- 300 MHz to 3 GHz

• super--high frequency (SHF) -- 3 GHz to 30 GHz

• extremely--high frequency (EHF) -- 30 GHz to 300 GHz.

Above the upper limit of 300 GHz other forms of electromagnetic energy such as, light waves, x rays and cosmic rays are encountered.

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FIGURE 225: Frequency Band

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3.13.4.6 Angular Velocity

The relationship between the instantaneous EMF in a sine wave and time is an important consideration in alternating voltage and current

circuits. The angle can be expressed in such a way that the instantaneous value of the EMF is made dependent on time. This angle is

expressed in RADIANS, instead of degrees. A radian is the angle at the centre of a circle subtended by an arc of the circumference equal in

length to the radius of the circle. The circumference of a circle contains 360 degrees. It length is 2 times the radius. Thus, the rotation through

360 degrees is the same as rotation through 2 radians. Refer to Figure 226.

3600 = 2 radians

1800 = radians

900 = / 2 radians

One radian is:

3600 / 2 = 3600 / 6.28 = 57.30.

If one revolution is performed the loop has passed through 3600 or 2 radians. If the loop rotates at f revolutions per second it passes 2 x f

radians per second. This is termed ’Angular Velocity’, which is equal to: 2 x f = (radians per second).

At any interval of t seconds from the commencement of rotation, the loop is rotated through an angle equal to 2 x f x t (radians)

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The instant voltage u at this instant is:

u = U sin

u = U sin t (volts).

Similar, with an alternating voltage in a circuit, the value of the current at any instant is:

i = I sin

i = I sin t (amperes).

FIGURE 226: The Radian

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3.13.4.7 Phase

Refer to Figure 227

The fractional part of a period through which the time variable of a periodic quantity (alternating electric current, vibration) has moved, as

measured at any point in time from an arbitrary time origin. In the case of a sinusoidal varying quantity, the time origin is usually assumed to

be the last point at which the quantity passed through a zero position from a negative to a positive direction.

In comparing the phase relationships at a given instant between two time-varying quantities, the phase of one is usually assumed to be zero,

and the phase of the other is described, with respect to the first, as the fractional part of a period through which the second quantity must vary

to achieve a zero of its own (see illustration). In this case, the fractional part of the period is usually expressed in terms of angular measure,

with one period being equal to 360° or 2 radians.

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FIGURE 227: An illustration of the meaning of phase for a sinusoidal wave. The difference in phase between waves 1 and 2 is and

is called the phase angle. For each wave, A is the amplitude and T is the period. Proprietary of




3.13.4.8 Phase Difference

It is often necessary to compare two AC wave--forms of the same frequency and to determine if the two wave--forms coincide, i.e. occur at the

same time. In many cases, two AC wave--forms within the same circuit will be displaced in time or by a given number of degrees.

When two alternating quantities of the same frequency pass through corresponding points in a circle at the same time they are ’In Phase’.

Figure 228

If they pass through the corresponding points in the circle at different instants of time, they are ’Leading or Lagging’ by a certain phase angle.

The instantaneous values can be solved by the use of the following equations:

I1 = I Sin wt

I2 = I Sin ( wt – )

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FIGURE 228: Sine Waves in Phase

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3.13.5 Triangular/Square waves

The fundamental waveform of electrical engineering is the sine wave, generated when a loop rotates in a magnetic field. If a sinusoidal current

is passed through a linear resistance, capacitance or inductance, then the voltage developed across the component is also sinusoidal.

For any other waveform shape the voltage will differ from the shape of the flown current, if there is some capacitance or inductance in the

circuit.

Refer to Figure 229

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FIGURE 229: Typical Wave-Forms

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Figure 230 shows typical examples of wave--form shapes used in electric circuits. Pulse trains and square waves are used extensively in

electronics, because of their fairly precise time at which the voltage levels change, in many timing applications.

In a radar system, for example, a pulse is transmitted and the radar receiver picks up any reflection from objects such as ships or aircraft. The

time between transmission and reception of the pulse is a measure of the distance away of the object.

Pulse generators usually generate a stream of pulses at regular intervals.

Two more quantities must therefore be considered:

• the number of pulses per second, known as pulse repetition frequency (PRF)

• the ratio of the pulse duration to the time between two pulses, known as mark--to--space ratio.

The pulses in Figure 230 contain a mark--to--space ratio of 1: 4 (mark = 1µs; space = 4µs).

The pulse repetition frequency (PRF) can be determined as follows:

PRF = 1 / PRT

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Whereby PRT is the time of mark plus the time of space.

PRF = 1 / tmark + tspace

PRF = 1 / (1 x 10−6 seconds) + (4 x 10−6 seconds)

PRF = 1 / (5 x 10−6 seconds)

PRF = 200 kHz.

FIGURE 230: PRT and Mark to Space Ratio

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3.13.6 Single/ Three phase principles

The basics of alternating current as described in the previous chapters are related to a so-called ’single phase’ or ’one phase’. However, many

ships and other consumers use ’three phase’ electrical power as their primary power. All rules and laws of alternating current are to be used

for ’single phase’ and ’three phase’ as well.

Figure 231, (detail a) shows the wave--form of a three phase alternating current. Each phase is shifted 1200 by another. The generation of

this wave--form is performed by an arrangement of coils and a rotating magnet as shown in Figure 231, (detail b).

Three coils are fitted on a core with a shift of 1200. The rotating magnet with constant speed induces in each coil a sinusoidal voltage

originated by cutting of flux lines of the magnet.

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FIGURE 231: Generation of Three Phase Alternating Current

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Three Phase Y and ∆∆∆∆Configurations

Y-Connected

The idea o three-phase power systems is by connecting three voltage sources together in what is commonly known as the “Y” (or “star”)

configuration. This configuration of voltage sources is characterized by a common connection point joining one side of each source. If we draw

a circuit showing each voltage source to be a coil of wire (alternator or transformer winding) and do some slight rearranging, the “Y”

configuration becomes more obvious in Figure 231(B)

The three conductors leading away from the voltage sources (windings) toward a load are typically called lines, while the windings themselves

are typically called phases. In a Y-connected system, there may or may not be a neutral wire attached at the junction point in the middle,

although it certainly helps alleviate potential problems should one element of a three-phase load fail open.

When we measure voltage and current in three-phase systems, we need to be specific as to where we’re measuring. Line voltage refers to the

amount of voltage measured between any two line conductors in a balanced three-phase system. With the above circuit, the line voltage is

roughly 208 volts. Phase voltage refers to the voltage measured across any one component shown in Figure 231(D), the phase voltage is 123

volts. The terms line current and phase current follow the same logic, the former referring to current through any one line conductor and the

latter to current through any one component.

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Y-connected sources and loads always have line voltages greater than phase voltage, and line current equal to phase currents. If the Y-

connected source or load is balanced, the line voltage will be equal to the phase voltage times the square root of 3

E line = √ 3 E phase

I line = I phase

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Delta Connected

The “Y” configuration is not only the valid one for connecting three-phase voltage source or load elements together. Another configuration is

known as the “Delta”, for its geometric resemblance to the Greek letter of the same name (∆). Take close notice of the polarity for each

winding in Figure 231 (E).

At first glance it seems as though three voltage sources like this would create a short-circuit, electrons flowing around the triangle with nothing

but the internal impedance of the windings to hold them back. Due to the phase angle of these three voltage sources, however, this is not the

case.

For Delta circuits:

E line = E phase

I line = √3 I Phase

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS RESISTIVE, CAPACITIVE & INDUCTIVE (DCAM 3.14 L2)


3.14 RESISTIVE (R), CAPACITIVE (C) AND INDUCTIVE (L) CIRCUITS (EASA 3.14) LEVEL 2

3.14.1 Introduction

We need to look at the effect of ac applied to resistance, inductance and capacitance as the results are important as we shall see.

There is no such thing as a 'pure' resistance, a 'pure' inductance or a 'pure' capacitance. A wire wound resistor, for instance, since it is wound

in the form of a coil has inductance as well as resistance, similarly, a capacitor has resistance as well as capacitance.

However, for the purposes of the next few pages we are going to assume 'pure' components as it makes the treatment easier and it is helpful

to show the 'ideal' conditions.

3.14.1.1 Pure Resistance in AC Circuits

With reference to the graph in Figure 232. It can be seen that the voltage and current are in-phase and the phasor diagram would be as

shown below the graph.

Ohms law and the use of rms values applies at all times to a purely resistive

circuit.

I = V V = IR R = V

R I

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FIGURE 232 :Resistor in AC Circuit

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3.14.1.2 Power in Pure Resistive Circuits

The power is the average value of all the instantaneous values of power for a complete cycle. To find the instantaneous power at any

moment, the instantaneous values of voltage and current at that moment are multiplied together.

Thus in Figure 233 ( a ) at moment X, the voltage is A volts and the current B amps. The power at this moment is therefore AB watts (V x I)

and is represented by point C on the graph.

If this process is carried out over the complete cycle the power curve is produced as shown in Figure 233 ( b ). The power is always positive

because current and voltage are in phase and when voltage and current are positive their product is positive when they are both negative their

product is still positive.

The average power over a complete cycle is the average value of the power curve and this is represented by a line halfway between

maximum and minimum values of the curve, since the shaded areas above and below the line are equal.

The power waveform has twice the frequency of the supply. Therefore in the Figure 233 (c) the power fluctuates rapidly between zero and 12

watts, but over a complete cycle, the average power is 6 watts.

We are only interested in average power as the frequency of the supply is usually high and this is what the device (lamp, electric motor etc)

actually consumes.

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(a) (b) (c)

FIGURE 233: Power in Resistive Circuits

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The average power will from now be referred to as 'power', is half the peak power in a resistive circuit, and this peak value is the maximum

voltage multiplied by the maximum current.

Pmax = Vmax x Imax

P average = Vmax x Imax

2

= Vmax x Imax

2 2

P = Vrms x Irms watts.

As Vrms = Irms x R

then P = 12rms x R watts

and Irms = Vrms

R

then P = V2rms watts

R

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So to sum up. In a resistive circuit:

1) V and I are in phase.

2) Normal ohms law calculations apply.

3) dc calculations apply for power.

4) Power is produced.

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3.14.1.3 Pure Inductance in AC Circuits

When an ac supply is connected to an inductance, as the current is continually varying then an emf (back emf) is induced into the coil. Its

value is dependent on the value of the inductor in henrys and the rate of change of current (di/dt).

e = - L di/dt volts. The e = emf, L = inductance in henrys and the minus sign indicates that it opposes the applied voltage.

This back emf opposes the rise of current in the circuit and therefore delays its rise as can be seen by the waveform diagram

in Figure 234 ( b ). In a pure inductive circuit V leads I by 90° or I lags V by 90°. The back-emf in the circuit provides the opposition to current

flow. It therefore acts in a similar manner to a resistance in the circuit. It is a form of ac resistance but is called REACTANCE, it is given in

ohms and has the symbol X, to identify it as reactance in an inductive circuit the symbol is XL is used.

The inductive reactance of a coil depends upon the rate of change of current (which is dependent on frequency) and the value of the

inductance. It iscalculated by the formula:

XL = 2rr fL ohms

Where

XL = Inductive reactance.

2= 6·28 (approx)

f = frequency in Hertz

L = Inductance in henrys

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As in any circuit the opposition to current flow is always V so in the pure inductive circuit XL = V ohms

I I

It is important for you to determine what happens in a pure inductive circuit when the frequency to a circuit is increased or decreased.

(a) (b) (c)

FIGURE 234: Inductor in AC Circuit

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3.14.1.4 Power in Pure Inductive Circuits

As the voltage and current are 90° out of phase positive and negative powers are produced. In the purely inductive circuit, the total power is

zero,since positive and negative powers cancel. Positive power is given to the circuit from the power supply on one half cycle and negative is

returned to the supply source on the other half cycle of power.

Over a complete cycle the net power is zero. It is important to note that current flows in the circuit but no work is being done when the current

is 90° out of phase with the voltage.

Summary

I lags V by 90° or V leads I by 90°

Opposition to current flow is INDUCTIVE REACTANCE (XL)

XL =2 fL ohms, XL = V ohms

I

NO POWER is produced in a purely inductive circuit.

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FIGURE 235: Power in Inductive Circuit

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3.14.1.5 Pure Capacitance in AC Circuits

Voltage exists across the plates of a capacitor only after the current has flowed to charge the plates. With reference to Figure 236 it can

be seen that the current leads the voltage and in a pure capacitive circuit it leads by 90°.

Remember, it can also be stated that voltage lags the current.

A capacitor opposes any change in the value of voltage applied to it and so presents an opposition to current at all times. This opposition is

called CAPACITIVE REACTANCE (Xc) and is measured in ohms.

Xc =_1_ ohms

2fC

Where

:

Xc = capacitive reactance in ohms

2 = 6·28 (approx)

f = frequency in Hz

C = Capacitance in Farads

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Again, this is an important formula to remember. Also as in any circuit the opposition to current flow is V/I .

You must be able to work out what happens to the current in a purely capacitive circuit when there is a frequency change.

FIGURE 236: Capacitor in AC Circuit

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3.14.1.6 Power in Pure Capacitive Circuits

The power curve is produced as previously illustrated in the pure resistive and pure inductive circuits. Looking at Figure 237 (the shaded

areas) it can be seen there are two positive peaks and two negative peaks of power over one complete cycle so the net power is zero.

SUMMARY

I leads V by 90° or

V lags I by 90°.

Opposition to current flow is CAPACITVE REACTANCE

Xc =_l_ohms

2fc

Xc = V ohms

I

NO POWER is produced in a purely capacitive circuit.

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FIGURE 237: Power in Capacitive Circuit

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3.14.2 Resistor and Inductor in Series

The concept of a pure inductor is not a practical one, as an inductor is a length of wire wound into a coil. This then will have resistance which

can be represented by a pure inductor in series with a resistor. Figure 238 ( a )

The waveform diagram Figure 238 ( b ) shows that voltage and current are out of phase by an angle less than 90° and with current lagging

voltage.

(a) (b)

FIGURE 238: Resistor and Inductor in Series

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To draw a phasor diagram for this circuit everything is drawn from a REFERENCE PHASOR, which in a series circuit is the current as it is the

same throughout the circuit. From this current phasor are drawn the voltage phasors. The voltage across the resistor VR is in phase with the

current and therefore drawn on the same line. The voltage across the inductor leads the current by 90° and is draw vertically as shown in

Figure 239. Remember phasors rotate anti-clockwise.

To find the supply voltage (V) we cannot just add these voltages together as you would do in a de circuit, because they are out of phase with

one another, so by completing the parallelogram (phasor addition) we can find the supply voltage ( V )

FIGURE 239: Phasor Diagram (RL Series Circuit)

In other words the ratio of the reactance to the resistance is the tangent of the phase angle.

The phase angle = tan- 1 XL

XR

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Impedance

The opposition to current flow in this circuit is provided by the resistance of the resistor and the reactance of the inductor and when there is a

combination like this the opposition to current flow is called IMPEDANCE (Z) in ohms.

The opposition to current flow is therefore Z = V ohms

I

We know VL = IXL

VR=IR

V by Pythagoras, V2 = (IXL)2 + (IR)2

V = (IXL)2 + ( IR )2

V/I = ( XL )2 + ( R )2

Z = ( XL )2 + ( R )2

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This is known as the impedance triangle and once again

Tan = XL

R

SUMMARY

1. Current lags the voltage or voltage leads the current by some angle between 0 and 90° which depends on values of L and R

Tan = XL

R

2. Opposition to current flow is impedance (Z) ohms

Z = (R) 2 + (XL) 2

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3.14.3 Resistor and Capacitor in Series

The waveform diagram (Figure 240 b) shows the voltage and current are out of phase by less than 90° with current leading the voltage.

Once again, to draw the phasor diagram use the current phasor as the reference, VR is in phase with the current so is drawn on top of I. The

voltage across the capacitor Vc is lagging the current by 90° and is drawn vertically downwards. The actual supply voltage can again be found

by phasor addition.

The opposition to current flow provided by the capacitive reactance (Xc) and resistance (R) is called impedance (Z) ohms

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(a) (b)

FIGURE 240: Resistor and Capacitor in Series

FIGURE 241: Phasor Diagram of Resistor and Capacitor in Series

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2. Opposition to current flows is impedance (Z) ohms

Z = V ohms

I

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The word CIVIL can be used as a convenient way of remembering the relative position of the phase between current and voltage in capacitive

and inductive circuits.

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NOTES

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3.14.4 Resistor, Inductor and Capacitor in Series

The circuit is shown in figure 242 (a) where resistance, inductance and capacitance are connected in series.

The phasor diagram (figure 242 ( b) would be drawn as before i.e. VR in phase, VL 90° ahead and Vc 90° behind. As VL and Vc are 180°

apart, in direct opposition it is the difference (VL - Vc in this case) that is used to find V the supply voltage.

Note. In this circuit as VL is greater than Vc then current lags the voltage and is therefore more inductive. The opposition to current flow is

again impedance and is:

Z = R2+(X L- XC )2 ohms

Or = V ohms

I

And tan = XL – Xc

R

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(a) (b)

FIGURE 242: Resistor, Inductor and Capacitor in Series

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3.14.5 Series Resonance

If we have a series circuit consisting of R, Land C, and we can vary the frequency to the circuit we can vary its properties. As the frequency

uses the inductive reactance XL (2 fl) rises but the capacitive reactance Xc (_1_) falls.

2fc

At one particular frequency XL = Xc resonance occurs, the frequency at which this happens is called the RESONANT FREQUENCY (fo).

The graph in Figure 243 illustrates this

At resonance we need to look at the conditions in the circuit.

XL = XC

Therefore VL = VC

The phasor diagrams are as shown in figure 244.

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FIGURE 243: Graph of XL and XC and Frequency FIGURE 244: Phasor Diagram of XL and XC

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If XL = Xc they are 180° apart (antiphase) so they will cancel leaving just the resistance of the circuit so Z = R.

If Z = R then the impedance is at a minimum and therefore the current must be at a maximum.

Also as VL and Vc are antiphase they also cancel so the applied voltage will equal the voltage across the resistor

VR = V. Current will be in phase with the supply voltage and the power factor is 1.

At resonance, as the current is high the voltages across Land C are equal and opposite so that their resultant is zero. However, when

considered alone they can be very high voltages, much greater than the supply and it is this voltage magnification which will be discussed

later.

The circuit is very often known as an ACCEPTOR CIRCUIT and the frequency at which resonance occurs can be found by:

fo = 1

2LC Hz

where

fo = resonant frequency in Hz.

2 = 6·28 (approx)

L = Inductance in henrys

C = Capacitance in farads

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FIGURE 245: Graph of Z and I against Frequency

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Circuit Magnification

At resonance we know the voltages across the inductor and capacitor can be very high.

At resonance VL = I XL

Current is a maximum and equal to .V as Z = R at resonance.

R

The ratio of reactance (2foL) to resistance (R) is the Q factor of the current Qo. Therefore the voltage across the inductor at resonance is

VL = Q0 x V

i.e. the Q factor times the applied voltage. If Qo is 100 and the supply voltage is 1 V then the voltage drop across L (and C of course) is 100 x

1 = 100V.

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That is VOLTAGE MAGNIFICATION has taken place which can be applied to another circuit. This magnified voltage is usually tapped off

across C. It is usual to have a fixed inductor and variable capacitor to adjust the resonant frequency to that required - for example, tuning a

radio station.

SUMMARY

Series Resonance

XL = Xc

VL = Vc

VR = V

I = Maximum

Z = Minimum = R

I and V in phase Power factor = 1

fo = 1

2LC

Q = selectivity of circuit depends on (a) resistance - (b) ratio of L

Qo = Reactance Bandwidth = f0,

Resistance Qo

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3.14.6 Resistor, Capacitor and Inductor in Parallel

There are many combinations of parallel ac circuits; however, we shall concentrate on the resistance - inductance and capacitive circuit

Figure 246

The phasor diagram for the above circuit is shown in Figure 247. Note that the reference phasor is voltage as this is common to all

components in a parallel circuit.

The current in the capacitor (Ic) leads the voltage by 90° and the current in the inductive circuit lags the voltage by some angle less than 90°

due to the resistance. The total current from the supply is the phasor addition of Ic and IL

IT = (IC) 2 + (IL) 2

The formula for impedance in a series circuit cannot be applied to a parallel circuit, instead we use

Z = V/IT or Z = (1/R) 2 + (1/XL – 1/ XC) 2

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FIGURE 246: R, L, C in Parallel FIGURE 247: Phasor Diagram

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3.14.7 Parallel Resonance

If the frequency to this circuit was varied then at one particular frequency XL = Xc. this is when the current taken from the supply is in phase

with the voltage. What is happening in the circuit is that the capacitor is charging

up and then discharging through the inductor, the emf induced in the inductor will then charge up the capacitor in the reverse direction and this

will continue to circulate a current between the two components.

The circuit is said to be at RESONANCE, so we are now looking at a PARALLEL RESONANT CIRCUIT. The conditions above would continue

forever but the inductor has resistance and there is a power loss here. In order to keep the current circulating it is necessary to 'top up' the

circuit from the supply.

At resonance the current drawn from the supply is very small and therefore the impedance is high (opposite to the series resonant circuit).

Figure 248 shows the relationship of Z and I at resonance It should be noted that the actual current circulating between the inductor and

capacitor is high. The phasor diagram (figure 249) shows the conditions at resonance with the supply current in phase with the supply

voltage.

The frequency at which resonance occurs in a parallel circuit can be found by:

fo = 1

2 LC

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FIGURE 248: Graph of Z and I against Frequency FIGURE 249: Phasor Diagram of Resonance

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At resonance the impedance of the circuit is high, the maximum possible and is called the DYNAMIC IMPEDANCE Zo and can be found by

the following formula:

ZD = L ohms

CR

The current in the circuit at resonance is therefore:

I = V

ZD

The circulating current at resonance has a high maximum value and is equal to Q0 (Q factor is XL remember) times the supply current.

R

So in a parallel resonant circuit CURRENT MAGNIFICATION takes place.

Figure 250 shows the impedance - frequency response curve. As for a series circuit the Qo value and selectivity and bandwidth depend on R

and the ratio of L to C

.

A parallel circuit is often termed a REJECTOR circuit since it presents maximum impedance at resonance.

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FIGURE 250: Impedance/ Frequency Response Curve

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SUMMARY

Conditions at Resonance - Parallel circuit.

XL = Xc

VL = Vc

IL = IC

fo =1/ 2 LC resistance neglected.

I in-phase with V = minimum

Z = L = maximum

CR

power factor = 1

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NOTES

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3.14.8 Power in an AC Circuits

A practical circuit will contain resistance, inductance and capacitance, and if we take the example of an ac generator supplying aircraft

systems (mainly inductance and resistance) then the current will lag the supply voltage.

The phasor diagram Figure 251 shows the current lagging the supply voltage by phase angle 0. From our previous theory, power is only

produced in an ac circuit when current and voltage are in phase. So we need to split the current I into its two components as shown.

The component 'in phase' with the voltage is known as the ACTIVE OR REAL component and the component at 90°' to the voltage is known

as the QUADRATURE or REACTIVE component.

It is very important to realize that only one current (1) flows in the circuit and this is the current that is measured by an ammeter in the circuit.

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FIGURE 251: Phasor Diagram of Supply Voltage and Current

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3.14.8.1 True or Real, Apparent and Reactive Power

The power in a purely resistive ac circuit is found by multiplying together the rms voltage and current. It follows then that in a resistive reactive

circuit, power dissipated can be found by multiplying together the voltage and the component of current in phase with it.

PREAL = V X IREAL

As Cos = I REAL

I

I REAL = I Cos

TRUE OR REAL POWER = V x I x Cos watts (W) or KILOWATTS (kW)

This then gives us the actual power being used by the system. The component of the current that does no work in the system still flows

through the system cables and produces power which as we know cancels over one cycle so no net power is produced.

PREACTIVE = V x component of current at 90°

= V X IREACTIVE

As Sin = IREACTIVE

I

IREACTIVE = I sin

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REACTIVE POWER = V x I x Sin VAR OR KVAR

The unit of reactive power is VOLT AMPS REACTIVE (VAR).

If the supply voltage is multiplied by the current (I) this will give us the APPARENT POWER being dissipated, we know that this is apparently

available but because current and voltage are not in phase then that is not the true power available from the system.

APPARENT POWER = V x I VOLT AMPS (VA) OR KVA

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3.14.8.2 Power Factor

As we have seen we can work out the apparent power of a system in KVA. What we need to know is how much of this available power is

producing actual work done in a circuit, i.e. producing True Power. So the ratio of

TRUE POWER is called the power factor (pf).

APPARENT POWER

Pf = Cos

So another formula for power factor is that it equals the cosine of the phase angle.

If we look back at the triangle related to impedance, then the cosine = R

Z

So another formula for power factor is pf = R

Z

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SUMMARY

The true power is produced when current and voltage are in phase.

T P = V x I x Cos KW

R P = V x I Sin KVAR

A P = V x I KVA

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS TRANSFORMER (DCAM 3.15) L2)


3.15 TRANSFORMER (EASA Ref. 3.15) Level 2

3.15.1 Transformer principles, construction, and operation

3.15.1.1 Transformer Principles

A transformer consists of two coils adjacent to each other and an ac supply is applied to one coil known as the PRIMARY. The other coil is

known as the SECONDARY. The changing current in the primary creates a fluctuating magnetic field that induces a voltage in the secondary

coil (mutual inductance).

For a transformer to work efficiently, all the lines of flux created by the current in the primary should link with the secondary, this is not possible

but to try and get close to this on low frequency transformers an iron core is used. It is suitably laminated to reduce eddy current losses.

Because of its high permeability the iron concentrates, and increase, the lines of flux, and flux loss is small. The principle is shown in figure

252. Each winding in the coil is insulated and the two coils are insulated from one another and the iron core. If the secondary is connected to a

load, a secondary (ac) current flows and power is developed in the load. A transformer does not generate power it merely transfers power

from the primary to the secondary

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FIGURE 252: Iron Cored Transformer

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3.15.1.2 Basic Construction of a Transformer

Two coils of wire (called windings) are wound on some type of core material. In some cases the coils of wire are wound on a cylindrical or

rectangular cardboard form. In effect, the core material is air and the transformer is called an air-core transformer. Transformers used at low

frequencies, such as 50 hertz and 400 hertz, require a core of low-reluctance magnetic material, usually iron. This type of transformer is called

an iron-core transformer. Most power transformers are of the iron-core type.

The principle parts of a transformer and their functions are:

• The CORE, which supports the coils or windings and provides a path for the magnetic lines of flux.

• The PRIMARY WINDING, which receives energy from the ac source.

• The SECONDARY WINDING, which receives energy from the primary winding and delivers it to the load.

• The ENCLOSURE, which protects the above components from dirt, moisture, and mechanical damage.

Core Characteristics

The composition of a transformer core depends on such factors as voltage, current, and frequency. Size limitations and construction costs are

also factors to be considered. Commonly used core materials are air, soft iron, and steel. Each of these materials is suitable for particular

applications and unsuitable for others. Generally, air-core transformers are used when the voltage source has a high frequency (above 20

kHz).

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Iron-core transformers are usually used when the source frequency is low (below 20 kHz). A soft-iron-core transformer is very useful where

the transformer must be physically small, yet efficient. The iron-core transformer provides better power transfer than does the air-core

transformer. A transformer whose core is constructed of laminated sheets of steel dissipates heat readily; thus it provides for the efficient

transfer of power. The majority of transformers contain laminated-steel cores.

These steel laminations (see figure 253a) are insulated with a non-conducting material, such as varnish, and then formed into a core. It takes

about 50 such laminations to make a core an inch thick. The purpose of the laminations is to reduce certain losses that will be discussed later

in this part. An important point to remember is that the most efficient transformer core is one that offers the best path for the most lines of flux

with the least loss in magnetic and electrical energy.

Figure 253: a) Hollow-core construction,

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Core Type Transformers

There are two main shapes of cores used in laminated-steel-core transformers. One is the Core Type, so named because the core is shaped

with a hollow square through the centre. Notice that the core is made up of many laminations of steel. Figure 253(b) illustrates how the

transformer windings are wrapped around both sides of the core.

Shell-Core Transformers

The most popular and efficient transformer core is the shell core, as illustrated in figure 253 (c). As shown, each layer of the core consists of

E- and I-shaped sections of metal. These sections are butted together to form the laminations. The laminations are insulated from each other

and then pressed together to form the core.

Transformer Windings

As stated above, the transformer consists of two coils called windings that are wrapped around a core. The transformer operates when a

source of ac voltage is connected to one of the windings and a load device is connected to the other. The winding that is connected to the

source is called the Primary Winding. The winding that is connected to the load is called the Secondary Winding. (Note: In this part the terms

"primary winding" and "primary" are used interchangeably; the term: "secondary winding" and "secondary" are also used interchangeably.)

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Figure 253 (b) Windings wrapped around laminations

Figure 253 (c) Shell-type core constructions

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3.15.2 Basic Operation of a Transformer

Refer to Figure 254; the primary winding is connected to ac voltage source. The magnetic field (flux) builds up (expands) and collapses

(contracts) about the primary winding. The expanding and contracting magnetic field around the primary winding cuts the secondary winding

and induces an alternating voltage into the winding. In other word, the changing current in the primary creates a fluctuating magnetic field that

induces a voltage in the secondary windings (mutual inductance). This voltage causes alternating current to flow through the load. The voltage

may be stepped up or down depending on the design of the primary and secondary windings.

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Figure 254: Mutual Inductance

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3.15.2.1 Schematic Symbols for Transformers

Figure 255 shows typical schematic symbols for transformers. The symbol for an air-core transformer is shown in figure (255-a). Parts (b)

and (c) show iron-core transformers. The bars between the coils are used to indicate an iron core. Frequently, additional connections are

made to the transformer windings at points other than the ends of the windings. These additional connections are called taps. When a tap is

connected to the centre of the winding, it is called a Centre Tap. Figure 255 ( c ) shows the schematic representation of a centre-tapped iron-

core transformer.

Parts (d) and (e) are simpler to draw or print. Two vertical lines indicate that primary and secondary coils share the core made of transformer

sheet metal. With the transformer, manufacturers usually supply a scheme containing info on the primary and secondary coil, voltage and

maximal currents. In case that this scheme is lacking, there is a simple method for determining which coil is the primary and which is the

secondary: as primary coil consists of thinner wire and greater number of curls than the secondary, it has higher resistance value - the fact

that can be easily tested by ohmmeter.

The figure 255 (e) shows the symbol for transformer with two independent secondary coils, one of them having three out connectors. The

secondary coil for getting 5V is made of thinner wire with maximal current O.3A, while the other coil is made of thicker wire with maximal

current 1.5A. Total voltage on the larger secondary coil is 48V, as shown on the figure (e). Note that voltage values other than those marked

on the scheme can be produced - for example, voltage between nodes marked as 27V and 36V equals 9V, voltage between nodes marked as

27V and 42V equals 15V, etc.

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Figure 255: Schematic symbols for various types of transformers.

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3.15.3 Transformer losses

A properly designed transformer is a very efficient device; there are certain factors that prevent the transformation of the input voltage and

current to the desired output voltage and current with 1000/0 efficiency. These factors are transformer losses, and they are of three general:

Copper losses, from the materials used in the transformer windings.

Core losses, which come principally from the material, size and shape of the transformer core.

Stray losses of various kinds. Power is lost in an inductor through several different mechanisms:

1. Resistance of the windings - 'copper loss'.

2. Magnetic friction in the core - 'hysteresis'.

3. Electric currents induced in the core - 'eddy currents'.

Copper losses occur in the form of heat which is produced by the currents in the conductors of the transformer windings. Called I squared R

losses, they relate to the amount of current in the windings and the resistance to the conductors. These losses are minimized by employing

large diameter conductors to reduce the resistance per unit length of the wires. Copper losses are generally about twice as great as core

losses in most transformers.

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Core losses, also called "iron losses", mainly affect transformers with cores of magnetic material and are of two kinds: Hysteresis losses and

eddy current losses. Hysteresis losses are the main type of core loss, comprising about three fourths of the total. "Hysteresis" describes the

tendency of the core material to oppose a change in magnetism.

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3.15.4 Methods of overcoming losses

Transfer of electrical energy from the primary to the secondary coil is carried out via magnetic field. To prevent energy losses, it is necessary

to assure that the whole magnetic field created by the primary coil encompasses the secondary. This is achieved by using the iron core, which

has much lower magnetic resistance value than the air, thus containing almost entire magnetic field within the core. It is suitably laminated to

reduce eddy current losses. Because of its high permeability the iron concentrates, and increase, the lines of flux, and flux loss is small.

Frequently, transformer cores are formed into a square or rectangular loop to provide a complete, closed path or circuit for the lines of

magnetic flux. A solid block of steel with a square hole in the centre has the primary coil wound around one leg and the secondary wound

around the other leg. Produce by the current in the primary, the flux is carried almost entirely by the core and passes through the secondary

winding to induce the desired emf (voltage).8y using laminated core, (thin sheets of metal instead of a solid iron core) the path of the eddy

current is broken up without increasing the reluctance of the magnetic circuit.

The laminations lie in the same direction as the flux. Therefore, the insulating surfaces are directly across the path of the eddy currents. The

resulting eddy current reduction improves the efficiency of the transformer.

All of these losses make the typical transformer hot when it operates under full load. In fact, the amount of heat the insulation can take without

breaking down helps to determine the power limitations of the transformer. Although some transformers operate too hot to hold comfortably,

there should be no odour of burning insulation or varnish, or signs of discoloration or smoke. Any of these conditions would indicate that the

transformer is overloaded.

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3.15.5 Transformer action Under No Load and On Load Conditions

The primary in figure 256 has a 100 volt ac supply and its secondary is open-circuited (no load). The current that flows in the primary will

cause an alternating flux in the core which will induce a voltage of 200 volts ac in the secondary winding. (Check the turns ratio)

The primary alternating flux will also induce a back-emf into the primary winding in opposition to the applied emf. The effective emf acting on

the primary is therefore very small and only a very small current will flow into the primary winding. (The foregoing is, of course, a description of

inductive reactance, XL). The very small current that flows in the primary is that current which is necessary to overcome losses and to

magnetize the core. The primary and secondary voltages are in anti-phase and it is usual to show them in this manner on a phasor diagram.

Because the circuit is inductive, the off-load primary current will lag behind the primary voltage. The in-phase component of this current is

overcoming copper losses and the quadrature component is magnetizing the core.

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FIGURE 256: Transformer- No Load

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If the secondary is now carrying current it is important to note that this current provides a flux in the core which opposes the primary flux and

so reduces the total flux in the core. This means that the primary back-emf is reduced, with a consequent increase ineffective emf in the

primary and so an increase in primary current.

Therefore increase in loading on the secondary increases primary current. The phasor diagram below shows the transformer on load.

The phasor diagram in figure 257 shows how the load current (Is) is transformed through 180° to become the primary load current (Ip) this is

combined with the off load current (Iou). To give the total primary current (Ip TOTAL) a phasor drawing as shown below is produced.

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FIGURE 257: Transformer - On Load

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3.15.6 Transformer Connections and Polarity Marking

Transformer Connections

A transformer is not confined to having just one output winding and voltage. It can have a secondary winding with various tapings to give

differing output voltages, or it can have a combination of both. It is therefore a very versatile piece of equipment. It must be realized that the

individual loads on all these secondary will all combine to be effectively one load as far as the primary winding is concerned.

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FIGURE 258: Secondary Connections

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Phasing Dots

The next diagram Figure 259 shows a transformer with three secondary windings The dots at the ends of the windings are called phasing

dots, they show that the polarity at those points will be the same at the same moment in time, i.e. points A, D and E will all be positive together

and all negative together. The centre winding is therefore of opposite polarity to the other two secondary windings. That is windings 1 and 3

will have a 180° phase shift from the input while winding 2 will be in phase with the input. It will of course be wound in the opposite sense.

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FIGURE 259: Polarity Marking -Dots

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3.15.7 Efficiency and Regulation

Efficiency

The efficiency of a transformer is

Output power x 100%

Input power

As the input is equal to the output + losses, so efficiency may be expressed as

Output power x 100%

Output power + copper losses + iron losses

Iron losses are reasonably constant, but copper losses vary as the square of the currents flowing. Efficiency is greatest when copper losses

are equal to iron losses.

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Regulation

As more current is drawn from the secondary of a transformer the terminal voltage falls as copper losses increase. The difference between the

secondary voltage at no load and the secondary voltage at full load is expressed as a percentage and is known as the REGULATION of the

transformer.

REGULATION = NO LOAD VOLTAGE - FULL LOAD VOLTAGE x 100%

FULL LOAD VOLTAGE

Typically this is 1- 2 %

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3.15.8 Three Phase Transformers

A 3 phase transformer is effectively three interconnected single phase transformers with their windings combined on a single magnetic circuit.

The most common method of construction is the core type shown in Figure 260.

FIGURE 260; Three Phase Transformer

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There are four combinations for three phase transformers:

* Star-star

* Delta-delta

* Delta-star

* Star-delta

FIGURE 261: Three Phase Transformers Configurations

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FIGURE 262: Star-Star Three Phase Transformer FIGURE 263: Delta- Delta Three Phase Transformer

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FIGURE 264: Star – Delta Three Phase Transformer FIGURE 265: Delta – Star Three Phase Transformer

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Calculations for STAR-STAR transformers are as for single phase transformers except for power. Power = 3 VL IL Cos .

There is no phase shift between input and output.

Again, for DELTA-DELTA transformers single phase calculations apply except for power. Power = 3 VL IL Cos .

Again there is no phase shift between input and output.

The STAR-DELTA transformer has a 3: 1 step-down ratio in addition to the effect of the turns ratio. Figure 264 assumes 1: 1 turns ratio.

With this step-down in line voltage there is a 30° phase shift.

The DELTA-STAR transformer has an l: 3 step-up ratio of line voltage in addition to the effect of the turns ratio. Figure 265 assumes 1: 1

ratio. With this step-up in line voltage there is a 30° phase shift.

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3.15.9 Turns Ratio

If the primary and secondary coils are identical, assuming no losses and the secondary coil is open circuit, the emf induced in the primary coil

will be almost equal to but opposite in phase to the applied voltage. This secondary coil will produce a mutually induced voltage which is

exactly the same as the primary back emf.

If the number of turns on the secondary is increased its inductance increases, and hence the induced emf increases. If the secondary has

twice the number of turns of the primary the secondary voltage will be twice the applied voltage at the primary. With three times as many turns

on the secondary as the primary, the secondary emf will be three times that in the primary. Secondary voltage (Vs) is T times the primary

voltage (Vp)

Vs = T x Vp

Where T is the TURNS RATIO

= Number of turns on the secondary (Ns

Number of turns on the primary (Np)

VS = NS x VP

NP

Or VS = NS

VP NP

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Transformation Ratio (T)

The ratio of Vs to Vp (or Ns to Np) is known as the Transformation Ratio. If Vs is smaller than Vp , then the output will be less than the input

and the transformer is called a Step-down transformer.

A Step-up transformer is one in which Vs is greater than Vp. When using Transformation Ratios, IT IS CONVENTIONAL TO ALWAYS PUT

THE SECONDARY VOLTAGE BEFORE THE PRIMARY VOLTAGE.

Thus, a transformation ratio of 4: 1 means that the output voltage will be four times the input voltage (step-up) and a transformation ratio of 1:3

means that the output voltage will be one-third the input voltage (step-down).

Any chance of confusion on this point can, of course, be obviated by the use of the appropriate term of 'step-up' or 'step-down' after the stated

ratio.

If there are more turns on the secondary than on the primary i.e. T greater than 1 the secondary voltage is greater than the primary and we

have a STEP-UP TRANSFORMER. (Figure 266)

If there are fewer turns on the secondary than on the primary i.e. T less than 1 then the secondary voltage is less than input voltage and we

have a STEP- DOWN TRANSFORMER. (Figure 267)

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FIGURE 266: Step up Transformer

FIGURE 267: Step down Transformer

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Assuming no losses then the input power of a transformer equals the output power.

Vp Ip= Vs Is

Therefore in a step-up transformer where the voltage is stepped up the current is stepped down and in a step-down transformer where the

voltage is stepped down the current is stepped up.

As Vp Ip = Vs Is, then Ip = Vs

Is Vp

and as Vs = Ns

Vp Np

Then Ip = Vs = Ns

Is Vp Np

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FIGURE 268: Voltage and Current in Secondary

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3.15.10 Autotransformers

This is a special type of transformer that has only a SINGLE winding, which serves as both the primary and the secondary. It follows that a

portion of the winding is common to both the input and to the output. It may be used either as a step-up or as a step-down transformer.

If an ac supply is applied to the primary terminals, an alternating current will flow through those coils connected across PI and P2. This will set

up an alternating flux which will link with all of the turns on the former, inducing a voltage in each.

The output voltage is therefore that which appears in the coils across terminals S1 and S2. Loading the secondary will have the same effect

as described for the Power Transformer. If the current flow is considered for one particular half-cycle, it will be seen that the primary and

secondary currents are opposing each other in the common portion of the winding.

The actual current flow in the common portion is therefore the difference between the two currents. This means that the cross-section area of

the copper can be decreased in the common portion, bringing about a saving in weight.

This saving is obviously most beneficial on auto-transformers where the input voltage and the output voltage are very close together and the

vast majority of the winding is common One disadvantage of this type of transformer, especially when used as a step-down is that, in the

event of an open-circuit occurring in the common portion of the winding, the input voltage will be applied to theload They are increasingly

found in aircraft lighting circuits for example.

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FIGURE 269: Auto Transformer

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The Current Transformer

The Current Transformer is designed to enable circuit currents to be measured without breaking into the circuit, as is necessary with an

ammeter or its shunt. The output of the current transformer may be applied directly to an instrument or be used in control circuits.

It works on the principle of mutual inductance but its construction and mode of operation are different to that of the power transformer. Current

transformers, use the load's supply cable as the primary winding.

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FIGURE 270: Current Transformer

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS FILTERS (DCAM 3.16 L1)


3.16 FILTERS (EASA Ref 3.16) Level 1

3.16.1 Introduction

The rectifier circuitry takes the initial ac sine wave from the transformer or other source and converts it to pulsating dc. A full wave rectifier will

produce the waveform shown in Figure, while a half-wave rectifier will pass only every other half-cycle to its output. This may be good enough

for a basic battery charger, although some types of rechargeable batteries still won't like it. In any case, it is nowhere near good enough for

most electronic circuitry. We need a way to smooth out the pulsations and provide a much "cleaner" dc power source for the load circuit.

To accomplish this, we need to use a circuit called a filter (Figure 271). In general terms, a filter is any circuit that will remove some parts of a

signal or power source, while allowing other parts to continue on without significant hindrance. In a power supply, the filter must remove or

drastically reduce the ac variations while still making the desired dc available to the load circuitry. Filter circuits aren't generally very complex,

but there are several variations. Any given filter may involve capacitors, inductors, and/or resistors in some combination. Each such

combination has both advantages and disadvantages, and its own range of practical application.

A common need for filter circuits is in high-performance stereo systems, where certain ranges of audio frequencies need to be amplified or

suppressed for best sound quality and power efficiency. You may be familiar with equalizers, which allow the amplitudes of several frequency

ranges to be adjusted to suit the listener's taste and acoustic properties of the listening area.

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Figure 271: full-wave rectifier waveform

Figure 272: Filter

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You may also be familiar with crossover networks, which block certain ranges of frequencies from reaching speakers. A tweeter (high-

frequency speaker) is inefficient at reproducing low-frequency signals such as drum beats, so a crossover circuit is connected between the

tweeter and the stereo's output terminals to block low-frequency signals, only passing high-frequency signals to the speaker's connection

terminals. This gives better audio system efficiency and thus better performance. Both equalizers and crossover networks are examples of

filters, designed to accomplish filtering of certain frequencies.

Another practical application of filter circuits is in the "conditioning" of non-sinusoidal voltage waveforms in power circuits. Some electronic

devices are sensitive to the presence of harmonics in the power supply voltage, and so require power conditioning for proper operation. If a

distorted sine-wave voltage behaves like a series of harmonic waveforms added to the fundamental frequency, then it should be possible to

construct a filter circuit that only allows the fundamental waveform frequency to pass through, blocking all (higher-frequency) harmonics.

The characteristics of a filter can be shown on a graph called a frequency response curve (Figure 273); the block symbols are shown in

Figure 274

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Figure 273: Frequency Response Curve

Figure 274: Block Diagram Symbols for Filters

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3.16.2 The Cut-off Frequency

The boundary line in question is somewhat arbitrary, because there is no clear frequency such that all signals above it are passed intact, while

all signals below that frequency are entirely blocked. Rather, there will be a "transition zone," or range of frequencies, over which the input

signals, will be partially transmitted to the output.

Nevertheless, we must select some specific frequency such that we can say (for the high-pass filter) that all signals above this frequency will

be passed without appreciable loss, while all signals below this frequency will be blocked to a significant extent. This frequency will be

designated as the cut-off frequency (often designated fco) for our filter. We have already noted that for very high frequencies there will be no

appreciable voltage drop across the capacitor, while for very low frequencies there will be no appreciable voltage drop across the resistor. The

transition zone, then, must be in between these extremes, where some of the signal voltage will be dropped across each of the components.

And the logical place to start is to set the cut-off frequency at the point where the voltage drops across the two components are the same.

This is also the frequency at which XC = R.

The cut-off frequency is also the frequency at which half of the power in the input signal is absorbed by the filter, and only the other half makes

it to the output. Therefore, it is sometimes known as the half power frequency, although that designation is no longer used as much as it was

in the past.

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3.16.3 Operation, application and uses: low-pass

A low-pass filter is a filter that passes low frequencies but attenuates (or reduces) frequencies higher than the cut-off frequency. The actual

amount of attenuation for each frequency varies from filter to filter. There are two basic kinds of circuits capable of accomplishing this objective

and many variations of each one.

Low pass filter: Made up of Inductors and Capacitors

The simple form of low pass filter that made up of inductors and capacitors are shown in Figure 275.

FIGURE 275 : Low Pass Filters

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At very low frequencies the impedance of the capacitor is high, acting almost like an open circuit. At very high frequencies the capacitor acts

almost like a short circuit.

The impedance of the inductor is low at low frequencies and high at high frequencies ( XL = 2 fl ). With a combination of these two different

effects the voltage gain tends to zero. By using a π type filter the voltage drops off more steeply.

The value of L and C for the filter can be calculated from:

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NOTES

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The Frequency Response Curve

All low-pass filters are rated at a certain cut-off frequency. That is, the frequency above which the output voltage falls below 70.7% of the input

voltage. This cut-off percentage of 70.7 is not really arbitrary, all though it may seem so at first glance. In a simple capacitive/resistive low-

pass filter, it is the frequency at which capacitive reactance in ohms equals resistance in ohms. In a simple capacitive low-pass filter (one

resistor, one capacitor); the cut-off frequency is given as:

A main characteristic of low pass filter is shown in Figure 276. Note that the frequency scale is logarithmic rather than linear. In addition, the

attenuation of the filter is shown in units called decibels (db). This is also a logarithmic unit used to show ratios. Mathematically, voltage gain

or loss is described as:

An ideal filter transmits frequencies in its pass-band un-attenuated and without phase shift, while not allowing any signal components in the

stop-band to get through. The cut-off frequency or corner frequency (fco) defines the start of the transition region between the pass-band and

the stop-band. Ideally this region should be zero.

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Real filters are far from ideal. Although they provide attenuation in the stop-band, they also subject the input signal in the pass-band to

attenuation, ripple and phase-shift. In addition there is the transition region between the pass-band and the stop-band. The specifications

define the fco as the frequency where attenuation reaches 3 dB. Within the transition region the specifications indicate how fast signals roll-off

during attenuation.

Figure 276; A main characteristic of low pass filter

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3.16.4 Operation, application and uses: high-pass

A high-pass filter's task is just the opposite of a low-pass filter: to offer easy passage of a high-frequency signal and difficult passage to a low-

frequency signal. As one might expect, the inductive and capacitive versions of the high-pass filter are just the opposite of their respective low-

pass filter designs. The capacitor's impedance increases with decreasing frequency. This high impedance in series tends to block low-

frequency signals from getting to load.

The simple form of low pass filter that made up of inductors and capacitors are shown in Figure 277.

Figure 277: High pass filter that made up of inductors and capacitors

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This filter requires components that allows current flow at high frequencies but also acts as an open circuit at low frequencies. This can be

achieved by a capacitor in series. The parallel element must have the property of a short circuit at low frequencies but have large impedance

at high frequencies and this is satisfied by an inductor.

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The Frequency Response Curve

As with low-pass filters, high-pass filters have a rated Gut-off frequency, above which the output voltage increases above 70.7% of the input

voltage. Just as in the case of the capacitive low-pass filter circuit, the capacitive high-pass filter's cut-off frequency can be found with the

same formula:

In the example circuit, there is no resistance other than the load resistor, so that is the value for R in the formula. A main characteristic of high

pass filter is shown in Figure 278. The shaded area is the ideal and the curve is the practical operation.

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Figure278: High-pass Frequency Response Curve Proprietary of




3.16.5 Operation, application and uses: band-pass

There are applications where a particular band, or spread, or frequencies need to be filtered from a wider range of mixed signals. Filter circuits

can be designed to accomplish this task by combining the properties of low-pass and high-pass into a single filter. The result is called a band-

pass filter. Creating a band-pass filter from a low-pass and high-pass filter can be illustrated using block diagrams in Figure 279.

Figure 279: Band-pass Block Diagram

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Band-pass Filter: Made up of Resistors and Capacitors

R1and C1 form a high-pass filter, while R2 and C2 form a low-pass filter (Figure 280 )the purpose of discussion, we arbitrarily assign a cut-off

frequency fco1= 10 radians/sec for R1 and C1, and a higher cut-off frequency fco2 = 10,000 radians/sec for R2 and C2. The actual

frequencies don't matter, so long as fcoi is less than fco2. That way, R1 and C1pass signals that will also be passed by R2 and C2.

It is equally possible to swap the two filter sections, putting the low-pass filter first. However, if we use the circuit shown here, the dc resistance

between VOUT and ground is R1+ R2. If we swap the two filters, R1 will be the only resistance from VOUT to ground. In addition, the second

filter section will present a load to the first section.

Since the low-pass section has a higher cut-off frequency (fco2), R2 and C2have higher impedances and constitute less of a load on R1and

C1than would be true if the sections were swapped. Therefore the two filters operate pretty much independently, even though they are

electrically connected.

Figure 280: Band-pass Filter That Made up of Resistors and Capacitors

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The Frequency Response

If we apply the cut-off frequencies assumed above, the frequency response curve for our filter will appear as shown in Figure. R1 and C1

govern the low-frequency cut-off, and will block signals at lower frequencies while passing higher-frequency signals. These signals will also be

passed by R2 and C2, so long as their frequency doesn't get too high. Frequencies above fc o2 pass through C2 to ground, and therefore are

kept away from VOUT.

Figure 281: Band-pass Frequency Response

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3.16.6 Operation, application and uses of the following filters: band stop

Band-stop is a filter that stops the transmission of frequencies between fco1 and fco2. A band-stop filter, also known as a notch, band-reject,

or band-elimination filter, passes all signals lying out with the band, in essence its operation is the opposite to that of a band-pass filter. Figure

282 shows the simple circuit for a band stop filter. Figure 283 shows the characteristics

Figure 282: Simple Circuit for a Band Stop Filter

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The bandwidth is defined as the difference between the upper critical frequency and the lower critical frequency. The critical frequency, fc

(also called the cut-off frequency) defines the end of the pass-band and is normally specified at the point where the response drops to -3 dB

(70.7%) from the pass band response. To put it another way the critical frequencies are defined as the points at which the response curves is

70.7% of it maximum.

The series element this time is parallel resonant circuits and the shunt element is a series resonant circuit. At the lower frequencies the series

resonant circuit impedance is high and the parallel resonant circuit impedance is low, around the resonant frequencies the parallel circuit

impedance is high and the series is low, therefore frequencies are blocked in this range. As the frequency increases the parallel circuit

impedance falls and the series circuit increases so frequencies are passed again.

Figure 283: Characteristics of a band-stop filter

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Applications

We have looked at some simple filter arrangements and it should be realised other filters will be quite sophisticated and will be combined with

operational amplifiers. Some applications of filters in aircraft are:

• HF Communication Transceiver

• VOR Receivers

• Marker Beacon Receiver

• ILS Receiver

• Engine Vibration Monitoring Systems

• Automatic Flight Control Systems

• Flight Director Systems

• Voice Recorder

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS AC GENERATORS (DCAM 3.17 L2)


3.17 AC GENERATORS (EASA Ref 3.17) Level 2

3.17.1 Rotation of a Loop in a Magnetic Field and Waveform Produced

Regardless of size, all electrical generators, whether dc or ac, depend upon the principle of magnetic induction. An emf is induced in a coil as

a result of a coil cutting through a magnetic field, or a magnetic field cutting through a coil. As long as there is relative motion between a

conductor and a magnetic field, a voltage will be induced in the conductor. That part of a generator that produces the magnetic field is called

the field. That part in which the voltage is induced is called the armature.

For relative motion to take place between the conductor and the magnetic field, all generators must have two mechanical parts a rotor and a

stator. The rotor is the part that rotates; the stator is the part that remains stationary. In a dc generator, the armature is always the rotor. In

alternators, the armature may be either the rotor or stator.

3.17.2 Rotating-Armature Alternators

This type of ac machine is similar in construction to a dc generator in that the rotor rotates in a fixed field with the emf picked off via slip rings.

The rotor windings are laid in slots along the rotor periphery, the armature being laminated to reduce eddy current losses. The stator carries

the dc excitation windings wound on the pole pieces to create alternate North and South poles around the stator. Figure 284 shows a single

phase 2 pole machine with output as shown in Figure 285.

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Figure 284: Rotating-armature Alternator ( 2 Pole ,Single Phase )

FIGURE 285 :Induced EMF –Single Phase AC

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One cycle of voltage is induced when the conductor moves through 360° past one pair of poles. If there are two pairs of poles then two cycles

of ac will be produced.

The number of cycles of induced voltage of an actual generator will correspond to the number of pairs of poles in the generator and is called

the frequency (f).

f = Np Hertz

60

where N = speed in rpm of the generator at which the generator must be driven in order to generate the required frequency

p = number of pairs of poles.

An ac generator in which the whole of the output consists of a single winding with the outer ends connected to a pair of slip rings is termed a

'single phase generator', if there were two windings at different angles connected to slip rings

then this would give two outputs and would be known as a 'two-phase generator'.

Figure 286 shows a three phase system, in which the coils are at 120° to each other and the 3 phase output generated. In other words it is

really 3 generators in one with 3 separate outputs each one 120° out of phase with the next.

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FIGURE 286: Three Phase 2 Pole AC Generator

FIGURE 287 : 3 Phase Induced EMF

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Three phase supplies are used extensively on (large) aircraft - as is most national grid systems. This type of generator, however, is not used

as a main generating source on its own as it has the following disadvantages.

(a) As all the power is taken from the rotor, the effective insulation and ventilation causes problems.

(b) All the (heavy) output is taken via slip rings and brushes.

(c) Centrifugal forces are considerable on the rotor windings.

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NOTES

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3.17.3 Rotating-Field Alternators

In this type of generator the dc field rotates and its field cuts the stationary (output) windings on the stator. The output windings consist of a

number of coils connected in series and inserted in slots in the laminated stator to give a single phase output. The field windings are fed via

two slip rings and brushes with dc. The principle of a two pole single phase ac generator is shown in figure 288.

The general arrangement of a single phase rotating field ac generator is shown in figure 289. If another set of single phase windings at 90° to

one another is added, then a two phase output is produced one being 90° out of phase with the other. Figure 290

FIGURE 288 : Single Phase 2 Pole Rotating Field Type

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FIGURE 289 : Single Phase AC Generator

FIGURE 290: Two Phase Rotating Field and Two Phase Output

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If another set of two coils is added and each coil in the complete system is spaced at 60° to each other then we have a three phase system.

Each pair of coils is spaced at 120° to one another so we have 3 phases where the 3 outputs are 120° out of phase. Figure 291

The advantages of the rotating field generator over the rotating armature type are:

(a) Only two slip rings and brushes taking much less current, ie field winding current only.

(b) Less problems with centrifugal effects on rotor windings.

© The output is taken from the stator, where ventilation and insulation of windings is less of a problem.

FIGURE 291: 2 Pole Three Phase AC Generator ( Rotating Field)

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The first ac generating systems on aircraft used rotating field ac generators in what was called a ‘frequency wild’ system. ( Figure 292 )

The 3 phase output was controlled and converted to dc and fed to the aircraft busbar (from which all services take their supplies). The

generator output voltage was controlled to 200 volts but the frequency varied with engine speed. This frequency wild ac was fed to resistive

loads such as heater mats, where the variable frequency has no effect. (With inductive and capacitive loads the total resistance of the circuit

would vary with frequency). The output of ac generators on most large aircraft today is 3 phase 200/ 115V 400Hz. 400Hz constant frequency

with 200V and 115V supplies available depending on how the load is connected to the generator

FIGURE 292: Three Phase AC Generator- Frequency Wild

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3.17.4 Three Phase Star and Delta Connections

Each phase of a three phase generator can be brought out to separate terminals and used to supply separate loads independently, which will

require six leads. However, considerable saving in cable (weight) and other advantages can be obtained by connecting a lead from one end of

each of the three phase windings as shown in figure 293.

This shows that the three windings are connected to one point and a lead is taken from that point. This configuration is called STAR

CONNECTION and the point where they meet is called the star point, and the lead taken from the star point is called the neutral

.

Figure 293 shows that the line current = the phase current. ( IL =IP )

The phase voltage (Vphase) on an aircraft generator would be 115v and the line voltage (Vline) which is the sum of the two phase voltages

across that line ie two 115v phases at 120° phase angle, which is 200V and mathematically is the same as multiplying the phase voltage

by3. ( VL = 3 VP

The big advantage of the star connection is that with the neutral line we are able to provide two voltages – 200V and 115V. Aircraft ac

generators are generally connected in star.

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FIGURE 293: Star Connection

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Another connection of the three coils would be to connect them as shown in figure 294, known as DELTA CONNECTION. In this case the

three windings are connected in series to form a closed mesh, with the three output lines at the junction points.

As can be seen from figure 294, VP =VL

In this connection the line current is composed of two components and mathematically it can be shown that: IL =3 IP

The delta connection does not have a neutral and cannot provide two outputs and must be connected to a balanced load, but does give

a higher current output than a star connected system.

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FIGURE 294: Delta Connections Proprietary of




3.17.5 Permanent Magnet Generator

With reference to figure 295, when the generator drive shaft rotates the Permanent Magnet Generator (PMG) rotates and its field cuts the

winding on the stator (3 star wound coils) and induces an ac into it. This is fed externally to the Voltage Regulator in the Generator Control

Unit (GCU).

The GCU is the 'brains' of the system which controls the generator output, looks after its well-being and its relationship with other generators

in the system. The ac is rectified to dc and adjusted to the correct voltage and returned to the main exciter stator field (stationary dc field

winding).

As the magnetic field is cut by the 3 rotating coils of the rotating assembly, a 3 phase ac output is generated. This ac is fed through the 3

phase full wave rectifier bridge (also rotating) to provide dc to the main generator field. This rotating field cuts the star connected stator

winding to produce a 3 phase 200/ 115V 400Hz output.

As you can see this generator consists of a permanent magnet generator, rotating armature and rotating field generators.

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.FIGURE 295: Permanent Magnet Generator ( Brushless AC Generator )

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3.17.6 Prime Movers

All generators, large and small, ac and dc, require a source of mechanical power to turn their rotors. This source of mechanical energy is

called a prime mover. Prime movers are divided into two classes for generators-high-speed and low-speed. Steam and gas turbines are high-

speed prime movers, while internal-combustion engines, water, and electric motors are considered low speed prime movers.

The type of prime mover plays an important part in the design of alternators since the speed at which the rotor is turned determines certain

characteristics of alternator construction and operation.

3.17.7 Alternator Rotors

There are two types of rotors used in rotating-field alternators. They are called the turbine-driven and salient-pole rotors. As you may have

guessed, the turbine-driven rotor shown in figure 296, view A, is used when the prime mover is a high-speed turbine. The windings in the

turbine-driven rotor are arranged to form two or four distinct poles. The windings are firmly embedded in slots to withstand the tremendous

centrifugal forces encountered at high speeds.

The salient-pole rotor shown in Figure 296 (B), is used in low-speed alternators. The salient-pole rotor often consists of several separately

wound pole pieces, bolted to the frame of the rotor.

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If you could compare the physical size of the two types of rotors with the same electrical characteristics, you would see that the salient-pole

rotor would have a greater diameter. At the same number of revolutions per minute, it has a greater centrifugal force than does the turbine-

driven rotor. To reduce this force to a safe level so that the windings will not be thrown out of the machine, the salient pole is used only in low-

speed designs.

Figure 296: Types of rotors used in alternators

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3.17.8 Alternator Characteristics and Limitations

Alternators are rated according to the voltage they are designed to produce the maximum current they are capable of providing. The maximum

current that can be supplied by an alternator depends upon the maximum heating loss that can be sustained in the armature. This heating loss

(which is a 12R power loss) acts to heat the conductors, and if excessive, destroys the insulation. Thus, alternators are rated in terms of this

current and in terms of the voltage output - the alternator rating in small units is in volt-amperes; in large units it is kilovolt-amperes.

When an alternator leaves the factory, it is already destined to do a very specific job. The speed at which it is designed to rotate, the voltage it

will produce, the current limits, and other operating characteristics are built in. This information is usually stamped on a nameplate on the case

so that the user will know the limitations.

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3.17.9 Power in a Three Phase System

The power in a single phase system is

True Power = V x I x Cos Watts

True Power in a balanced three phase Star or Delta system must be three times that in a single phase system.

True Power = 3 Vph Iph cos Watts

In a star connected system IL = Iph

So the formula can be written

True Power = 3VphILcos Watts

And as VL = 3 VP VP = VL

3

Then True Power = 3 x VL IL Cos

3

= 3 VL IL Cos Watts

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For a delta connected system VL = Vph

then the formula can be rewritten

True Power = 3VL I ph Cos watts

And as IL = 3 IP IP = IL

3

True Power = 3 VL IL Cos Watts

3

= 3 VL IL Cos Watts

So for Star or Delta connected systems there are two formulas for power.

1. True Power = 3Vph Iph cos watts

2. True Power = 3 VL IL cos watts

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NOTES

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PART 66 CAT B1.1/B2 MODULE 3 ELECTRICAL FUNDAMENTALS AC MOTORS (DCAM 3.18 L2)


3.18 AC MOTORS (EASA Ref 3.18) Level 2

3.18.1 Introduction

There are advantages in the use of ac motors besides the wide availability of ac power. In general, ac motors cost less than dc motors. Some

types of ac motors do not use brushes and commutators. This eliminates many problems of maintenance and wear. It also eliminates the

problem of dangerous sparking. An ac motor is particularly well suited for constant-speed applications. This is because its speed is

determined by the frequency of the ac voltage applied to the motor terminals.

Also, in aircraft employing constant-frequency alternating current either as the primary or secondary source of electrical power, it is of course

logical to utilize ac motors and although they do not always serve as a complete substitute for dc machine, the advantages and special

operating characteristic of certain types are applied to a number of systems which rely upon mechanical energy from electromotive power

source.

The dc motor is better suited than an ac motor for some uses, such as those that require variable- speeds. An ac motor can also be made with

variable speed characteristics but only within certain limits. Industry builds ac motors in different sizes, shapes, and ratings for many different

types of jobs. These motors are designed for use with either poly-phase or single-phase power systems. It is not possible here to cover all

aspects of the subject of ac motors. Only the principles of the most commonly used types are dealt with in this chapter.

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In this chapter, ac motors will be divided into:

(1) Synchronous

(2) Induction motors

Single-phase and poly-phase motors will be discussed. Synchronous motors, for purposes of this chapter, may be considered as poly-phase

motors, of constant speed, whose rotors are energized with dc voltage. Induction motors, single-phase or poly-phase, whose rotors are

energized by induction, are the most commonly used ac motor.

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3.18.2 Rotating Magnetic Fields

The principle of rotating magnetic fields is the key to the operation of most ac motors. Both synchronous and induction types of motors rely on

rotating magnetic fields in their stators to cause their rotors to turn. The idea is simple. A magnetic field in a stator can be made to rotate

electrically, around and around. Another magnetic field in the rotor can be made to chase it by being attracted and repelled by the stator field.

Because the rotor is free to turn, it follows the rotating magnetic field in the stator.

Rotating magnetic fields may be set up in two-phase or three-phase machines. To establish a rotating magnetic field in a motor stator, the

number of pole pairs must be the same as (or a multiple of) the number of phases in the applied voltage. The poles must then be displaced

from each other by an angle equal to the phase angle between the individual phases of the applied voltage.

3.18.2.1 Two-Phase Rotating Magnetic Fields

A rotating magnetic field is probably most easily seen in a two-phase stator. The stator of a two-phase induction motor is made up of two

windings (or a multiple of two). They are placed at right angles to each other around the stator. The simplified drawing in Figure 297 illustrates

a two-phase stator. If the voltages applied to phase 1-1A and 2-2A are 90° out of phase, the currents that flow in the phases are displaced

from each other by 90°. Since the magnetic fields generated in the coils are in phase with their respective currents, the magnetic fields are

also 90° out of phase with each other. These two out-of-phase magnetic fields, whose coil axes are at right angles to each other, add together

at every instant during their cycle. They produce a resultant field that rotates one revolution for each cycle of ac.

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Figure 297: Two-phase Motor Stator

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To analyze the rotating magnetic field in a two-phase stator, refer to Figure 298. The arrow represents the rotor. For each point set up on the

voltage chart, consider that current flows in a direction that will cause the magnetic polarity indicated at each pole piece. Note that from one

point to the next, the polarities are rotating from one pole to the next in a clockwise manner. One complete cycle of input voltage produces a

360-degree rotation of the pole polarities. Let's see how this result is obtained. The waveforms in Figure 298 are of the two input phases,

displaced 90° because of the way they were generated in a two-phase alternator. The waveforms are numbered to match their associated

phase. Although not shown in this figure, the windings for the poles 1-1A and 2-2A would be as shown in the previous figure. At position 1, the

current flow and magnetic field in winding 1-1 A is at maximum (because the phase voltage is at maximum). The current flow and magnetic

field in winding 2-2A is zero (because the phase voltage is zero). The resultant magnetic field is therefore in the direction of the 1-1A axis.

At the 45-degree point (position 2), the resultant magnetic field lies midway between windings 1-1A and 2-2A. The coil currents and magnetic

fields are equal in strength.

At 900 (position 3), the magnetic field in winding 1-1A is zero. The magnetic field in winding 2-2A is at maximum. Now the resultant magnetic

field lies along the axis of the 2-2A winding as shown. The resultant magnetic field has rotated clockwise through 900 to get from position 1 to

position 3. When the two-phase voltages have completed one full cycle (position 9), the resultant magnetic field has rotated through 3600

Thus, by placing two windings at right angles to each other and exciting these windings with voltages 900 out of phase, a rotating magnetic

field results. Two-phase motors are rarely used except in special purpose equipment. They are discussed here to aid in understanding rotating

fields. You will, however, encounter many single phase and three-phase motors.

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.

FIGURE 298: Two-Phase Rotating Field

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3.18.2.2 Three-Phase Rotating Fields

The three-phase induction motor also operates on the principle of a rotating magnetic field. The following discussion shows how the stator

windings can be connected to a three-phase ac input and has a resultant magnetic field that rotates. Figure 299, views a - c show the

individual windings for each phase. Figure 299, view d, shows how the three phases are tied together in a Y-connected stator. The dot in

each diagram indicates the common point of the Y-connection. You can see that the individual phase windings are equally spaced around the

stator. This places the windings 1200 apart.

The three-phase input voltage to the stator of Figure 299 is shown in the graph of Figure 300. Use the left-hand rule for determining the

electromagnetic polarity of the poles at any given instant. In applying the rule to the coils in Figure 299, consider that current flows toward the

terminal numbers for positive voltages, and away from the terminal numbers for negative voltages. The results of this analysis are shown for

voltage points 1 through 7 in Figure 300.

At point 1, the magnetic field in coils 1-1A is maximum with polarities as shown. At the same time, negative voltages are being felt in the 2-2A

and 3-3A windings. These create weaker magnetic fields, which tend to aid the 1-1A field. At point 2, maximum negative voltage is being felt in

the 3-3A windings. This creates a strong magnetic field that, in turn, is aided by the weaker fields in 1-1A and 2-2A. As each point on the

voltage graph is analyzed, it can be seen that the resultant magnetic field is rotating in a clockwise direction. When the three-phase voltage

completes one full cycle (point 7), the magnetic field has rotated through 3600.

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Figure 299: Three-phase, Y-connected Stator

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3.18.2.3 Rotor Behavior in a Rotating Field

For purposes of explaining rotor movement, let's assume that we can place a bar magnet in the centre of the stator diagrams of Figure 300.

We'll mount this magnet so that it is free to rotate in this area. Let's also assume that the bar magnet is aligned so that at point 1 its south pole

is opposite the large N of the stator field. You can see that this alignment is natural. Unlike poles attract, and the two fields are aligned so that

they are attracting.

Now, go from point 1 through point 7. As before, the stator field rotates clockwise. The bar magnet, free to move, will follow the stator field,

because the attraction between the two fields to exist. A shaft running through the pivot point of the bar magnet would rotate at the same

speed as the rotating field. This speed is known as synchronous speed. The shaft represents the shaft of an operating motor to which the load

is attached. Remember, this explanation is an oversimplification. It is meant to show how a rotating field can cause mechanical rotation of a

shaft. Such an arrangement would work, but it is not used. There are limitations to a permanent magnet rotor.

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Figure 300: Three-phase Rotating Field Polarities and Input Voltages

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3.18.3 Construction, Principles of operation and Characteristics of AC Synchronous Motor

The construction of the synchronous motors is essentially the same as the construction of the salient-pole alternator. In fact, such an

alternator may be run as an ac motor. It consists essentially of an AC armature, normally wound on the stator frame, with a DC field winding

wound on a salient--pole rotor. The AC voltage is applied to the armature and a separate DC supply usually 110 V, is connected to the rotor

through slip rings. In itself, the synchronous motor has no starting torque, and special starting arrangements are necessary. Figure 301

Synchronous motors have the characteristic of constant speed between no load and full load. They are capable of correcting the low power

factor of an inductive load when they are operated under certain conditions. They are often used to drive dc generators. Synchronous motors

are designed in sizes up to thousands of horsepower. They may be designed as either single phase or multiphase machines. The discussion

that follows is based on a three-phase design.

To understand how the synchronous motor works, assume that the application of three-phase ac power to the stator causes a rotating

magnetic field to be set up around the rotor. The rotor is energized with dc (it acts like a bar magnet). The strong rotating magnetic field

attracts the strong rotor field activated by the dc. This results in a strong turning force on the rotor shaft. The' rotor is therefore able to turn a

load as it rotates in step with the rotating magnetic field. It works this way once it's started. However, one of the disadvantages of a

synchronous motor is that it cannot be started from a standstill by applying three-phase ac power to the stator. When ac is applied to the

stator, a high-speed rotating magnetic field appears immediately.

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Figure 301: Revolving-field synchronous motor.

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This rotating field rushes past the rotor poles so quickly that the rotor does not have a chance to get started. In effect, the rotor is repelled first

in one direction and then the other. A synchronous motor in its purest form has no starting torque. It has torque only when it is running at

synchronous speed. A squirrel-cage type of winding is added to the rotor of a synchronous motor to cause it to start. The squirrel cage is

shown as the outer part of the rotor in figure 302. It is so named because it is shaped and looks something like a turnable squirrel cage.

Simply, the windings are heavy copper bars shorted together by copper rings. A low voltage is induced in these shorted windings by the

rotating three-phase stator field. Because of the short circuit, a relatively large current flows in the squirrel cage. This causes a magnetic field

that interacts with the rotating field of the stator. Because of the interaction, the rotor begins to turn, following the stator field; the motor starts.

Figure 302: Self-starting synchronous AC Motor

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FIGURE 303: Action of A Synchronous Motor

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As the name implies the motor runs at the same speed as the rotating field (synchronous speed) and this speed is dependent on the supply

frequency. Reversal of rotation is achieved by changing over any two of the three phase inputs. The machine runs at a speed proportional to

input frequency and is therefore used as the motor in engine speed indicators. With an input of 400Hz from an aircraft system it is a constant

speed machine and so was used to drive the earlier flight data recorders.

3.18.4 Construction , Principles of operation and Characteristics of AC Induction Motor

The induction motor is the most commonly used type of ac motor. Its simple, rugged construction costs relatively little to manufacture. The

induction motor has a rotor that is not connected to an external source of voltage. The induction motor derives its name from the fact that ac

voltages are induced in the rotor circuit by the rotating magnetic field of the stator. In many ways, induction motor is similar to the induction

between the primary and secondary windings of a transformer. Large motors and permanently mounted motors that drive loads at fairly

constant speed are often induction motors. Examples are found in washing machines, refrigerator compressors, bench grinders, and table

saws. The stator construction of the three-phase induction motor and the three-phase synchronous motor are almost identical.

However, their rotors are completely different (see Figure 304 (a)). The induction rotor is made of a laminated cylinder with slots in its surface.

The windings in these slots are one of two types (shown in Figure 304 (b), (c)). The most common is the squirrel-cage winding. This entire

winding is made up of heavy copper bars connected together at each end by a metal ring made of copper or brass. No insulation is required

between the core and the bars. This is because of the very low voltages generated in the rotor bars. The other type of winding contains actual

coils placed in the rotor slots. The rotor is then called a wound rotor.

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Regardless of the type of rotor used, the basic principle is the same. The rotating magnetic field generated in the stator induces a magnetic

field in the rotor. The two fields interact and cause the rotor to turn. To obtain maximum interaction between the fields, the air gap between the

rotor and stator is very small.

Figure 304: Induction motor and the types of ac induction motor rotors.

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Principle of Operation

When a three phase ac supply is applied to the stator we know it creates a rotating magnetic field whose speed is directly proportional to the

input frequency. This rotating magnetic field cuts the copper or aluminium bars and induces an emf into them, this emf produces a current in

the bars which sets up a magnetic field. The rotor field and rotating stator field interact causing the rotor to turn in an attempt to line up the two

magnetic fields. As the stator field is rotating the rotor never quite catches up but follows a little behind.

The basic principle is, assuming the rotating field is stopped for a moment as shown in figure 305

The conductor shown is one of the bars on the rotor showing an induced current direction as shown. Then the motor principle applies and by

Fleming's Left Hand Rule the bar experiences a force acting on it, and the conductor tends to follow the movement of the field

As the rotor follows the field, the relative motion between the two is reduced and therefore the voltage induced into the bars. This reduces the

rotor current and the turning force on the rotor. The rotor speed is automatically adjusted to something less than that of the rotating field ,

otherwise there would be no relative motion, no current and no movement of the rotor.

The difference between the rotor speed and rotating magnetic field speed is called the SLIP SPEED.

The ratio of the slip speed to the rotating magnetic field speed is known as SLIP.

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FIGURE 305: Principle of Induction Motor

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The starting torque of induction motors is poor. On start, the frequency is at its maximum in the rotor and the rotor has low resistance but high

inductance. This causes the rotor current to lag the induced emf by almost 90° so interaction between the rotor field and the rotating field is

poor. To improve the starting torque it is necessary to bring rotor current and emf more into phase. This can be achieved by using aluminium

bars on the rotor instead of copper. This increases the resistance of the rotor bringing voltage and current more into phase and there is

greater interaction between the two fields and better starting torque results.

To reverse the rotation of this machine, change over any two connections of the three phase input and this will cause the rotating field to

reverse direction and consequently the rotor will reverse its rotation.

Speed of the motor for a set number of poles per phase is purely dependent on input frequency, which on an aircraft with Constant Frequency

generating system is set at 400Hz. These motors are used on aircraft as hydraulic pumps, fuel pumps, flap motors.

3.18.5 Two Phase Induction Motor

Note the inputs to the two phases are 900 out of phase with each other. One of these phases is normally called the 'reference phase' and has

a fixed supply fed to it. The other phase is called the 'control phase' which is 900 ahead or 900 behind the reference phase ie has a variable

phase supply to allow for reversal of rotation of the motor. 900 ahead of the reference will produce the opposite direction of rotation of the

magnetic field and thus the motor; so the input to the control phase must be able to produce 1800 phase reversal (900 ahead of reference to

900 behind the reference).

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The speed of the motor once again depends on the input frequency. These motors are used extensively as servo-motors in instruments

systems and other systems on aircraft.

FIGURE 306: Two Phase Induction Motor

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3.18.6 Single-Phase Induction Motors

There are probably more single-phase ac induction motors in use today than the total of all the other types put together. It is logical that the

least expensive, lowest maintenance type of ac motor should be used most often. The single-phase ac induction motor fits that description.

Unlike poly-phase induction motors, the stator field in the single-phase motor does not rotate. Instead it simply alternates polarity between

poles as the ac voltage changes polarity.

Voltage is induced in the rotor as a result of magnetic induction, and a magnetic field is produced around the rotor. This field will always be in

opposition to the stator field (Lenz's law applies). The interaction between the rotor and stator fields will not produce rotation, however. The

double-ended arrow in figure 307, view A shows the interaction. Because this force is across the rotor and through the pole pieces, there is

no rotary motion, just a push and/or pull along this line.

Now, if the rotor is rotated by some outside force (a twist of your hand, or something), the push-pull along the line in figure 307, view A, is

disturbed. Look at the fields as shown in figure 307, view B. At this instant the south pole on the rotor is being attracted by the left-hand pole.

The north rotor pole is being attracted to the right-hand pole. All of this is a result of the rotor being rotated 900 by the outside force. The pull

that now exists between the two fields becomes a rotary force, turning the rotor toward magnetic correspondence with the stator. Because the

two fields continuously alternate, they will never actually line up, and the rotor will continue to turn once started. It remains for us to learn

practical methods of getting the rotor to start.

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There are several types of single-phase induction motors in use today. Basically they are identical except for the means of starting. In this

chapter we will discuss the split-phase and shaded-pole motors; so named because of the methods employed to get them started. Once they

are up to operating speed, all single-phase induction motors operate the same.

Figure 307: Rotor Currents in a Single-Phase AC Induction Motor

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3.18.6.1 Single-phase Induction Motors

Single--phase induction motors are not inherently self-starting, and function subject to a pulsating magnetic field. Consequently, the torque

produced is also pulsating and not constant. With a three-phase motor the field is displaced by 120°. In the case of a single phase supply

there is no phase displacement and hence the rotor has equal and opposing forces acting on it and there will be no movement. The motor is

therefore not self--starting. However, if the rotor is spun mechanically, it will accelerate in the direction it was turned, until a speed is reached

which is just below that of synchronous speed. The creation of an artificial phase displacement is therefore required. This is much the same

way as a three--phase induction motor operates.

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NOTES

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3.18.6.2 Split-phase Induction Motor

This type of machine can be tailored to be self-starting by adding another winding, displaced exactly 900 electrically on the stator and

connected in parallel with the original winding. Known as a split-phase induction motor; the two windings are wired in parallel, producing a two

phase rotating magnetic field due to a difference of impedance. In practice, the 'start' winding has a higher resistance than the 'run' winding

and is taken out of circuit automatically by means of a centrifugal switch or timed relay. This is illustrated in Figure 308.The start winding in

general practice has a smaller gauge wire for higher resistance and low reactance. The main winding is of thick wire, with a low resistance and

high reactance. As the start and run windings are not pure inductors but have an element of resistance in them owing to the natural resistance

of the coils, it causes the current flow to be less than 900 out of phase with the voltage. In practice this type of motor will develop a phase

differential of about 400 between the current in the start windings and the current in the run windings. This results in poor starting torque and a

slight drop in speed when load is applied. In this motor the start winding is much thinner than the run winding.

Consequently, should the centrifugal switch fuse, or not function, the starting winding will be permanently connected in the circuit during

normal operation. Although in principle this does not affect motor operation significantly, it must be realized that this winding is designed for

intermittent operation (for start-up only). Therefore, when permanently connected in the circuit due to switch failure, it will quickly heat up and

raise the motor temperature excessively and eventually burn out the windings. The split-- phase induction motor is employed when the starting

load is small or there is no load at all, as, for example, in large domestic appliances such as vacuum cleaners, or workshop pedestal drills.

The split--phase motor is factory connected, and such its direction of rotation is fixed (counter--clockwise when viewed from the opposite end

of the shaft extension). To reverse the direction of rotation it is necessary to reverse the connection to the starting winding or the run winding

but not both together.

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Figure 308: Single-Phase Induction Motors-Circuit Diagrams Proprietary of




3.18.6.3 Split-Phase Induction Motors

One type of induction motor, which incorporates a starting device, is called a split-phase induction motor. Split-phase motors are designed to

use inductance, capacitance, or resistance to develop a starting torque. The principles are those that you learned in your study of alternating

current.

3.18.6.4 Capacitor-Start

The first type of split-phase induction motor that will be covered is the capacitor-start type. Figure 309 shows a simplified schematic of a

typical capacitor-start motor. The stator consists of the main winding and a starting winding (auxiliary). The starting winding is connected in

parallel with the main winding and is placed physically at right angles to it. A 90-degree electrical phase difference between the two windings

is obtained by connecting the auxiliary winding in series with a capacitor and starting switch.

When the motor is first energized, the starting switch is closed. This places the capacitor in series with the auxiliary winding. The capacitor is

of such value that the auxiliary circuit is effectively a resistive-capacitive circuit (referred to as capacitive reactance and expressed as Xc). In

this circuit the current leads the line voltage by about 450 (because X C about equals R). The main winding has enough resistance-inductance

(referred to as inductive reactance and expressed as XL) to cause the current to lag the line voltage by about 450 (because X L about equals

R). The currents in each winding are therefore 900 out of phase - so are the magnetic fields that are generated. The effect is that the two

windings act like a two-phase stator and produce the rotating field required to start the motor.

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When nearly at full speed is obtained, a centrifugal device (the starting switch) cuts out the starting winding. The motor then runs as a plain

single-phase induction motor. Since the auxiliary winding is only a light winding, the motor does not develop sufficient torque to start heavy

loads. Split-phase motors, therefore, come only in small sizes.

Figure 309: Capacitor-start, AC Induction Motor

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3.18.6.5 Resistance-Start

Another type of split-phase induction motor is the resistance-start motor. This motor also has a starting winding (shown in Figure 310) in

addition to the main winding. It is switched in and out of the circuit just as it was in the capacitor-start motor. The starting winding is positioned

at right angles to the main winding. The electrical phase shift between the currents in the two windings is obtained by making the impedance

of the windings unequal. The main winding has a high inductance and a low resistance. The current, therefore, lags the voltage by a large

angle. The starting winding is designed to have a fairly low inductance and a high resistance. Here the current lags the voltage by a smaller

angle. For example, suppose the current in the main winding lags the voltage by 700.

The current in the auxiliary winding lags the voltage by 400. The currents are, therefore, out of phase by 300. The magnetic fields are out of

phase by the same amount. Although the ideal angular phase difference is 900 for maximum starting torque, the 30-degree phase difference

still generates a rotating field. This supplies enough torque to start the motor. When the motor comes up to speed, a speed-controlled switch

disconnects the starting winding from the line, and the motor continues to run as an induction motor. The starting torque is not as great as it is

in the capacitor-start.

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Figure 310: Resistance-Start AC Induction Motor

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3.18.6.6 Shaded-Pole Induction Motors

The shaded-pole induction motor is another single-phase motor. It uses a unique method to start the rotor turning. Constructing the stator in a

special way produces the effect of a moving magnetic field. This motor has projecting pole pieces just like some dc motors. With reference to

Figure, each of the poles is split into two with one half fitted with a copper or aluminium ring (shading). The rotor is of the normal induction

motor design. As the single-phase supply starts to rise flux builds up in the pole pieces and there is a flux path (φ1) across the pole pieces.

The build up of flux in the other half pole pieces cuts the copper ring, and emf is induced whose field opposes the build up of flux (Lenz's Law)

in the shaded portion of the pole pieces.

As the supply falls to zero the field collapse φ1 dies away. However, this change of flux in the shaded portion induces an emf in the shading

ring and this time the induced emf tries to keep the original flux from decaying in the shaded portion of the pole pieces and the field φ2 is

formed. The next half cycle this is repeated creating not a rotating field more of a rocking field between φ1 and φ2. In addition, a copper strap

called a shading coil surrounds portions of the pole piece surfaces. A pole piece with the strap in place is shown in Figure 311.

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Figure 311: Shaded-Pole Induction Motors

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The strap causes the field to move back and forth across the face of the pole piece. Note the numbered sequence and points on the

magnetization curve in the figure. As the alternating stator field starts increasing from zero (1), the lines of force expand across the face of the

pole piece and cut through the strap. A voltage is induced in the strap. The current that results generates a field that opposes the cutting

action (and decreases the strength) of the main field. This produces the following actions: As the field increases from zero to a maximum at

900, a large portion of the magnetic lines of force are concentrated in the un-shaded portion of the pole (1).

At 900 the field reaches its maximum value. Since the lines of force have stopped expanding, no emf is induced in the strap, and no opposing

magnetic field is generated. As a result, the main field is uniformly distributed across the pole (2). From 900 to 1800 the main field starts

decreasing or collapsing inward. The field generated in the strap opposes the collapsing field. The effect is to concentrate the lines of force in

the shaded portion of the pole face (3).

You can see that from O0 to 1800, the main field has shifted across the pole face from the un-shaded to the shaded portion. From 1800 to 3600,

the main field goes through the same change as it did from O0 to 1800; however, it is now in the opposite direction (4). The direction of the field

does not affect the way the shaded pole works. The motion of the field is the same during the second half-cycle as it was during the first half of

the cycle. The motion of the field back and forth between shaded and un-shaded portions produces a weak torque to start the motor.

Because of the weak starting torque, shaded-pole motors are built only in small sizes. They drive such devices as fans, clocks, blowers, and

electric razors. As the field is not fully rotating, the starting torque of this motor is poor it is used for light loads only. Speed again is determined

by input frequency. Reversal of rotation cannot be achieved unless the shading rings are transferred to the other half of the pole pieces which

is not a practical proposition. They are used in some engine pressure indication instruments.

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Figure 312: Shaded poles as used in shaded-pole ac induction motors

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3.18.7 Speed of Single-Phase Induction Motors

The speed of induction motors is dependent on motor design. The synchronous speed (the speed at which the stator field rotates) is

determined by the frequency of the input ac power and the number of poles in the stator. The greater the number of poles, the slower the

synchronous speed. The higher the frequency of applied voltage, the higher the synchronous speed. Remember, however, that neither

frequency nor numbers of poles are variables. The manufacturer fixes them both. The relationship between poles, frequency, and

synchronous speed is as follows:

where n is the synchronous speed in rpm, f is the frequency of applied voltage in hertz, and p is the number of poles in the stator. Let's use an

example of a 4-pole motor, built to operate on 60 hertz. The synchronous speed is determined as follows:

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Common synchronous speeds for 60-hertz motors are 3600, 1800, 1200, and 900 rpm, depending on the number of poles in the original

design. As we have seen before, the rotor is never able to reach synchronous speed. If it did, there would be no voltage induced in the rotor.

No torque would be developed. The motor would not operate. The difference between rotor speed and synchronous speed is called slip. The

difference between these two speeds is not great. For example, a rotor speed of 3400 to 3500 rpm can be expected from a synchronous

speed of 3600 rpm.

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3.18.8 Speed Control of AC Motor

Single--phase Motors

Single--phase speed control is generally confined to split phase capacitor aided motors where automatic mechanical switching to isolate the

start winding is not required. Motors employed in such circuits are designed with high impedance windings to limit the current at lower speeds.

Both series and shaded pole machines are also ideally suited for speed control and examples may be drawn from the modern record deck

and the hand--held electric drill. For obvious reasons, speed control is not suitable for all types of machines but for the machines which are

suited, control may be gained by use of the following ways:

• Series impedance control (linear resistance)

• Solid state linear control (electronic)

• Autotransformer control (electro--mechanical

Figure 313, detail a) illustrates schematically how speed control is effected by means of an autotransformer. The transformer is constructed

from a single length of copper wire wound many times around a laminated iron core. Throughout its length, output tapping V1 to V4 provides

steps either to increase or to decrease the voltage supplied to the motor. These, in turn, are connected mechanically to an adjustable voltage

selector device and the complete assemblage is wired in series formation with the connected load. Should the motor fail to respond to the

minimum voltage range, the output tapings may be adjusted to a higher value.

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Advantages gained from using this method of speed control include

• reduced starting current

• torque proportional to voltage applied

• smoother starting sequence.

Disadvantages are

• higher installation costs

• regular maintenance required

• only certain types of motors are suitable

FIGURE 313 (A): AC Motor Speed Control

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Speed Control of Induction and Synchronous Motors

Historically both induction and synchronous motors have been considered to be single--speed machines because the synchronous (rotating

magnetic field) speed has always been fixed by the supply frequency, which is constant. Pole changing motors have been used to give some

control of speed, but continuous control is not possible with this method.

The speed of a wound--rotor induction motor can be reduced by adding resistance to the rotor circuit via the slip rings, but this is an expensive

and inefficient method of speed control. However, starting torque is higher although the wound rotor motor is inherently less robust than the

cage--rotor type. Excluding this method, the speed of an induction motor will be only slightly lower than synchronous speed, so some running

speeds are impossible at normal power frequencies

The traditional single--speed role of the induction motor has been changed by the use of modern power electronics. Using such methods, it is

possible to rectify the three--phase supply to give a direct current, and then to invert this direct supply to provide a three--phase system of any

required frequency.

Since the synchronous speed of the motor, and hence its running speed, are directly related to supply frequency, electronic frequency control

will also give speed control (see Figure 313, detail b)). In some cases battery--driven vehicles use this method, the DC battery supply being

inverted to the variable--frequency supply needed to give speed control. Since the induction motor is far more rugged and is likely to need less

maintenance than its direct--current counterpart, the advantage is clear.

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FIGURE 313 (B): AC Motor Speed Control

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a) dcam part 66 - module 3

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