Chapter 18: Direct-Current CircuitsSource of EMF

What is emf? • A current is maintained in a closed circuit by a source of emf. The term emf was originally an abbreviation for electromotive force but emf is NOT really a force, so the long term is discouraged.

• Among such sources are any devices (batteries, generators etc.) that increase the potential energy of the circulating charges.• A source of emf works as “charge pump” that forces electrons to move in a direction opposite the electrostatic field inside the source.

Homework assignment : 9,16,28,41,50

Maintaining a steady current and electromotive force• When a charge q goes around a complete circuit and returns to its starting point, the potential energy must be the same as at the beginning.• But the charge loses part of its potential energy due to resistance in a conductor.• There needs to be something in the circuit that increases the potential energy.• This something to increase the potential energy is called electromotive force (emf).• Emf () makes current flow from lower to higher potential. A device that produces emf is called a source of emf.

Units: 1 V = 1 J/C

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source of emf

ab-If a positive charge q is moved from b to a inside the source, the non-electrostatic force Fn does a positive amount of work Wn=q on the charge.-This replacement is opposite to the electrostatic force Fe, so the potential energy associated with the charge increases by qV. For an ideal source of emf Fe=Fn

in magnitude but opposite in direction. -Wn=q=qVab, so Vab==IR for an ideal source.

Source of EMF

Source of EMF Internal resistance

• Real sources in a circuit do not behave ideally; the potential difference across a real source in a circuit is not equal to the emf.

Vab=– Ir (terminal voltage, source with internal resistance r)

• So it is only true that Vab= only when I=0. Furthermore,

–Ir = IR or I = / (R + r)

Source of EMF Real battery

br

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−

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• Real battery has internal resistance, r. • Terminal voltage, ΔVoutput = (Va −Vb) = − I r.

•

a b

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Source of EMF Potential in a resistor circuit in realistic situation

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Example 1:

Resistors in Series and Parallel

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Example: (cont’d)

Kirchhoff’s Rules

Introduction

Loop 1

Loop 2i i

i

ii1

i2

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• Many practical resistor networks cannot be reduced to simple series-parallel combinations (see an example below).• Terminology:

-A junction in a circuit is a point where three or more conductors meet.-A loop is any closed conducting path.

junction

junction

Kirchhoff’s Rules Kirchhoff’s junction rule

• The algebraic sum of the currents into any unction is zero:

junction any at 0I

Kirchhoff’s Rules Kirchhoff’s loop rule

• The algebraic sum of the potential differences in any loop, including those associated with emfs and those of resistive elements, must equal zero. loopany for 0V

Kirchhoff’s Rules Rules for Kirchhoff’s loop rule

junction any at 0I

loopany for 0V

Kirchhoff’s Rules Rules for Kirchhoff’s loop rule (cont’d)

Kirchhoff’s Rules Solving problems using Kirchhoff’s rules

Kirchhoff’s Rules Example 1

Kirchhoff’s Rules Example 1 (cont’d)

Kirchhoff’s Rules Example 1 (cont’d)

Find all the currents including directions.

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Kirchhoff’s Rules Example 2

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R-C Circuits Charging a capacitor

R-C Circuits Charging a capacitor (cont’d)

R-C Circuits Charging a capacitor (cont’d)

R-C Circuits Charging a capacitor (cont’d)

R-C Circuits Charging a capacitor (cont’d)

R-C Circuits Discharging a capacitor

R-C Circuits Discharging a capacitor (cont’d)

R-C Circuits Discharging a capacitor (cont’d)

R-C Circuits Example 18.6 : Charging a capacitor in an RC circuitAn uncharged capacitor and a resistorare connected in series to a battery.If =12.0 V, C=5.00 F, and R=8.00x105 , find (a) the time constantof the circuit, (b) the maximum chargeon the capacitor, (c) the charge on thecapacitor after 6.00 s, (d) the potentialdifference across the resistor after6.00 s, and (e) the current in the resistorat that time.(a) s 4.00F) 10)(5.00 1000.8( -65 RC

(b) From Kirchhoff’s loop rule: 0 RCbat VVV

C 0.600 CQIRcq

when I=0, q=Q at max.

R-C Circuits Example 18.6 : Charging a capacitor in an RC circuitAn uncharged capacitor and a resistorare connected in series to a battery.If =12.0 V, C=5.00 F, and R=8.00x105 , find (a) the time constantof the circuit, (b) the maximum chargeon the capacitor, (c) the charge on thecapacitor after 6.00 s, (d) the potentialdifference across the resistor after6.00 s, and (e) the current in the resistorat that time.(c) C 6.46)1C)( 0.60()1( s s/4.00 00.6/ eeQq t

(d) V 32.9/ CqVC

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