Direct-Current Circuits
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1 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
2 Resistors in Series and Parallel Resistors in Series Figure 26-1 V ab Vax Vxy Vyb IR1 IR2 IR3 ab I( R1 R2 R3 ) IR eq R eq R1 R2 R3 V Resistors in Parallel Figure 26-1 Vab Vab Vab I I1 I2 I3 R1 R2 R I V ab Vab R1 R2 R3 R R R R R eq eq Chapter 26 2
3 Series and parallel combination resistors Consider Problem-Solving Strategy Follow Example 26.1 guided by Figure 26.3 below. Follow Example 26.2.
4 Kirchoff s Rules I junctions The algebraic sum of the currents into any junction is zero.
5 Chapter 26 5
6 Kirchhoff s Current Law Kirchhoff s Laws Figure 26-7 Kirchhoff s Current Law - Example Proof Charge can t build up at the junction. Figure 26-8 Chapter 26 6
7 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.
8 Kirchhoff s Laws - A Single Loop Circuit Example 26-3 a) Solve for I b) Solve for V ab c) Solve for power output of the emf of each battery Figure Chapter 26 8
9 9 Figure R I R I r I R I R I r I 0 ) ( R I I R I r I 0 ) ( R I R I I r I Loop 1 Loop 2 Loop 1 Loop 2 Kirchhoff s Voltage Law Two Loop Example
10 Apply the junction rule to a point a reduces the number of unknown currents from three to two Chapter 26 10
11 Kirchoff s Rules III examples and strategy Read through Problem-Solving Strategy Figure 26.9 illustrates this strategy. Refer to Example 26.3, illustrated by Figure
12 Chapter 26 12
13 Chapter 26 13
14 Chapter 26 14
15 Kirchoff s Rules IV examples Refer to Example 26.4, illustrated by Figure Consider Example Refer to Example 26.6, illustrated by Figure Review Example 26.7.
16 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.
17 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
18 Chapter 26 18
19 Chapter 26 19
20 Ohmmeters and digital multimeters An ohmmeter is designed specifically to measure resistance. Refer to Figure and Figure 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.
21 Chapter 26 21
22 Capacitor Charging Solution qt () V0 I( t) R 0 C dq SubstitutingI dt dq q() t V0 R 0 dt C dq V0 q dt R RC dq dt q V C RC q 0 dq 1 q V C RC q V0C t ln V0C RC t dt t 0 1 RC Chapter q V C e dq It () dt V 0 I() t e R V ( t) I( t) R c 0 t RC V ( t) V 1e c t RC
23 R-C Circuits (Chapter 26, Sec 4) Charging a Capacitor R 0.37 I 0 C 0.63 Q f vab v bc q v bc C v ab ir q v bc C vab i R Figure Figure Time Constant RC (26-14) Chapter 26 23
24 R-C Circuits (Chapter 26, Sec 4) Discharging a Capacitor Q 0 RC 0 vab v bc vab v bc q v bc C v ab ir q v bc C vab i R Time Constant RC (26-14) Figure Figure Chapter 26 24
25 Power Distribution Systems 240-V line black, red Neutral Black White 120 v One phase of the 240-V line We buy energy from the Power Company, not power kw x time = watt-seconds = Joules 1 kwh = (1000W) (3600 s ) = 3.6 x 10 6 W-s = 3.6 x 10 6 J 25
26 Fuses, circuit breakers, and GFI A fuse will melt and a breaker will open the circuit if maximum current is reached. See Figure 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 who didn t use a grounded drill.
27 The wiring diagram for a typical kitchen Consider Figure below. Follow Example
28 Average Retail Price of Electricity cents per kilowatt-hour Census Division and State Residential Commercial 1 Industrial 1 Nov-07 Nov-06 Nov-07 Nov-06 Nov-07 Nov-06 New England Connecticut Maine Massachusetts New Hampshire Rhode Island Vermont U.S. Total
29 Q26.1 Which of the two arrangements shown has the smaller equivalent resistance between points a and b? A. the series arrangement B. the parallel arrangement C. The equivalent resistance is the same for both arrangements. D. The answer depends on the values of the individual resistances R 1, R 2, and R 3.
30 A26.1 Which of the two arrangements shown has the smaller equivalent resistance between points a and b? A. the series arrangement B. the parallel arrangement C. The equivalent resistance is the same for both arrangements. D. The answer depends on the values of the individual resistances R 1, R 2, and R 3.
31 Q26.2 Three identical resistors, each of resistance R, are connected as shown. What is the equivalent resistance of this arrangement of three resistors? A. 3R B. 2R C. 3R/2 D. 2R/3 E. R/3
32 A26.2 Three identical resistors, each of resistance R, are connected as shown. What is the equivalent resistance of this arrangement of three resistors? A. 3R B. 2R C. 3R/2 D. 2R/3 E. R/3
33 Q26.3 A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in parallel as shown. 120 V 60 W The voltage between points a and b is 120 V. Through which bulb is there the greatest voltage drop? a 120 V 120 W b A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb 120 V 240 W D. All three light bulbs have the same voltage drop.
34 A26.3 A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in parallel as shown. 120 V 60 W The voltage between points a and b is 120 V. Through which bulb is there the greatest voltage drop? a 120 V 120 W b A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb 120 V 240 W D. All three light bulbs have the same voltage drop.
35 Q26.4 A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in parallel as shown. 120 V 60 W The voltage between points a and b is 120 V. Which bulb glows the brightest? a 120 V 120 W b A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb 120 V 240 W D. All three light bulbs glow with equal brightness.
36 A26.4 A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in parallel as shown. 120 V 60 W The voltage between points a and b is 120 V. Which bulb glows the brightest? a 120 V 120 W b A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb 120 V 240 W D. All three light bulbs glow with equal brightness.
37 Q26.5 a A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are 120 V connected in series as shown. 60 W The voltage between points a and b is 120 V. Through which bulb is there the greatest voltage drop? A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb D. All three light bulbs have the same voltage drop. 120 V 120 W 120 V 240 W b
38 A26.5 A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in series as shown. The voltage between points a and b is 120 V. Through which bulb is there the greatest voltage drop? A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb D. All three light bulbs have the same voltage drop. a 120 V 60 W 120 V 120 W 120 V 240 W b
39 Q26.6 A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in series as shown. The voltage between points a and b is 120 V. Which bulb glows the brightest? A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb D. All three light bulbs glow with equal brightness. a 120 V 60 W 120 V 120 W 120 V 240 W b
40 A26.6 A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in series as shown. The voltage between points a and b is 120 V. Which bulb glows the brightest? A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb D. All three light bulbs glow with equal brightness. a 120 V 60 W 120 V 120 W 120 V 240 W b
41 Q26.7 Three identical light bulbs are connected to a source of emf as shown. Which bulb is brightest? A. light bulb A B. light bulb B C. light bulb C D. both light bulbs B and C (Both are equally bright and are brighter than light bulb A.) E. All bulbs are equally bright.
42 A26.7 Three identical light bulbs are connected to a source of emf as shown. Which bulb is brightest? A. light bulb A B. light bulb B C. light bulb C D. both light bulbs B and C (Both are equally bright and are brighter than light bulb A.) E. All bulbs are equally bright.
43 Q26.8 You wish to study a resistor in a circuit. To simultaneously measure the current in the resistor and the voltage across the resistor, you would place A. an ammeter in series and an voltmeter in series. B. an ammeter in series and an voltmeter in parallel. C. an ammeter in parallel and an voltmeter in series. D. an ammeter in parallel and an voltmeter in parallel.
44 A26.8 You wish to study a resistor in a circuit. To simultaneously measure the current in the resistor and the voltage across the resistor, you would place A. an ammeter in series and an voltmeter in series. B. an ammeter in series and an voltmeter in parallel. C. an ammeter in parallel and an voltmeter in series. D. an ammeter in parallel and an voltmeter in parallel.
45 Q26.9 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the maximum charge stored on the capacitor? A. the emf of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both and C E. all three of, C, and R
46 A26.9 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the maximum charge stored on the capacitor? A. the emf of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both and C E. all three of, C, and R
47 Q26.10 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the rate at which the capacitor charges? A. the emf of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both C and R E. all three of, C, and R
48 A26.10 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the rate at which the capacitor charges? A. the emf of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both C and R E. all three of, C, and R
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