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CHAPTER 19

Current, Resistance and Direct Current (DC) Circuits

Goals for Chapter 19

• To understand the concept of current.

• To study resistance and Ohm’s Law.

• To observe examples of electromotive force and circuits to learn Ohm’s Law’s application.

• To calculate the energy and power in electric circuits.

• To study the similarity and differences in the combination of resistors in parallel and those connected in series.

• To apply Kirchhoff’s Rules to combinations of resistors.

• To observe and understand devices which measure electricity in circuits.

• To combine resistors and capacitors then calculate examples of the results.

Introduction– Electric currents flow

through light bulbs.

– Electric circuits contain charges in motion.

– Circuits are at the heart of modern devices such as computers, televisions, and industrial power systems.

Electric Current

– A current is any motion of charge from one region to another. Current is defined as

I = ∆Q/ ∆ t.

Unit: 1 Coulomb/sec = 1 ampere (A)

– An electric field in a conductor causes charges to flow

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Current defined

– A current can be produced by positive or negative charge flow.

– Conventional current is treated as a flow of positive charges.

– The moving charges in metals are electrons

19.2 Resistance; Ohm’s Law

• The resistance of an object in a circuit may be calculated from the voltage and current in a closed circuit.

• Commercial resistors carry coded labels.

Tolerance CodeNone 20%Silver 10%Gold 5%

• This resistor has a resistance of 5.7 kΩ with a tolerance of ±10%.

Resistance

When the potential difference V between the ends of a conductor is proportional to the current I in the conductor, the ratio V/I is called the resistance of the conductor:

UNITS: OHM

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OHM’S LAW

If V is directly proportional to I (that is, if R is constant), the equation

V = IR is called Ohm’s law.

Electric components obeying Ohm’s law are said to be Ohmic devices…

Resistivity

Resistivity

Temperature dependence of Resistance

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Resistivity and temperature

• Resistivity depends on temperature.

• Table shows some temperature coefficients of resistivity.

Ohmic and nonohmic resistors 19.3 Electromotive force

The potential difference can draw an analogy from a waterfall.

• An electromotive force (emf) makes current flow. In spite of the name, an emf is not a force.

• The figures below show a source of emf in an open circuit (left) and in a complete circuit (right).

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Electricity flowing – Example 19.4A patient is undergoing open heart surgery. A sustained current as small as 25 μA passing

through the heart can be fatal. Assume that the heart has a constant resistance of 250 Ω. Determine

the minimum voltage that poses a danger to the patient.

Supporting Example 19.4

Supporting Analysis 19.2

Note: even a small voltage when applied directly to the heart can be fatal. Most surgeries require that patients sometimes be “grounded” to prevent unwanted voltages to the heart.

Electricity flowing – Example 19.4

Note: current drawn depends on the resistance of the bulb.

Each circuit may be drawn symbolically.

Each device will be represented by brief symbols. The utility of the method becomes clear as soon as soon as you must represent a car or a blender. There are too many parts to draw them as they actually appear.

Internal resistance in an emf source

• Real sources of emf actually contain some internal resistance r.

• The terminal voltage of an emf source is

Vab = ξ – Ir.

The potential Vab is called terminal voltage and is less than the emf because of the term Ir representing the potential drop across the internal resistance r

•The terminal voltage of the 12-V battery shown at the right is less than 12 V when it is connected to the light bulb.

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Internal resistance in an emf source

Note: current in external circuit is still determined by Vab = IR so

It follows:

Several examples of circuits with different element s

Refer to worked examples 19.5, 19.6, 19.7. The same basic elements are arranged on slightly different parallel or series combinations. Notice the dramatic differences.

Several examples of circuits with different element s

Potential drops and rise in a circuit

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19.4 Energy and power in electric circuits

– The rate at which energy is delivered to (or extracted from) a circuit element is P = VabI.

Work done on charge:

Rate at which work is done:

UNITS:

Power delivered to a Pure resistance

The power delivered to a pure resistor is

P = I 2 R = Vab2/R.

19.5 Resistors in series and/or parallel

Like capacitors in the previous chapter, resistors can be connected end-to-end (series) or simultaneously (parallel).

Resistors in series

Equivalent resistance of resistors in series equals the sum of their individual resistances:

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Resistors in parallel Kirchhoff’s Rules – Figure 19.23

Many actual networks cannot be described with simple series-parallel combinations. What then? One method is described by Gustav Kirchhoff in the 1800s.

Kirchhoff’s Rules I

• A junction is a point where three or more conductors meet.

• A loop is any closed conducting path.

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Kirchoff’s Rules II• Kirchhoff’s junction rule: The algebraic sum of the currents

into any junction is zero: ΣI = 0. (See Figure 26.7 below.)

• Kirchhoff’s loop rule: The algebraic sum of the potential differences in any loop must equal zero: ΣV = 0.

Sign convention for the loop rule

• Figure below shows the sign convention for emfs and resistors.

Junction rule at a:

1A – I +2A = 0 so I = 3A

Find r: Loop rule (loop 1) start at pt. a

12V -Ir -2A(3Ω) = 0 but I = 3A

so r = 2ΩTo find ε: loop rule (loop 2): start at pt. a

-ε + (1A)(1Ω) – 2A (3 Ω) = 0 so ε = -5V.

Negative means actually polarity of emf is reversed.

Check: use loop 3: start at pt. a

ε + 12V – Ir – (1A)(1Ω) = 0 so ε = -5V.

Negative means actually polarity of emf is reversed.

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Recharging situations – Figures 19.28 and 19.29

Rechargeable batteries and jump-starting a dead car battery contain some complexities. Refer to Examples 19.10 and 19.11.

19.8 Electrical measuring intruments

• A d’Arsonval galvanometer measures the current through it (see Figures below).

• Many electrical instruments, such as ammeters and voltmeters, use a galvanometer in their design.

D’Arsonval galvanometer

Ammeters and voltmeters• An ammeter measures

the current passing through it. (ideal ammeter have zero resistance so it does not affect the circuit while connected to it)

• A voltmeter measures the potential difference between two points. An ideal voltmeter have infinite resistance so no current flows through it…)

• Figure at the right shows how to use a galvanometer to make an ammeter and a voltmeter.

Ammeters and voltmeters in combination• An ammeter and a voltmeter may be used together to

measure resistance and power. Figure below illustrates how this can be done.

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Ohmmeters and potentiometers• An ohmmeter is designed to measure resistance. (See

Figure below left.)

• A potentiometer measures the emf of a source without drawing any current from the source. (See Figure below right.)

19.9 RC Circuits

ε = iR + q/c

Charging a capacitor• The time constant is τ = RC.

Discharging a capacitor

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Power distribution systems

Household wiring• Figure at the right shows why it is safer to use a

three-prong plug for electrical appliances.