# Chapter 28 Direct Current Circuits

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1 Chapter 28 Direct Current Circuits Multiple Choice 1. t what rate is thermal energy being generated in the 2-resistor when = 12 V and = 3.0 Ω? 2 a. 12 W b. 24 W c. 6.0 W d. 3.0 W e. 1.5 W 2. t what rate is thermal energy generated in the 30-Ω resistor? 30 V 30 Ω 5.0 Ω a. 20 W b. 27 W c. 60 W d. 13 W e. 30 W 5.0 Ω 105

2 106 CHPT What is the magnitude of the potential difference across the 20-Ω resistor? 11 V 20 Ω a. 3.2 V b. 7.8 V c. 11 V d. 5.0 V e. 8.6 V 5.0 Ω 4. What is the current in the 10-Ω resistor? 21 V 5 Ω 5 Ω 5 Ω a b. 3.0 c. 1.2 d. 2.4 e t what rate is thermal energy generated in the 20-Ω resistor when = 20 V? 40 Ω 30 Ω 30 Ω 30 Ω 20 Ω a. 6.5 W b. 1.6 W c. 15 W d. 26 W e. 5.7 W

3 Direct Current Circuits t what rate is thermal energy generated in the 5-Ω resistor when = 24 V? 5.0 Ω a. 13 W b. 3.2 W c. 23 W d. 39 W e. 51 W 7. When a 20-V emf is placed across two resistors in series, a current of 2.0 is present in each of the resistors. When the same emf is placed across the same two resistors in parallel, the current through the emf is 10. What is the magnitude of the greater of the two resistances? a. 7.2 Ω b. 7.6 Ω c. 6.9 Ω d. 8.0 Ω e. 2.8 Ω 8. resistor of unknown resistance and a 15-Ω resistor are connected across a 20-V emf in such a way that a 2.0 current is observed in the emf. What is the value of the unknown resistance? a. 75 Ω b. 12 Ω c. 7.5 Ω d. 30 Ω e. 5.0 Ω 9. What is the current in the 15-Ω resistor when = 9.0 V? 20 Ω 15 Ω 30 Ω a b c d e. 0.60

4 108 CHPT How much heat is produced in the 10-Ω resistor in 5.0 s when = 18 V? 15 Ω 12 Ω a. 72 J b. 32 J c. 50 J d. 18 J e. 90 J 11. Determine when = 0.50 and = 12 Ω. 2 2 a. 12 V b. 24 V c. 30 V d. 15 V e. 6.0 V 12. Determine when = 0.20 and = 18 V a. 50 Ω b. 8.0 Ω c. d. 20 Ω e. 30 Ω

5 Direct Current Circuits Determine the current in the 10-V emf. 5.0 Ω 10 V 5.0 Ω 15 V a. 2.3 b. 2.7 c. 1.3 d e Ω 14. What is the magnitude of the current in the 20-Ω resistor? 10 V 20 Ω 15 V a b c d e Determine the potential difference V a V b shown in the circuit below. b 10 V a 15 V a. 5.0 V b. 5.0 V c. 10 V d. 10 V e. 0 V

6 110 CHPT What is the potential difference V b V a shown in the circuit below. a 10 V 30 V 20 Ω b a. 8.0 V b. 8.0 V c. 18 V d. 18 V e. 12 V 17. t what rate is power supplied by the 10-V emf shown below? 10 V 20 V a. 10 W b. 10 W c. zero d. 20 W e. 20 W 20 Ω 18. f = 8.0 V, at what rate is that emf providing energy to the circuit shown below? 15 Ω 12 V a. 8.4 W b. 7.6 W c. 5.6 W d. 11 W e. 2.0 W

7 Direct Current Circuits Determine the magnitude and sense (direction) of the current in the 500-Ω resistor when = 30 m. 500 Ω 30 V 15 V 10 V 400 Ω a. 56 m left to right b. 56 m right to left c. 48 m left to right d. 48 m right to left e. 26 m left to right 20. Determine the magnitude and sense (direction) of the current in the 10-Ω resistor when = V 50 V 20 Ω a. 1.6 right to left b. 1.6 left to right c. 1.2 right to left d. 1.2 left to right e. 1.8 left to right

8 112 CHPT Determine the resistance when = V 50 V 20 Ω a. 40 Ω b. 8.0 Ω c. 85 Ω d. 28 Ω e. 32 Ω 22. What is the potential difference V V when the = 1.5 in the circuit segment below? 20 V 20 Ω 12 V a. 22 V b. 22 V c. 38 V d. 38 V e. 2.0 V 23. What is the potential difference V V when = 0.50 in the circuit segment shown below? 15 V 16 Ω a. 28 V b. 2.0 V c. 28 V d. 2.0 V e. 18 V

9 Direct Current Circuits f = 2.0 kω, C = 4.0 mf, = 8.0 V, Q = 20 mc, and = 3.0 m, what is the potential difference V b V a? a C Q b a. 7.0 V b. 19 V c. 9.0 V d. 3.0 V e. 14 V 25. f = 3.0 kω, C = 5.0 mf, = 6.0 V, Q = 15 mc, and = 4.0 m, what is the potential difference V b V a? a C Q b a. 3.0 V b. 9.0 V c. 15 V d. 21 V e. 6.0 V 26. f = 4.0 kω, C = 3.0 mf, = 15 V, Q = 12 mc, and = 2.0 m, what is the potential difference V b V a? a C Q b a. 3.0 V b. 19 V c. 3.0 V d. 27 V e. 21 V 27. f = 3.0 kω, C = 6.0 nf, 1 = 10.0 V, Q = 18 nc, 2 = 6.0 V, and = 5.0 m, what is the potential difference V b V a? a 1 C Q 2 b a. 13 V b. 28 V c. 13 V d. 28 V e. 2.0 V

10 114 CHPT f 1 = 4.0 V, 2 = 12.0 V, 1 = 4 Ω, 2 = 12 Ω, C = 3 μf, Q = 18 μc, and = 2.5, what is the potential difference V a V b? a C b Q 2 a. 30 V b. 30 V c. 5.0 V d. 5.0 V e. 1.0 V 29. f the current in the 4.0-Ω resistor is 1.4, what is the magnitude of the potential difference, V V? 2 Ω 2 Ω 8 Ω 2 Ω 16 Ω 4 Ω a. 69 V b. 55 V c. 62 V d. 48 V e. 31 V 30. f = 0.40 in the circuit segment shown below, what is the potential difference V a V b? a 8 Ω 12 Ω b a. 31 V b. 28 V c. 25 V d. 34 V e. 10 V

11 Direct Current Circuits f = 2.0 in the circuit segment shown below, what is the potential difference V V? 20 V 10 V a. 10 V b. 20 V c. 10 V d. 20 V e. 30 V 32. Determine the potential difference, V V in the circuit segment shown below when = 2.0 m and Q = 50 μc. 15 V Q 2.0 μf 15 k Ω a. 40 V b. 40 V c. 20 V d. 20 V e. 10 V 33. f Q = 400 μc and the potential difference V V = 10 V in the circuit segment shown below, what is the current in the resistor? Q 10 μf 20 k Ω 30 V a. 1.0 m right to left b. 1.0 m left to right c. 3.5 m right to left d. 3.5 m left to right e. None of the above 34. f Q = 350 μc and = 4.0 m in the circuit segment shown below, determine the potential difference, V V. 25 V Q 10 μf 5.0 k Ω a. 30 V b. 80 V c. 40 V d. 40 V e. 10 V

12 116 CHPT n an C circuit, how many time constants must elapse if an initially uncharged capacitor is to reach 80% of its final potential difference? a. 2.2 b. 1.9 c. 1.6 d. 3.0 e How many time constants must elapse if an initially charged capacitor is to discharge 55% of its stored energy through a resistor? a b c d e n an C circuit, what fraction of the final energy is stored in an initially uncharged capacitor after it has been charging for 3.0 time constants? a b c d e How long will it take a charged 80-μF capacitor to lose 20% of its initial energy when it is allowed to discharge through a 45-Ω resistor? a ms b ms c ms d ms e ms 39. t t = 0 the switch S is closed with the capacitor uncharged. f C = 50 μf, = 20 V, and = 4.0 kω, what is the charge on the capacitor when = 2.0 m? S Q C a. 360 μc b. 480 μc c. 240 μc d. 600 μc e. 400 μc

13 Direct Current Circuits t t = 0 the switch S is closed with the capacitor uncharged. f C = 30 μf, = 30 V, and = 5.0 kω, at what rate is energy being stored in the capacitor when = 2.0 m? S Q C a. 32 mw b. 40 mw c. 44 mw d. 36 mw e. 80 mw 41. t t = 0 the switch S is closed with the capacitor uncharged. f C = 40 μf, = 50 V, and = 5.0 kω, how much energy is stored by the capacitor when = 2.0 m? S Q C a. 20 mj b. 28 mj c. 32 mj d. 36 mj e. 40 mj

14 118 CHPT t t = 0 the switch S is closed with the capacitor uncharged. f C = 30 μf, = 50 V, and = 10 kω, what is the potential difference across the capacitor when = 2.0 m? S Q C a. 20 V b. 15 V c. 25 V d. 30 V e. 45 V 43. capacitor in a single-loop C circuit is charged to 85% of its final potential difference in 2.4 s. What is the time constant for this circuit? a. 1.5 s b. 1.3 s c. 1.7 s d. 1.9 s e. 2.9 s 44. What is the equivalent resistance between points a and b when = 13 Ω? 2 b 3 a a. 29 Ω b. 23 Ω c. 26 Ω d. 20 Ω e. 4.6 Ω

15 Direct Current Circuits What is the equivalent resistance between points a and b when = 30 Ω? a b a. 27 Ω b. 21 Ω c. 24 Ω d. 18 Ω e. 7.5 Ω 46. What is the equivalent resistance between points a and b when = 12 Ω? a b a. 20 Ω b. 16 Ω c. 24 Ω d. 28 Ω e. 6.0 Ω 47. What is the equivalent resistance between points a and b? a 20 Ω b a. 14 Ω b. 8.0 Ω c. 6.0 Ω d. 25 Ω e. 40 Ω 5 Ω

16 120 CHPT f 1 =, 2 = 15 Ω, 3 = 20 Ω, and = 0.50, at what rate is heat being generated in these resistors? a. 29 W b. 16 W c. 22 W d. 11 W e. 1.1 W 49. f 1 = 3.0 Ω, 2 = 6.0 Ω, 3 = 12 Ω, and = 0.50, at what rate is heat being generated in 1? a. 20 W b. 17 W c. 12 W d. 31 W e. 6.0 W 50. certain brand of hot dog cooker applies a potential difference (120 V) to opposite ends of the hot dog and cooks by means of the joule heat produced. f 60 kj is needed to cook each hot dog, what current is needed to cook four hot dogs simultaneously in 3.0 min? a. 11 b. 2.8 c. 8.3 d. 2.1 e f 480 C pass through a 4.0-Ω resistor in 10 min, what is the potential difference across the resistor? a. 3.6 V b. 2.8 V c. 2.4 V d. 3.2 V e. 5.0 V

17 Direct Current Circuits V battery is connected to a 15-Ω resistor and an unknown resistor, as shown. The current in the circuit is How much heat is produced in the 15-Ω resistor in 2.0 min? 15 Ω a kj b kj c kj d kj e kj 10 V 53. What is the equivalent resistance between points and in the figure when = 20 Ω? a. 77 Ω b. 63 Ω c. 70 Ω d. 84 Ω e. 140 Ω 54. What is the equivalent resistance between points and in the figure when = 18 Ω? a. 48 Ω b. 64 Ω c. 80 Ω d. 96 Ω e. 1

18 122 CHPT What is the equivalent resistance between points and in the figure when =? a. 20 Ω b. c. 25 Ω d. 15 Ω e. 3.2 Ω 56. n a loop in a closed circuit, the sum of the currents entering a junction equals the sum of the currents leaving a junction because a. the potential of the nearest battery is the potential at the junction. b. there are no transformations of energy from one type to another in a circuit loop. c. capacitors tend to maintain current through them at a constant value. d. current is used up after it leaves a junction. e. charge is neither created nor destroyed at a junction. 57. When a capacitor is fully charged, the current through the capacitor is a. zero. b. at its maximum value. c. equal to the current in a resistive circuit in parallel with the capacitor circuit. d. greater than the current in a resistor that is farther from the battery than the capacitor. e. zero if it is the only capacitor, but maximum if there is another capacitor in series with it. 58. The algebraic sum of the changes of potential around any closed circuit loop is a. zero. b. maximum. c. zero only if there are no sources of emf in the loop. d. maximum if there are no sources of emf in the loop. e. equal to the sum of the currents in the branches of the loop.

19 Direct Current Circuits The circuit below contains three 100W light bulbs. The emf = 110 V. Which light bulb(s) is(are) brightest? C a. b. c. C d. and C e. ll three are equally bright. 60. The circuit below contains three 100 watt light bulbs. The emf = 110 V. Which light bulb(s) is(are) the brightest? C a. b. c. C d. and C e. ll three are equally bright. 61. The circuit below contains three light bulbs and a capacitor. The emf = 110V. The capacitor is fully charged. Which light bulb(s) is(are) dimmest? C a. b. c. C d. and e. ll three are equally bright (or dim).

20 124 CHPT The circuit below contains three light bulbs and a capacitor. The emf = 110V. t the instant the switch S is closed, which light bulb is brightest? C S a. b. c. C d. and e. ll three are equally bright. 63. The circuit below contains three resistors,,, and C, which all have equal resistances. The emf = 110V. Which resistor generates the most thermal energy after the switch is closed? C S a. b. c. C d. and e. ll three generate equal amounts of thermal energy.

21 Direct Current Circuits The diagram shown represents a portion of a wire in a circuit. current is flowing in the wire in the direction shown. Under the convention that it is positive charge that flows the electric field points in the direction of the current. How can the electric field change direction where the wire bends? a. There is an excess of negative charge in the center of the wire. b. There is an excess of positive charge at the bottom end of the wire. c. There is an excess of negative charge at the right end of the upper portion of the wire. d. There is an accumulation of positive charge on the surface, particularly at the bend, such that the sum of electric fields gives the new electric field. e. There is an accumulation of electrical potential as the current traverses the wire: The higher potential in the lower half is the source of the field. 65. The circuit below contains three light bulbs and a capacitor. The emf is 110 V and the capacitor is fully charged. Which light bulb(s) is (are) brightest? C 110 V a. b. c. C d. and e. and C

22 126 CHPT The circuit below contains 4 light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest? C D 110 V a. b. c. C d. D e. C and D 67. The circuit below contains 4 light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest? C D 110 V a. b. c. C d. D e. C and D

23 Direct Current Circuits The circuit below contains 3 light bulbs and a capacitor. The emf is 110 V. Which light bulb(s) is(are) brightest? (ssume the capacitor is fully charged.) C 110 V a. b. c. C d. and e. ll three are equally bright. 69. Which light bulb(s) is(are) brightest when the capacitor has half its maximum charge? C 110 V a. b. c. C d. and e. ll three are equally bright. 70. The circuit below contains 5 light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest? C 110 V D a. : The one closest to the positive terminal of the battery. b. and C: The bulbs closest to the positive terminal of the battery. c. and : ecause they are closest to the terminals of the battery. d. C and D: ecause they receive current from and and from. e. : ecause the potential difference across is that of the battery.

24 128 CHPT The battery is disconnected from a series C circuit after the capacitor is fully charged and is replaced by an open switch. When the switch is closed, a. the current through the resistor is always greater than the current through the capacitor. b. the current through the resistor is always less than the current through the capacitor. c. the current through the resistor is always equal to the current through the capacitor. d. the capacitor does not allow current to pass. e. the current stops in the resistor. 72. The capacitors are completely discharged in the circuit shown below. S C 1 C V 1 2 The two resistors have the same resistance and the two capacitors have the same capacitance C. fter the switch is closed, the current C 1 a. is greatest in. b. is greatest in C 2. c. is greatest in 1. d. is greatest in 2. e. is the same in, C, and. C

25 Direct Current Circuits Which two circuits are exactly equivalent? V 110V 110V C V 110V 3 3 a. and b. and C c. C and D d. D and e. and D 74. circuit consists of 2N resistors, all of resistance, connected as shown below. potential difference V is applied to one end, and the other end is at ground potential. The equivalent resistance of the circuit is V.. a. 2. b.. c. N 2. d. N. e. 2N.

26 130 CHPT circuit consists of 4N resistors, all of resistance, connected as shown below. potential difference V is applied to the circuit. The equivalent resistance of the circuit is a.. 2 b.. c. d. e. N. 2 N. 2N. 76. circuit consists of N resistors, all of resistance, connected as shown below. potential difference V is applied to the circuit. The equivalent resistance of the circuit is b. a.. 2N N. c.. d. N. e. 2N. 77. The circuit below shows three resistors in parallel. 3 > 2 > 1. The resistors are all made of the same wire with the same diameter but have different lengths. ank the magnitudes of the electric fields in the resistors from least to greatest. a. 3 < 2 < 1. b. 2 < 1 = 3. c. 1 = 2 = 3. V d. 1 = 3 < 2. e. 1 < 2 < 3.

27 Direct Current Circuits The circuit below shows three resistors in series. 3 > 2 > 1. The resistors are all made of the same wire with the same diameter but have different lengths. ank the magnitudes of the electric fields in the resistors from least to greatest. a. 3 < 2 < 1. b. 2 < 1 = c. 1 = 2 = 3. d. 1 = 3 < 2. e. 1 < 2 < series circuit consists of a 100 V DC power source, a 100 Ω resistor, and a variable resistor of resistance, which varies from 0 to 100 Ω. The current in the circuit is 100 V 100 Ω a. directly proportional to. b. inversely proportional to. c. directly proportional to (100 Ω ). d. inversely proportional to (100 Ω ). e. neither directly nor inversely proportional to or to ( 100 Ω). 80. parallel circuit consists of a 100 V DC power source, a 100 Ω resistor, and a variable resistor of resistance, which varies from 0 to 100 Ω. The current in the circuit is 100 V 100 Ω a. directly proportional to. b. inversely proportional to. c. directly proportional to (100 Ω ). d. inversely proportional to ( 100 Ω ). e. neither directly nor inversely proportional to or to ( 100 Ω).

28 132 CHPT 28 Open-nded Problems 81. What is the maximum number of 100-W lightbulbs you can connect in parallel in a 120-V home circuit without tripping the 20- circuit breaker? Ω resistor and a 50-μF capacitor are connected in series at t = 0 with a 6-V battery. The capacitor is initially uncharged. What is the current in the circuit at t = 0? t t = 0.5 s? What is the maximum charge stored on the capacitor? 83. n initially uncharged 10-μF capacitor is charged by a 10-V battery through a resistance. The capacitor reaches a potential difference of 4 V in a period of 3 s after the charging began. Find the value of.

29 Direct Current Circuits 133 Chapter 28 Direct Current Circuits 1. c 2. d 3. b 4. a 5. b 6. b 7. a 8. d 9. a 10. d 11. b 12. d 13. a 14. d 15. a 16. a 17. b 18. c 19. a 20. a 21. b 22. b 23. a 24. c 25. a 26. c 27. d 28. a 29. d 30. c 31. c 32. d 33. a 34. d 35. c 36. d 37. b 38. c 39. d 40. b 41. c 42. d 43. b 44. d 45. d 46. b 47. d 48. d 49. c 50. a 51. d 52. c 53. c 54. d 55. b 56. e 57. a 58. a 59. a 60. a 61. c 62. c

30 134 CHPT c 64. d 65. b 66. b 67. b 68. d 69. b 70. e 71. c 72. e 73. e 74. c 75. d 76. b 77. a 78. c 79. d 80. e m, m, 300 μc kω

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