chapter circuits 27 - kfupm · dr. m. f. al-kuhaili – phys 102 – chapter 27 page 2 14. two...

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 27

PHYS102 Previous Exam Problems

CHAPTER

27

Circuits

Combination of resistors Potential differences Single loop circuits Kirchhoff laws Multiloop circuits RC circuits General

1. Figure 1 shows two resistors 3.0 Ω and 1.5 Ω connected in parallel, and the combination is connected in

series to a 4.0-Ω resistor and a 10-V emf device. What is the potential difference Va - Vb? (Ans: 2.0 V)

2. A certain capacitor, C, in series with a resistor, R, is being charged. At the end of 10 ms, its charge is half

the maximum value. What is the time constant of the RC circuit? (Ans: 14 ms)

3. In figure 3, what is the potential difference Va-Vb? (Ans: 12 V)

4. Figure 4 shows two resistors, each of the resistance R, connected to two ideal batteries of emf E1 and E2

(E 1> E 2). The potential difference Va – Vb is equal to 0.2E 1. What is the ratio E 2/E 1? ( Ans: 3/5)

5. Three resistors and two batteries are connected as shown in figure 5. What is the potential difference

Va – Vb? (Ans: 15 V)

6. Determine the power dissipated by the 4.0-Ω resistor in the circuit shown in figure 6. (Ans:16 W)

7. A capacitor of capacitance C takes 2 s to reach 63 % of its maximum charge when connected in series to a

resistance R and a battery of emf E. How long does it take this capacitor to reach 95 % of its maximum charge

(from zero initial charge)? (Ans: 6 s)

8. A single-loop circuit contains two external resistors and two emf sources as shown in the figure 7. Assume

the emf sources are ideal, what is the power dissipation across resistor R1? (Ans: 0.9 W)

9. A capacitor of capacitance 5.0×10-6 F is discharging through a 4.0-MΩ resistor. At what time will the

energy stored in the capacitor be half of its initial value? (Ans: 7 s)

10. Four resistors are connected as shown in figure 8. What is the current through the 4-Ω resistor when a

potential difference of 30.0 V is applied between points a and b? (Ans: 1.75 A)

11. For the circuit shown in figure 9, find the current through the 3 Ω resistor. (Ans: 1.0 A)

12. A 6-V battery supplies a total of 48 W to three identical light bulbs connected in parallel. What is the

resistance of each bulb? (Ans: 2.25 Ω)

13. In figure 11, find the current in 3-Ω resistor, and the resistance R for the given currents. (Ans: 8 A, 9 Ω)


14. Two resistors r and R are connected in series across a 100-V line. If r = 30 kΩ and the voltage across it is

found to be 60 V, find the resistance of R. (Ans: 20 kΩ)

15. A 30.0-kΩ resistor and a capacitor are connected in series and a 15.0-V potential difference is suddenly

applied across them. The potential difference across the capacitor rises to 5.00 V in 1.50 µs. Find the

capacitance of the capacitor. (Ans: 123 pF)

16. Four resistors, each of 20 Ω, are connected in parallel, and the combination is connected to a 20-V emf

device. What is the current in any one of the resistors? (Ans: 1.0 A)

17. Find the potential difference across a 30-Ω resistor, when it is connected across a battery of emf 6 V

and internal resistance of 0.5 Ω. (Ans: 5.9 V)

18. Three resistors are connected, as shown in figure 12. The potential difference between points A and B is

30 V. How much current flows through the 4-Ω resistor? (Ans: 2.3 A)

19. Two ideal emf sources along with two resistors are connected as shown in figure 13. If the potential at A

is 150 V, what would be the potential at point B? (Ans: - 5 V)

20. What is the total power dissipation in the circuit shown in figure 14? (Ans: 43 W)

21. Consider the series RC circuit shown in figure 15, where R = 1.0×106 Ω, C = 5.0 μF, and E = 30 V. If the

switch is closed at t = 0, what is the current in resistance R at time t = 10 s after the switch is closed?

(Ans: 4.1×10-6 A)

22. Calculate the equivalent resistance between points a and b in the circuit shown in figure 16. (Ans: 2.4 Ω)

23. In figure 17: R1 = 2.0 Ω, R2 = 4.0 Ω, R3 = 8.0 Ω, E1 = 2.0 V, E2 = 4.0 V and E3 = 6.0 V. What is the rate of

energy dissipation in R1? (Ans: 0.32 W)

24. A 12-V battery supplies 100 W to two identical bulbs connected in series. What is the resistance of each

bulb? (Ans: 0.72 Ω)

25. In figure 18, R1 = R2

= R3

= 5 Ω. What is the value of the emf of the second battery E 2? (Ans: 5 V)

26. In figure 19, each resistor has a resistance of 1 Ω. Calculate the emf of the battery if the current I is 4 A.

(Ans: 7V) 27. In figure 20, the potential difference between points 1 and 2, (V2-V1), is -40 V, and the current is equal to

4.0 A, what is the value of the resistance R? (Ans: 3 Ω)

28. A 2.0-V battery with an internal resistance r = 0.2 Ω is used to operate a lamp of resistance R = 2.3 Ω.

What is the percentage of the power delivered to the lamp relative to the total power supplied by the battery?

(Ans: 92 %)

29. An uncharged capacitor is connected as shown in figure 21. When the switch is closed, the charge on the

capacitor reaches half its maximum value in 20 ms. If R = 500 Ω and the voltage of the battery is 10 V, what is

the capacitance of the capacitor? (Ans: 58 μF)

30. In the circuit shown in figure 22, I = 0.65 A and R = 15 Ω. What is the value of the emf of the battery?

(Ans 39 V)

31. A 5.0-μF capacitor is fully charged by connecting it to a 12-V battery. After disconnecting the battery, the

capacitor was allowed to discharge through a simple RC circuit, with a time constant of 4.0 s. What is the charge

on the capacitor after one time constant has elapsed? (Ans: 2.2×10-5 C)


32. In the circuit shown in figure 23, what is the current in the 8.00-Ω resistor? (Ans: 2.25 A to the left)

33. A number of 240-Ω resistors are connected in parallel to a 120-V source. If the maximum current allowed

in the circuit is 9 A, determine the largest number of resistors, which can be used in this circuit without

exceeding the maximum current. (Ans: 18)

34. The current in a single-loop circuit is 5.0 A. When an additional resistance of 2.0 Ω is added in series, the

current drops to 4.0 A. What was the resistance in the original circuit? (Ans: 8.0 Ω)

35. In the circuit shown in figure 25, calculate potential difference VB-VA. The points A, B and C are three

junctions. [Take the current I = 2.0 A] (Ans: 8.0 V)

36. Three wires are joined together at a junction. A 0.40-A current flows toward the junction from one wire

and a 0.3-A current flows away from the junction in the second wire. What is the current in the third wire?

(Ans: 0.10 A, away from the junction)

37. A capacitor of capacitance C is discharging through a resistor of resistance R. In terms of RC, when will

the energy stored in the capacitor reduce to one fifth of its initial value? (Ans: 0.8RC)

38. A capacitor, initially uncharged in a single-loop RC circuit, is charged to 85% of its final potential

difference in 2.4 s. What is its time constant? (Ans: 1.3 s)

39. Find the potential difference (VB-VA) between points B and A of the circuit shown in figure 26.

(Ans: - 10 V)

40. Find the value of R1 in the circuit of figure 27. (Ans: 6.0 Ω)

41. In figure 28, a battery with an emf of 12 V and internal resistance r = 3.0 Ω is connected to a bulb of

resistance R. If the bulb will light at a steady current of 0.1 A, what should be the value of R? (Ans: 117 Ω)

42. A resistor R = 30×106 Ω is connected in series with a capacitor C = 3.0 μF and a 21-V battery for long

time. The battery was removed, then R and C are connected in a loop. What is the energy stored in the capacitor

C after one minute? (Ans: 174 μJ)

43. In the circuit shown in figure 29, the capacitor is initially uncharged. At t = 0, switch S is closed. If τ

denotes the time constant, then what is the current passing through the 3.0-Ω resistor at t = τ/100? (Ans: 0.6 A)

44. Three resistors, of resistances 2.0 Ω, 4.0 Ω and 6.0 Ω, are connected to a 24-V battery, as shown in

figure 30. How much power is dissipated in the 2.0-Ω resistor? (Ans: 8.0 W)

45. What is the current in the 8.0-Ω resistor shown in the circuit of figure 31? (Ans: 1.5 A)

46. The capacitor in figure 32 is initially charged to 50 V and then the switch is closed. What charge flows out

of the capacitor during the first minute after the switch was closed? (Ans: 4.8 mC)

47. In figure 33, if Vc-Vd = 6.0 V, what is the emf of the battery? (Ans: 10.8 V)

48. Find the values of the currents in figure 34. (Ans: I1 = 2 A, I2 = 2 A, I3 = -4 A)

49. Calculate the voltage E of the battery shown in figure 35. (Ans: 20 V)

50. The circuit in figure 36 has been connected for a long time. Find the potential difference Vb - Va.

(Ans: 8 V)

51. A 4.00-μF capacitor is charged to 24.0 V. Find the charge on the capacitor 4.00 ms after it is connected

across a 200-Ω resistor. (Ans: 0.647 μC)


52. In the circuit shown in figure 38: E1 = 28 V, E2 = 42 V, R1 = 2.0 Ω, R2 = 5.0 Ω, R3 = 1.0 Ω, and I1 = 7.5

A. Calculate the potential difference VA – VB. (Ans: +13 V)

53. If Q = 400 μC and the potential difference VA-VB = - 30 V in the circuit segment shown in figure 40,

what is the current in the resistor R? (Ans: 1.0 mA, counterclockwise)

54. The four resistors shown in figure 41 are identical, and each has a resistance of 6.0 Ω. The battery is ideal

and has emf E = 12 V. What is the value of the current i2 passing through R2? (Ans: 0.50 A)

55. In the circuit shown in figure 42, E1 = 6.00 V, E2 = 12.0 V, R1 = 200 Ω, and R2 = 100 Ω. What is the

power supplied by E1? (Consider the two emf to be ideal). (Ans: 1.08 W)

56. Consider the circuit shown in figure 43. When the capacitor is fully charged, the current I is 3.00 A.

What is the charge on the capacitor if its capacitance is 10.0 μF? (Ans: 150 μC)

57. The resistance between points a and b in figure 44 is 60 Ω. What is the value of R? (Ans: 42 Ω)

58. In figure 46, E = 4.2 kV, C = 6.5 μF, R1 = R2 = R3 = 0.92 MΩ. After switch S has been closed for a long

time, what is the current in R2? (Ans: 2.3 mA)

59. A battery has an emf of 12.00 V. When a current I = 1.00 A flows through the battery, the terminal voltage

is 11.99 V. What is the internal resistance of the battery? (Ans: 0.01 Ω)

60. A 22-V battery is connected across the terminals a and b in figure 47. If each resistor is 40 Ω, what is the

potential drop across the resistor labeled R? (Ans: 8 V)

61. In figure 48, all the batteries are ideal with E1 = 6.0 V, E2 = 5.0 V, and E3 = 4.0 V. What is the potential

difference across resistor R2? (Ans: 7 V)

62. Three resistors and two batteries are connected as shown in figure 49. What is the magnitude of the

current through the 12-V battery? (Ans: 0.52 A)

63. What maximum power can be generated from an 18-V battery using any combination of a 6.0-Ω resistor

and a 9.0- Ω resistor? (Ans: 90 W)

64. For the circuit shown in figure 50, find the potential difference VA - VB, if I1 = 3.0 A and I3 = 4.0 A.

(Ans: -20 V)

65. Resistor R1 has five times the resistance of resistor R2. They are connected in parallel to a battery (see

figure 51). If the power dissipated in R1 is P1 and the power dissipated in R2 is P2, what is P1/P2? (Ans: 0.20)

66. A battery with a 12-V emf and an internal resistance r is connected to a resistor R = 10 Ω, as shown in

figure 52. The voltage across R is 10 V. Find r. (A: 2.0 Ω)

67. For the circuit shown in figure 53, if Va – Vc = 20 V, what is the potential difference Vb – Vd? (Ans: 55 V)

68. In Figure 54, E1 = 4.0 V, E2 = 12 V, R1 = 4.0 Ω, R2 = 12 Ω, C = 3.0 μF, Q = 18 μC, and I = 2.5 A. What is

the potential difference Va – Vb? (Ans: –30 V)

69. Each of the three resistors shown in figure 56 has a resistance of 2.4 Ω and can dissipate a maximum

power of 36 W without becoming excessively heated. What is the maximum power the circuit can dissipate?

(Ans: 54 W)

70. Calculate the potential difference Vb–Va shown in figure 57. Assume that the same current I flows

through the 2 Ω and the 4 Ω resistors. (Ans: –5 V)

71. Determine values of the currents I6 in the 6 Ω and I8 in the 8 Ω resistors in the circuit shown in figure 58.

(Ans: I6 = 1.3 A, I8 = 0.38 A)


72. Consider the five 10-Ω resistors connected as shown in figure 59. Find the equivalent resistance between

points A and B. (Ans: 6.3 Ω)

73. A battery with an emf of 24 V is connected to a 6.0 Ω resistor. As a result, a current of 3.0 A flows

through the resistor. What is the potential difference that appears at the terminals of the battery? (Ans: 18 V)

74. Each of the resistors in the diagram of figure 60 has a resistance of 12 Ω. The potential difference between

points a and b is 10 V. What is the power dissipated in the entire circuit? (Ans: 4.0 W)

75. In the circuit shown in figure 48, R1 = 100 Ω, R2 = 50 Ω, and the ideal batteries have emfs E1 = 6.0 V, E2

= 5.0 V, and E3 = 4.0 V. Find the potential difference VB – VA. (Ans: + 1.0 V)

76. A 0.20-A current flows across a metallic rod of length 1.0 m when connected to a 1.0-V battery. The rod

is then cut into four identical pieces each having a length of 0.25 m, which are then connected in parallel to the

same 1.0-V battery. What is the new current delivered by the battery? (Ans: 3.2 A)

77. A capacitor of capacitance C is connected to a 12-V battery, as shown in figure 63. First, switch S2 was

open, and switch S1 was closed until the capacitor is fully charged. Then, S1 is open and S2 is closed. If the

voltage across the capacitor decays and reaches 6.0 V after 0.10 s, what is the capacitance C? (Ans: 24 μF)

78. Find the equivalent resistance between points a and b in figure 67. (Ans: 7.0 Ω)

79. A 1.0 μF capacitor with an initial stored energy of 0.50 J is discharged through 1.0 MΩ resistor. Find the

charge on the capacitor at t = 0.40 s. (Ans: 670 μC)

80. In the multi-loop circuit of figure 68, what is the current through the 2.0 kΩ resistor? (Ans: 1.2 mA)

81. When two unknown resistors are connected in series with a battery, the battery delivers 225 W of electric

power, and carries a total current of 5 A. For the same total current, 50 W is delivered when the resistors are

connected in parallel. Determine the resistance of each resistor. (Ans: 3Ω, 6Ω)

82. In figure 70, R1 = 5.0 Ω, R2 = 10 Ω, R3 = 15 Ω, C1 = C2 = 5.0 μF, and E = 24 V. Assume the circuit is in

the steady state. What is the power dissipated in the resistor R3? (Ans: 9.6 W)


A B C D E Conceptual Problems

1. When switch S is open, the ammeter in the circuit shown in figure 2 reads 2.0 A. When S is closed, the

ammeter reading: A. increases

B. remains the same

C. decreases

D. doubles

E. gives zero current

2. Two resistors have resistances R1 and R2, such that R1 < R2. If R1 and R2 connected in… A) parallel, then Req < R1 and Req < R2

B) parallel, then Req > R1 and Req < R2

C) parallel, then Req > R1 and Req > R2

D) series, then Req > R1 and Req < R2

E) series, then Req < R1 and Req < R2

3. Figure10 shows 3 identical light bulbs connected to a battery. What happens to the power of light bulb 1

when the switch is closed? A. The power increases.

B. The power will increase momentarily then returns to its initial value.

C. The power will decrease momentarily then returns to its previous value.

D. The power remains the same.

E. The power decreases.

4. In figure 24, three identical light bulbs are connected to a battery. Which statement is correct? A. The largest current passes through A.

B. The smallest current passes through A.

C. The largest current passes through B.

D. The largest current passes through C.

E. The current through all resistors is the same.

5. The sum of the currents entering a junction equals the sum of the currents leaving that junction is a

consequence of: A. conservation of charge

B. conservation of energy

C. Coulomb's law

D. Ampere's law

E. Newton's second law

6. Two light bulbs, with power ratings 25 W and 100 W, are connected in series to 110-V. Which of the

following statements is correct? A. The current in the 100-W bulb is the same as that in the 25-W bulb.

B. The current in the 100-W bulb is greater than that in the 25-Watts bulb.

C. Both bulbs will light with equal brightness.

D. Each bulb will have a potential difference of 55 V.

E. The current in the 100-W bulb is less than that in the 25-W bulb.


7. Which of the following statements are wrong? 1. In order to achieve the lowest resistance from several resistors, they should be

connected in parallel.

2. In order to achieve the lowest capacitance from several capacitors, they should be

connected in parallel.

3. The resistance of a conductor does not depend on temperature.

4. A dielectric increases the capacitance of a capacitor.

5. The electric flux through a closed surface is always zero.

A. 2, 3 and 5.

B. 2 and 4.

C. 1, 2 and 3.

D. 1 and 4.

E. 1 and 3.

8. Kirchoff’s two laws for electric circuits can be derived by using certain conservation laws. On which

conservation laws do Kirchoff’s laws depend? A. charge ; energy

B. current ; charge

C. mass ; energy

D. charge ; mass

E. current ; angular momentum 9. The circuit in figure 37 shows three identical resistors connected to a battery and an ammeter. The current

measured by the ammeter is Io. If resistor R2 is removed, the current measured by the ammeter will be A. 3Io/4.

B. Io/4.

C. the same.

D. 4Io/3.

E. 4Io.

10. Resistors A, B and C have resistances R, 2R, and R, respectively as shown in figure 39. Which resistor

dissipates the most power? A. C

B. B

C. A

D. A & B dissipate the same amount of power.

E. All 3 resistors dissipate the same amount of power 11. A single resistor R1 is connected to a battery. A second resistor R2 is then connected to R1 in parallel.

Which of the following statements is correct? A. The current through R1 will not change.

B. The current through R1 will increase.

C. The current through R1 will decrease.

D. The current through the battery will decrease.

E. The current through the battery will not change.


12. A battery is connected across a series combination of two identical resistors. If the potential difference

across the terminals is V and the current in the battery is i, then A. the potential difference across each resistor is V/2 and the current

in each resistor is i.

B. the potential difference across each resistor is V and the current

in each resistor is i.

C. the potential difference across each resistor is V/2 and the current

in each resistor is i/2.

D. the potential difference across each resistor is V and the current

in each resistor is i/2.

E. the potential difference across each resistor is V and the current

in each resistor is 2 i. 13. The emf of a battery is equal to its terminal potential difference

A. only when there is no current in the battery.

B. under all conditions.

C. only when the battery is being charged.

D. only when a large current is in the battery.

E. only when a small current is in the battery.

14. The capacitor shown in figure 45 is fully charged by connecting switch S to contact a. If switch S is

thrown to contact b at time t = 0, which of the curves represents the magnitude of the current through the resistor

R as a function of time? A. 5

B. 4

C. 3

D. 2

E. 1

15. Which of the following statements is wrong? A. A charged capacitor connected to a resistor will discharge faster when the

resistance is increased.

B. Tow resistor connected in parallel have the same potential difference across them.

C. If the voltage is held constant across a resistor, the power dissipated in the

resistor decreases when the resistance increases.

D. The emf of a battery is equal to the terminal voltage when there is no current

passing through the battery.

E. Kirchhoff’s rules are statements of conservation of charge and energy. 16. The circuit shown in figure 55 has three 100-Ω light bulbs connected to a 110 V battery. Which light

bulb(s) is (are) brightest? A. 2

B. 1

C. 3

D. 1 and 2

E. 2 and 3


17. The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in series and a

potential difference is maintained across the combination. Then: A. the potential difference across resistor 1 is twice that across resistor 2

B. the current in resistor 1 is twice that in resistor 2

C. the potential difference across resistor 1 is half that across resistor 2

D. the current in resistor 1 is half that in resistor 2

E) the potential difference across resistor 1 is 4 times that across resistor 2

18. Consider the five resistors connected as shown in figure 61. Find the equivalent resistance between the

points A and B. A. 3R/2

B. 3R

C. 15R

D. 6R

E. 36R/5

19. In the circuit shown in figure 62, an ideal battery is connected to two resistors (R1 > R2). The section lying

along an x axis is divided into five segments of equal length. Rank the segments according to the magnitude of

the electric field in them, greatest first. A. b, then d, then a and c and e tie

B. d, then b, then a and c and e tie

C. a and c and e tie, then b, then d

D. a and c and e tie, then d, then b

E. The electric field is the same in all segments. 20. Figure 64 shows a portion of an electric circuit that includes a battery connected in series to a resistor of

resistance R. Considering the variation of the electric potential along the circuit shown in the figure, which one

of the following statements is CORRECT? A. Current in R flows to the left and the + terminal of the battery is at point 1.

B. Current in R flows to the left and the + terminal of the battery is at point 2.

C. Current in R flows to the right and the + terminal of the battery is at point 1.

D. Current in R flows to the right and the + terminal of the battery is at point 2.

E. Current is zero.

21. Four resistors are connected to an ideal battery, as shown in figure 65. The current supplied by the battery

is Io. If R3 → ∞, the current supplied by the battery is A. 3Io/4

B. 4Io

C. Io/4

D. 4Io/3

E. 15Io/11

22. In the circuit shown in figure 66, what should be the ratio E3/E1 if E1 = E2 and the electric current in the

circuit equal to zero? A. 2.0

B. 0.50

C. 1.0

D. 4.0

E. 0.25


23. For a capacitor which is being charged, which one of the following statements is FALSE?

A. Initially (at t = 0) the capacitor acts like a broken wire in the circuit.

B. Initially (at t = 0) the capacitor acts like ordinary conducting wire.

C. After a long time the voltage across the capacitor is equal to the emf of the battery.

D. Initially the current through the capacitor is maximum.

E. Initially (at t = 0) the potential difference across the capacitor is equal to zero. 24. In the circuits shown in figure 69, all the capacitors have the same capacitance and initial charge, and all

the resistors have the same resistance. At time t = 0, switch S is closed such that each capacitor discharges

through its resistors network. Rank the time taken for discharging the capacitor, shortest time first. A) B, C, A

B) C, B, A

C) A, C, B

D) C, A, B

E) B, A, C

25. Several identical lamps are connected in parallel. What happens if one lamp burns out? A) The power dissipated in each of the remaining lamps will not change.

B) The power dissipated in each of the remaining lamps will increase.

C) The power dissipated in each of the remaining lamps will decrease.

D) The current passing through each of the remaining lamps will decrease.

E) The current passing through each of the remaining lamps will increase.

26. In FIGURE 71, four identical resistors are connected to an ideal battery. S1 and S2 are switches. Which of

the following actions would result in the minimum power dissipated in resistor A? A) keeping both switches open

B) closing both switches

C) closing S1 only

D) closing S2 only

E) The answer depends on the value of the emf of the battery


Figure 1 Figure 2 Figure 3


Figure 7 Figure 8 Figure 9 Figure 10






Figure 71

chapter circuits 27 - kfupm · dr. m. f. al-kuhaili – phys 102 – chapter 27 page 2 14. two...

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