INDUCTANCE OF AN INDUCTORCompiled and presented by:D. Nedrick

WHAT IS AN INDUCTOR?An inductor is a coil of wire. Two types of inductors are air core and iron core

Induced Electromotive Force (EMF)When a conductor cuts, or is cut by, magnetic lines of force, an e.m.f. (voltage) is induced into that conductor

Relative motionWhen a wire is moved across a magnetic field, there is a relative motion between the wire and the magnetic field.When a magnetic field is moved past a stationary wire, there is also relative motion.In either case, the relative motion results in an induced voltage in the wire.

The induced voltage due to the relative motion between the conductor and the magnetic field when the motion is perpendicular to the field is given by SummaryInduced voltage B = flux density in T l = length of the conductor in the magnetic field in m v = relative velocity in m/s (motion is perpendicular) vind = Blv

Faraday experimented with generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors:SummaryFaradays lawVoltage is indicated only when magnet is moving.

Faraday also experimented generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors:SummaryThe rate of change of the magnetic flux with respect to the coil.Faradays lawVoltage is indicated only when magnet is moving.

Faradays LawThe magnitude of an electromagnetic force induced in a circuit is proportional to the rate of change of the magnetic flux that cuts across the circuit.

INDUCTANCEInductance is the ability of a conductor to produce an induced voltage also called counter EMF, back EMF when the current varies. The symbol for inductance is L, and the unit is the Henry (H). An inductor has an inductance of 1 henry (H) if a current changing in it at the rate of 1 ampere per second induces an e.m.f. of 1 volt. If the induced e.m.f. is 2 V, the inductance is 2 H.

INDUCTANCE ContdThe millihenry (1 mH = 10-3 H) and the micro henry (1 H = 10-6 H) are more convenient sub-units.

Self Induced EMFSelf-induced e.m.f. is the e.m.f. which is induced in a coil due to the changing flux in the coil cutting the conductors of the coil. This self-induced e.m.f. is in opposition to the voltage producing it. CHANGING CURRENT FLOWING IN COIL CAUSES FIELD TO GROW AND COLLAPSE

Self Inductance ContdThe self-induced e.m.f. tends to limit the current in the circuit: it chokes the current flowing in a coil when it is carrying an alternating, or changing, current. The greater the change in the current the greater the e.m.f.

Lenz LawAn induced electromotive force (voltage) in any circuit is always in a direction in opposition to the current that produced it.

An induced electromotive force generates a current that induces a counter magnetic field that opposes the magnetic field generating the current.

Factors affecting inductanceThere are four basic factors of inductor construction determining the amount of inductance created. These factors all dictate inductance by affecting how much magnetic field flux will develop for a given amount of magnetic field force (current through the inductors wire coil):

Factors That Affect the Inductance of an InductorThe number of turns of wire with which the coil is wound The cross sectional area of the coil It has a core of magnetic material.Length of the coil

In DC CircuitsWhen a dc current increases in a coil from zero to its steady value, the accompanying magnetic field builds up to its final shape.

During the process the field is changing and induced an EMF in the coil itself which opposes the change causing it, i.e. the rising current that is trying to establish the field.

In DC Circuit Contd

When the current is switched off, the collapsing field caused by the collapsing current (and field). It tries to keep the current flowing longer, so delaying its fall to zero.

Time ConstantThe time constant can also be used as a measure of the time taken by the current to rise or fall in a circuit containing inductance (L) and resistance (R). The time required for the current in a series RL circuit to increase to 63.2 % of its maximum (steady state) value is known as the RL Time Constant of the circuit. Time constant is given in seconds

How long Does It Take For Current Rise To Its Maximum? It is expressed as the formula: t = L/R where t = time constant, in seconds L = inductance, in Henrys R = resistance, in ohmsIt takes 5 time constants to reach 100% of its maximum value

Example:Calculate the time constant for a circuit having an inductance of 5H and a resistance of 100?T = L/R = 5/100 = 0.05sb. How long will it take for the current to rise to its maximum? IMax = 5 x t = 5 x 0.05s = 0.25s

ActivityCalculate the time constant of an inductor of 30mH if it is connected in series with a 10 ohm resistor. b) how long will it take for the current to reach its maximum value?Calculate the value resistor that must be connected in series with a 50mH inductor to delay the rise of current to its maximum to 0.0001 sec.

Energy Stored by an Inductor It can be shown that the energy W stored in the magnetic field of an inductor of inductance L carrying a current I since this magnetic field can attract and repel magnetic materials.Energy stored in its magnetic field can be found by using the formula: W = X L X I2 Where W = Energy or Work done in Joules, L = Inductance in Henrys and I = Current in Amperes.

ExampleCalculate the energy stored in the magnetic field of an inductor of inductance 40 mH when 7.5Amps flows through it. W = X L X I2 = x 0.04H x 7.5A2 = 1.125 Joules

ActivityCalculate the amount of energy stored in the magnetic field of an inductor of 100mH if 2mA of current flows through it.What value current will cause an inductor of value 150mH to stored 300mJ?

Inductors connected in series A series circuit is a circuit in which the current has only one path. In a series circuit, all of the current passes through each of the components in the circuit.

If the inductors are shielded, or far enough apart to prevent mutual inductance, the total inductance of the circuit is cumulative

Magnetic shield used to protect an inductor from stray magnetic fields

MAGNETIC SHIELD

SHIELDED COMPONENT

External magnetic field

Path of flux line through shield material

Calculating Total InductanceLT = L1 + L2 + L3 . . .where LT is the total inductance in the circuit, and L1 through L3 . . . are the inductance ratings of the individual inductors in the circuit. LT = 50 + 40 + 20 LT = 110 H

Inductors Connected in ParallelA parallel circuit is a circuit in which components are arranged so that the path for the current is divided. If the inductors are shielded, or far enough apart to prevent mutual inductance, the total inductance of the circuit can be calculated using the following formula:

Example 1 = 1 1 1 LT L1 + L2 + L31 1 1 1LT = 5 + 15 + 30

1/LT = 0.2 + 0.066 + 0.0331/LT = 0.299LT = 1/0.299LT = 3.344 mH

Inductive ReactanceThe effect of self-induction in a coil is to oppose any change in current flow in the coil. For example, when voltage is applied to a coil, current begins to flow in the coil. This current induces a magnetic field around it. As the field is expanding, a counter voltage, sometimes called back voltage, is generated in coil. This back voltage opposes the main current flow. This opposition to current flow is called inductive reactance and is measured in ohms.

Inductive Reactance ContdThe amount of inductive reactance in a circuit depends on the frequency and amount of alternating current, and the amount of inductance. Calculated using the following formula: XL = 2fLwhere XL is inductive reactance in ohms, 2 is a calculus derived constant that is normally rounded off to 6.28, f is the frequency of the applied alternating current in hertz, and L is the inductance of the circuit in henries.

ExampleWhat current will flow in an inductance of 0.1H when an alternating supply of 200V, 50c/s is applied across it?IL = V/xL and XL = 2fLXL = 2 x 3.14 x 50 x 0.1 = 31.4IL = V/xL = 200V/ 31.4 = 6.369A

ActivityWhat current will flow in an inductance of 0.2H when connected across a 100V, 50Hz supply?

Application of InductanceThe properties of inductors make them very useful in various applications. For example, inductors oppose any changes in current. Therefore, inductors can be used to protect circuits from surges of current. Inductors are also used to stabilize direct current and to control or eliminate alternating current. Inductors used to eliminate alternating current above a certain frequency are called chokes.

Applications ContdGenerators One of the most common uses of electromagnetic inductance is in the generation of electric current Radio Receivers Inductors can be used in circuits with capacitors to generate and isolate high-frequency currents. For example, inductor coils are used with capacitors in tuning circuits of radios.

Application ContdMetal Detectors Metal detectors contain one or more inductor coils. When metal passes through the magnetic field generated by the coil or coils, the field induces electric currents in the metal. These currents are called eddy currents. These eddy currents in turn induce their own magnetic field, which generates current in the detector that powers a signal indicating the presence of the metal.