Chapter 26 Direct-Current Circuits

• Study resistors in series and parallel • Consider Kirchoff’s Rules• The design and use of electronic measuring

instruments• R-C circuits• The applications of circuits in household wiring

Chapter 26 2

Resistors in Series

Resistors in Series and Parallel

Figure 26-1321 RRRReq

321 IRIRIRVVVV ybxyaxab

eqab IRRRRIV )( 321

Resistors in Parallel

Figure 26-1

321321 R

V

R

V

R

VIIII ababab

eqabab RV

RRRVI

1111

321

321

1111

RRRReq

Series and parallel combination resistors

– Consider Problem-Solving Strategy 26.1.

– Follow Example 26.1 guided by Figure 26.3 below.

– Follow Example 26.2.

Kirchoff’s Rules I—junctions• The algebraic sum of the currents into any junction is zero.

Chapter 26 5

Kirchhoff’s LawsKirchhoff’s Current Law

Figure 26-7

Figure 26-8

ProofCharge can’t build up at the junction.

Kirchhoff’s Current Law - Example

Kirchoff’s Rules II—loops

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

7

03311111 RIRIrI

02233222 RIRIrI

0)( 32111111 RIIRIrI

0)( 22321222 RIRIIrI

Loop 1

Loop 2

Loop 1

Loop 2

Kirchhoff’s Voltage Law – Two Loop Example

Chapter 26 8

Kirchhoff’s Laws - A Single Loop Circuit

Example 26-3

Figure 26-10

a) Solve for I

b) Solve for Vab

c) Solve for power output of the emf of each battery

Kirchoff’s Rules III—examples and strategy

• Read through Problem-Solving Strategy 26.2. Figure 26.9 illustrates this strategy.

• Refer to Example 26.3, illustrated by Figure 26.10.

Kirchoff’s Rules IV—examples• Refer to Example 26.4, illustrated by Figure 26.11.• Consider Example 26.5.• Refer to Example 26.6, illustrated by Figure 26.12.• Review Example 26.7.

Chapter 26 11

R-C Circuits (Chapter 26, Sec 4)Charging a Capacitor

Figure 26-20 Figure 26-21

C

qvbc

Time ConstantRC (26-14)

0.63 Qf

0.37 I0

iRvab

bcab vv

R

vi ab

Cvq bc

R

C

Chapter 26 12

R-C Circuits (Chapter 26, Sec 4)Discharging a Capacitor

Figure 26-22

Figure 26-23

Time Constant

RC (26-14)

C

qvbc

iRvab

bcab vv 0

R

vi ab

Cvq bc

bcab vv

RC

Q0

D’Arsonval’s galvanometer• We’ll call it simply “meter” henceforth.• The meter is a coil of wire mounted next to a permanent

magnet. Any current passing through the coil will induce magnetism in the coil. The interaction of the new electromagnetism and the permanent magnet will move the meter indicator mounted to the coil.

The Ammeter and Voltmeter • The ammeter (sometimes prefixed with milli or micro because the

currents to be measured are routinely thousandths or millionths of an ampere) may be used to measure current OR voltage. A shunt resistor makes this conversion as shown below in Figure 26.15.

• Consider Example 26.8 to follow a current example. Consider Example 26.9 to follow a voltage example.

Ammeter Design

Ifs = 1 mA Rc = 50 ohm

Ia = 50 mA Rsh = ?

Vab = Vab

Ifs Rc = (Ia – Ifs) Rsh

Voltmeter Design

Ifs = 1 mA Rc = 20 ohm

Vab = 10 v Rs = ?

Vab = Ifs (Rc + Rs )

Solve for Rs

Rs= (Vab - Ifs Rc)/ Ifs

Ohmmeters and digital multimeters• An ohmmeter is designed specifically to measure resistance. • Refer to Figure 26.17 and Figure 26.18 below to see an

ohmmeter wiring diagram and a photograph of a digital multimeter. The multimeter can measure current, voltage, or resistance over a wide range.

18

Power Distribution Systems

Black

White

120 v

240-V line black, red Neutral

One phase of the 240-V line

We buy energy from the Power Company, not powerkW x time = watt-seconds = Joules1 kWh = (1000W) (3600 s ) = 3.6 x 106 W-s = 3.6 x 106 J

Fuses, circuit breakers, and GFI• A fuse will melt and a breaker will

open the circuit if maximum current is reached. See Figure 26.26.

• GFI stops further current flow when a sudden drop in resistance indicates that someone has offered a new path to ground. I don’t know if it will save this worker we see in Figure 26.27 who didn’t use a grounded drill.

The wiring diagram for a typical kitchen– Consider Figure 26.28 below.– Follow Example 26.14.

21

 

Residential Commercial1 Industrial1

Census Division

and State

  Nov-07 Nov-06 Nov-07 Nov-06 Nov-07 Nov-06

New England 16.18 15.58 14.19 13.78 12.75 11.44

Connecticut 18.33 16.92 14.91 14.24 12.46 12.08

Maine 15.42 14.06 13.04 11.91 12.12 9.45

Massachusetts 15.69 15.74 14.38 14.22 14.01 12.53

New Hampshire 14.8 14.22 13.26 13.28 12.32 10.78

Rhode Island 14.62 14.34 13.2 12.81 12.18 12.28

Vermont 14.35 13.57 12.36 11.84 8.79 8.31

U.S. Total 10.69 10.18 9.6 9.24 6.22 6.04

Average Retail Price of Electricitycents per kilowatt-hour