Circuits Ch27 Exam Prep

Chapter: Chapter 27

Learning Objectives

LO 27.1.0 Solve problems related to single-loop circuits.

LO 27.1.1 Identify the action of an emf source in terms of the work it does.

LO 27.1.2 For an ideal battery, apply the relationship between the emf, the current, and the power (rate of energy transfer).

LO 27.1.3 Draw a schematic diagram for a single-loop circuit containing a battery and three resistors.

LO 27.1.4 Apply the loop rule to write a loop equation that relates the potential differences of the circuit elements around a (complete) loop.

LO 27.1.5 Apply the resistance rule in crossing through a resistor.

LO 27.1.6 Apply the emf rule in crossing through an emf.

LO 27.1.7 Identify that resistors in series have the same current, which is the same value that their equivalent resistor has.

LO 27.1.8 Calculate the resistance of the equivalent of several resistors in series.

LO 27.1.9 Identify that a potential applied to resistors wired in series is equal to the sum of the potentials across the individual resistors.

LO 27.1.10 Calculate the potential difference between any two points in a circuit.

LO 27.1.11 Distinguish a real battery from an ideal battery and, in a circuit diagram, replace a real battery with an ideal battery and an explicitly shown resistance.

LO 27.1.12 With a real battery in a circuit, calculate the potential difference between its terminals for current in the direction of the emf and in the opposite direction.

LO 27.1.13 Identify what is meant by grounding a circuit, and draw a schematic diagram for such a connection.

LO 27.1.14 Identify that grounding a circuit does not affect the current in a circuit.

LO 27.1.15 Calculate the dissipation rate of energy in a real battery.

LO 27.1.16 Calculate the net rate of energy transfer in a real battery for current in the direction of the emf and in the opposite direction.

LO 27.2.0 Solve problems related to multiloop circuits.

LO 27.2.1 Apply the junction rule.

LO 27.2.2 Draw a schematic diagram for a battery and three parallel resistors and distinguish it from a diagram with a battery and three series resistors.

LO 27.2.3 Identify that resistors in parallel have the same potential difference, which is the same value that their equivalent resistor has.

LO 27.2.4 Calculate the resistance of the equivalent resistor of several resistors in parallel.

LO 27.2.5 Identify that the total current through parallel resistors is the sum of the currents through the individual resistors.

LO 27.2.6 For a circuit with a battery and some resistors in parallel and some in series, simplify the circuit in steps by finding equivalent resistors, until the current through the battery can be determined, and then reverse the steps to find the currents and potential differences of the individual resistors.

LO 27.2.7 If a circuit cannot be simplified by using equivalent resistors, identify the several loops in the circuit, choose names and directions for the currents in the branches, set up loop equations for the various loops, and solve these simultaneous equations for the unknown currents.

LO 27.2.8 In a circuit with identical real batteries in series, replace them with a single ideal battery and a single resistor.

LO 27.2.9 In a circuit with identical real batteries in parallel, replace them with a single ideal battery and a single resistor.

LO 27.3.0 Solve problems related to the ammeter and the voltmeter.

LO 27.3.1 Explain the use of an ammeter and a voltmeter, including the resistance required of each in order to not affect the measured quantities.

LO 27.4.0 Solve problems related to RC circuits.

LO 27.4.1 Draw schematic diagrams of charging and discharging RC circuits.

LO 27.4.2 Write the loop equation (a differential equation) for a charging RC circuit.

LO 27.4.3 Write the loop equation (a differential equation) for a discharging RC circuit.

LO 27.4.4 For a capacitor in a charging or discharging RC circuit, apply the relationship giving the charge as a function of time.

LO 27.4.5 From the function giving the charge as a function of time in a charging or discharging RC circuit, find the capacitor’s potential difference as a function of time.

LO 27.4.6 In a charging or discharging RC circuit, find the resistor’s current and potential difference as functions of time.

LO 27.4.7 Calculate the capacitive time constant τ.

LO 27.4.8 For a charging RC circuit and a discharging RC circuit, determine the capacitor’s charge and potential difference at the start of the process and then a long time later.

Multiple Choice

1. "The sum of the emf's and potential differences around a closed loop equals zero" is a consequence of:

A) Newton's third law

B) Ohm's law

C) Newton's second law

D) conservation of energy

E) conservation of charge

Difficulty: E

Section: 27-1

Learning Objective 27.1.0

2. An emf source is defined in terms of:

A) the force it exerts on charges

B) the work it does on charges

C) the electric field it generates

D) the current it generates

E) the charge it emits

Difficulty: E

Section: 27-1

Learning Objective 27.1.1

3. An ideal battery has an emf of 12 V. If it is connected to a circuit and creates a current of 4.0 A, what is the power?

A) 0.3 W

B) 3.0 W

C) 36 W

D) 48 W

E) cannot tell without knowing the resistance of the circuit

Difficulty: E

Section: 27-1

Learning Objective 27.1.2

4. A battery with an emf of 12 V and an internal resistance of 1  is used to charge a battery with an emf of 10 V and an internal resistance of 1 . The current in the circuit is:

A) 1 A

B) 2 A

C) 4 A

D) 11 A

E) 22 A

Difficulty: M

Section: 27-1

Learning Objective 27.1.4

5. In the diagram R₁ > R₂ > R₃. Rank the three resistors according to the current in them, least to greatest.

A) 1, 2, 3

B) 3, 2, 1

C) 1, 3, 2

D) 3, 1, 2

E) All are the same

Difficulty: E

Section: 27-1

Learning Objective 27.1.7

6. Two 110-V light bulbs, one labeled 25 W and the other 100 W, are connected in series to a 110 V source. Then:

A) the current in the 100-W bulb is greater than that in the 25-W bulb

B) the current in the 100-W bulb is less than that in the 25-W bulb

C) both bulbs will light with equal brightness

D) each bulb will have a potential difference of 55 V

E) none of the above

Difficulty: M

Section: 27-1

Learning Objective 27.1.7

7. A series circuit consists of a battery with internal resistance r and an external resistor R. If these two resistances are equal (r = R) then the energy dissipated per unit time by the internal resistance r is:

A) the same as by R

B) half that by R

C) twice that by R

D) one third that by R

E) unknown unless the emf is given

Difficulty: E

Section: 27-1

Learning Objective 27.1.7

8. Two wires made of the same material have the same length but different diameters. They are connected in series to a battery. The quantity that is the same for the wires is:

A) the end-to-end potential difference

B) the current

C) the current density

D) the electric field

E) the electron drift velocity

Difficulty: E

Section: 27-1

Learning Objective 27.1.7

9. Two wires are made of the same material and have the same length but different radii. They are joined end-to-end and a potential difference is maintained across the combination. Of the following the quantity that is the same for both wires is:

A) potential difference

B) current

C) current density

D) electric field

E) conduction electron drift speed

Difficulty: E

Section: 27-1

Learning Objective 27.1.7

10. Four 20- resistors are connected in series and the combination is connected to a 20-V emf device. The current in any one of the resistors is:

A) 0.25 A

B) 1.0 A

C) 4.0 A

D) 5.0 A

E) 100 A

Difficulty: M

Section: 27-1

Learning Objective 27.1.8

11. Nine identical wires, each of diameter d and length L, are connected in series. The combination has the same resistance as a single similar wire of length L but whose diameter is:

A) 9d

B) 3d

C) d/3

D) d/9

E) d/81

Difficulty: M

Section: 27-1

Learning Objective 27.1.8

12. Resistances of 2.0 , 4.0 , and 6.0  and a 24-V battery are all in series. The current in the 2.0  resistor is:

A) 12 A

B) 4.0 A

C) 2.4 A

D) 2.0 A

E) 0.50 A

Difficulty: M

Section: 27-1

Learning Objective 27.1.8

13. Four 20- resistors are connected in series and the combination is connected to a 20-V emf device. The potential difference across any one of the resistors is:

A) 1 V

B) 4 V

C) 5 V

D) 20 V

E) 80 V

Difficulty: M

Section: 27-1

Learning Objective 27.1.9

14. In the diagram, the current in the 3- resistor is 4 A. The potential difference between points 1 and 2 is:

A) 0.75 V

B) 0.8 V

C) 1.25 V

D) 12 V

E) 20 V

Difficulty: M

Section: 27-1

Learning Objective 27.1.9

15. 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 and the current in each resistor is i

B) the potential difference across each resistor is V/2 and the current in each resistor is i/2

C) the potential difference across each resistor is V and the current in each resistor is i/2

D) the potential difference across each resistor is V/2 and the current in each resistor is i

E) none of the above are true

Difficulty: E

Section: 27-1

Learning Objective 27.1.10

16. 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 current in 1 is twice that in 2

B) the current in 1 is half that in 2

C) the potential difference across 1 is twice that across 2

D) the potential difference across 1 is half that across 2

E) none of the above are true

Difficulty: M

Section: 27-1

Learning Objective 27.1.10

17. Resistor 1 has twice the resistance of resistor 2. The two are connected in series and a potential difference is maintained across the combination. The rate of thermal energy dissipation in 1 is:

A) the same as that in 2

B) twice that in 2

C) half that in 2

D) four times that in 2

E) one fourth that in 2

Difficulty: M

Section: 27-1

Learning Objective 27.1.10

18. Resistances of 2.0 , 4.0 , and 6.0  and a 24-V emf device are all in series. The potential difference across the 2.0- resistor is:

A) 4 V

B) 8 V

C) 12 V

D) 24 V

E) 48 V

Difficulty: M

Section: 27-1

Learning Objective 27.1.10

19. The emf of a battery is equal to its terminal potential difference:

A) under all conditions

B) only when the battery is being charged

C) only when a large current is in the battery

D) only when there is no current in the battery

E) under no conditions

Difficulty: E

Section: 27-1

Learning Objective 27.1.11

20. The terminal potential difference of a battery is less than its emf:

A) under all conditions

B) only when the battery is being charged

C) only when the battery is being discharged

D) only when there is no current in the battery

E) under no conditions

Difficulty: E

Section: 27-1

Learning Objective 27.1.12

21. A battery has an emf of 9 V and an internal resistance of 2 . If the potential difference across its terminals is greater than 9 V:

A) it must be connected across a large external resistance

B) it must be connected across a small external resistance

C) the current must be out of the positive terminal

D) the current must be out of the negative terminal

E) the current must be zero

Difficulty: E

Section: 27-1

Learning Objective 27.1.12

22. A battery of emf 24 V is connected to a 6- resistor. As a result, current of 3 A exists in the resistor. The terminal potential difference of the battery is:

A) 0 V

B) 6 V

C) 12 V

D) 18 V

E) 24 V

Difficulty: M

Section: 27-1

Learning Objective 27.1.12

23. Resistances of 2.0 , 4.0 , and 6.0  and a 24-V emf device are all in series. The circuit is initially ungrounded. After grounding, the current in the circuit:

A) increases

B) decreases

C) does not change

D) depends on where in the circuit the ground wire is attached

E) depends on what the circuit is grounded to

Difficulty: E

Section: 27-1

Learning Objective 27.1.14

24. A battery of emf 24 V is connected to a 6.0- resistor. As a result, current of 3.0 A exists in the resistor. The rate at which energy is being dissipated in the battery is:

A) 3.0 W

B) 6.0 W

C) 18 W

D) 54 W

E) 72 W

Difficulty: M

Section: 27-1

Learning Objective 27.1.15

25. The positive terminals of two batteries with emf's of ₁ and ₂, respectively, are connected together. Here ₁ > _2. The circuit is completed by connecting the negative terminals. If each battery has an internal resistance of r, the rate in watts at which electrical energy is converted to chemical energy in the smaller battery is:

A) /r

B) /2r

C) (₂ – ₁)₁/r

D) (₂ – ₁)₁/2r

E) /2r

Difficulty: M

Section: 27-1

Learning Objective 27.1.16

26. "The sum of the currents into a junction equals the sum of the currents out of the junction" is a consequence of:

A) Newton's third law

B) Ohm's law

C) Newton's second law

D) conservation of energy

E) conservation of charge

Difficulty: E

Section: 27-2

Learning Objective 27.2.0

27. In the context of the loop and junctions rules for electrical circuits a junction is:

A) where a wire is connected to a resistor

B) where a wire is connected to a battery

C) where only two wires are joined

D) where three or more wires are joined

E) where a wire is bent

Difficulty: E

Section: 27-2

Learning Objective 27.2.0

28. A portion of a circuit is shown, with the values of the currents given for some branches. What is the direction and value of the current i?

A) , 6A

B) , 6A

C) , 4A

D) , 4A

E) , 2A

Difficulty: E

Section: 27-2

Learning Objective 27.2.1

29. Four wires meet at a junction. The first carries 4 A into the junction, the second carries 5 A out of the junction, and the third carries 2 A out of the junction. The fourth carries:

A) 7 A out of the junction

B) 7 A into the junction

C) 3 A out of the junction

D) 3 A into the junction

E) 1 A into the junction

Difficulty: E

Section: 27-2

Learning Objective 27.2.1

30. A 120-V power line is protected by a 15-A fuse. What is the maximum number of 120 V, 500 W light bulbs that can be operated at full brightness from this line?

A) 1

B) 2

C) 3

D) 4

E) 5

Difficulty: M

Section: 27-2

Learning Objective 27.2.3

31. A resistor with resistance R₁ and a resistor with resistance R₂ are connected in parallel to an ideal battery with emf . The rate of thermal energy generation in the resistor with resistance R₁ is:

A) ²/R₁

B) ² R₁/(R₁ + R₂)²

C) ² /(R₁ + R₂)

D) ²/R₂

E)

Difficulty: M

Section: 27-2

Learning Objective 27.2.3

32. Four 20- resistors are connected in parallel and the combination is connected to a 20-V emf device. The current in the device is:

A) 0.25 A

B) 1.0 A

C) 4.0 A

D) 5.0 A

E) 100 A

Difficulty: M

Section: 27-2

Learning Objective 27.2.4

33. A total resistance of 3.0  is to be produced by combining an unknown resistor R with a 12  resistor. What is the value of R and how is it to be connected to the 12  resistor?

A) 2.4 , parallel

B) 2.4 , series

C) 4.0 , parallel

D) 4.0 , series

E) 9.0 , series

Difficulty: M

Section: 27-2

Learning Objective 27.2.4

34. By using only two resistors, R₁ and R₂ a student is able to obtain resistances of 3 , 4 , 12 , and 16 . The values of R₁ and R₂ are:

A) 3 , 4 

B) 2 , 12 

C) 3 , 16 

D) 4 , 12 

E) 4 , 16 

Difficulty: M

Section: 27-2

Learning Objective 27.2.4

35. In an antique automobile, a 6-V battery supplies a total of 48 W to two identical headlights in parallel. The resistance of each bulb is:

A) 0.75 Ω

B) 1.5 Ω

C) 3 Ω

D) 4 Ω

E) 8 Ω

Difficulty: M

Section: 27-2

Learning Objective 27.2.4

36. A battery is connected across a parallel 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 and the current in each resistor is i

B) the potential difference across each resistor is V/2 and the current in each resistor is i/2

C) the potential difference across each resistor is V and the current in each resistor is i/2

D) the potential difference across each resistor is V/2 and the current in each resistor is i

E) none of the above are true

Difficulty: E

Section: 27-2

Learning Objective 27.2.5

37. Four 20- resistors are connected in parallel and the combination is connected to a 20-V emf device. The current in any one of the resistors is:

A) 0.25 A

B) 1.0 A

C) 4.0 A

D) 5.0 A

E) 100 A

Difficulty: M

Section: 27-2

Learning Objective 27.2.5

38. Two wires made of the same material have the same length but different diameter. They are connected in parallel to a battery. The quantity that is NOT the same for the wires is:

A) the end-to-end potential difference

B) the current

C) the current density

D) the electric field

E) the electron drift velocity

Difficulty: M

Section: 27-2

Learning Objective 27.2.5

39. The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in parallel and a potential difference is maintained across the combination. Then:

A) the current in 1 is twice that in 2

B) the current in 1 is half that in 2

C) the potential difference across 1 is twice that across 2

D) the potential difference across 1 is half that across 2

E) none of the above are true

Difficulty: E

Section: 27-2

Learning Objective 27.2.5

40. Resistor 1 has twice the resistance of resistor 2. The two are connected in parallel and a potential difference is maintained across the combination. The rate of thermal energy dissipation in 1 is:

A) the same as that in 2

B) twice that in 2

C) half that in 2

D) four times that in 2

E) one fourth that in 2

Difficulty: M

Section: 27-2

Learning Objective 27.2.5

41. Resistor 1 has twice the resistance of resistor 2. They are connected in parallel to a battery. The ratio of the thermal energy dissipation by 1 to that by 2 is:

A) 1:4

B) 1:2

C) 1:1

D) 2:1

E) 4:1

Difficulty: M

Section: 27-2

Learning Objective 27.2.5

42. The equivalent resistance between points 1 and 2 of the circuit shown is:

A) 2.5 

B) 4.0 

C) 5.0 

D) 6.5 

E) 16 

Difficulty: M

Section: 27-2

Learning Objective 27.2.6

43. Each of the resistors in the diagram is 12 . The resistance of the entire circuit is:

A) 5.8 

B) 25 

C) 48 

D) 120 

E) none of these

Difficulty: M

Section: 27-2

Learning Objective 27.2.6

44. The current in the 5.0- resistor in the circuit shown is:

A) 0.42 A

B) 0.67 A

C) 1.5 A

D) 2.4 A

E) 3.0 A

Difficulty: M

Section: 27-2

Learning Objective 27.2.6

45. In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (I, II, III, IV, V) will the bulbs glow with the same brightness as in circuit X?

A) I

B) II

C) III

D) IV

E) V

Difficulty: M

Section: 27-2

Learning Objective 27.2.6

46. In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (I, II, III, IV, V) will the bulbs be dimmest?

A) I

B) II

C) III

D) IV

E) V

Difficulty: M

Section: 27-2

Learning Objective 27.2.6

47. A 3- and a 1.5- resistor are wired in parallel and the combination is wired in series to a 4- resistor and a 10-V emf device. The current in the 3- resistor is:

A) 0.33 A

B) 0.67 A

C) 2.0 A

D) 3.3 A

E) 6.7 A

Difficulty: M

Section: 27-2

Learning Objective 27.2.6

48. A 3- and a 1.5- resistor are wired in parallel and the combination is wired in series to a 4- resistor and a 10-V emf device. The potential difference across the 3- resistor is:

A) 2.0 V

B) 6.0 V

C) 8.0 V

D) 10 V

E) 12 V

Difficulty: M

Section: 27-2

Learning Objective 27.2.6

49. For any circuit the number of independent equations containing emf's, resistances, and currents equals:

A) the number of junctions

B) the number of junctions minus 1

C) the number of branches

D) the number of branches minus 1

E) the number of closed loops

Difficulty: E

Section: 27-2

Learning Objective 27.2.7

50. If a circuit has L closed loops, B branches, and J junctions the number of independent loop equations is:

A) B – J + 1

B) B – J

C) B

D) L

E) L – J

Difficulty: E

Section: 27-2

Learning Objective 27.2.7

51. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 , are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4- resistor. The current in the 4- resistor is:

A) 2.0 A

B) 3.6 A

C) 4.0 A

D) 7.2 A

E) 9.0 A

Difficulty: M

Section: 27-2

Learning Objective 27.2.7

52. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 , are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4- resistor. The current in each battery is:

A) 1.0 A

B) 2.0 A

C) 3.6 A

D) 4.0 A

E) 4.5 A

Difficulty: M

Section: 27-2

Learning Objective 27.2.7

53. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 , are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4- resistor. The potential difference across the 4- resistor is:

A) 4.0 V

B) 8.0 V

C) 14 V

D) 16 V

E) 29 V

Difficulty: M

Section: 27-2

Learning Objective 27.2.7

54. The circuit shown was wired for the purpose of measuring the resistance of the lamp L. Inspection shows that:

A) voltmeter V and rheostat R should be interchanged

B) the circuit is satisfactory

C) the ammeter A should be in parallel with R, not L

D) the meters, V and A, should be interchanged

E) L and V should be interchanged

Difficulty: E

Section: 27-3

Learning Objective 27.3.1

55. When switch S is open, the ammeter in the circuit shown reads 2.0 A. When S is closed, the ammeter reading:

A) increases slightly

B) remains the same

C) decreases slightly

D) doubles

E) halves

Difficulty: E

Section: 27-3

Learning Objective 27.3.1

56. A certain galvanometer has a resistance of 100  and requires 1 mA for full scale deflection. To make this into a voltmeter reading 1 V full scale, connect a resistance of:

A) 1000  in parallel

B) 900  in series

C) 1000  in series

D) 10  in parallel

E) 0.1  in series

Difficulty: M

Section: 27-3

Learning Objective 27.3.1

57. In the figure, voltmeter V₁ reads 600 V, voltmeter V₂ reads 580 V, and ammeter A reads 100 A. The power wasted in the transmission line connecting the power house to the consumer is:

A) 1 kW

B) 2 kW

C) 58 kW

D) 59 kW

E) 60 kW

Difficulty: M

Section: 27-3

Learning Objective 27.3.1

58. To make a galvanometer into an ammeter, connect:

A) a high resistance in parallel

B) a high resistance in series

C) a low resistance in series

D) a low resistance in parallel

E) a source of emf in series

Difficulty: E

Section: 27-3

Learning Objective 27.3.1

59. A certain voltmeter has an internal resistance of 10,000  and a range from 0 to 100 V. To give it a range from 0 to 1000 V, one should connect:

A) 100,000  in series

B) 100,000  in parallel

C) 1000  in series

D) 1000  in parallel

E) 90,000  in series

Difficulty: M

Section: 27-3

Learning Objective 27.3.1

60. A certain ammeter has an internal resistance of 1  and a range from 0 to 50 mA. To make its range from 0 to 5 A, use:

A) a series resistance of 99 

B) an extremely large (say 10⁶ ) series resistance

C) a resistance of 99  in parallel

D) a resistance of 1/99  in parallel

E) a resistance of 1/1000  in parallel

Difficulty: M

Section: 27-3

Learning Objective 27.3.1

61. A galvanometer has an internal resistance of 12  and requires 0.01 A for full scale deflection. To convert it to a voltmeter reading 3 V full scale, one must use a series resistance of:

A) 102 

B) 288 

C) 300 

D) 360 

E) 412 

Difficulty: M

Section: 27-3

Learning Objective 27.3.1

62. A certain voltmeter has an internal resistance of 10,000  and a range from 0 to 12 V. To extend its range to 120 V, use a series resistance of:

A) 1,111 

B) 90,000 

C) 100,000 

D) 108,000 

E) 120,000 

Difficulty: M

Section: 27-3

Learning Objective 27.3.1

63. The time constant RC has units of:

A) second/farad

B) second/ohm

C) 1/second

D) second/watt

E) none of these

Difficulty: E

Section: 27-4

Learning Objective 27.4.0

64. Suppose the current charging a capacitor is kept constant. Which graph below correctly gives the potential difference V across the capacitor as a function of time?

A) I

B) II

C) III

D) IV

E) V

Difficulty: E

Section: 27-4

Learning Objective 27.4.0

65. Here is a loop equation: . What does this equation represent?

A) a charging capacitor

B) a discharging capacitor

C) a capacitor that has been disconnected

D) a charging resistor

E) an oscillating circuit

Difficulty: E

Section: 27-4

Learning Objective 27.4.2, 27.4.3

66. A certain capacitor, in series with a resistor, is being charged. At the end of 10 ms its charge is half the final value. The time constant for the process is about:

A) 5.0 ms

B) 6.9 ms

C) 10 ms

D) 14 ms

E) 20 ms

Difficulty: M

Section: 27-4

Learning Objective 27.4.4

67. In the capacitor discharge formula q = q₀e^–t/RC the symbol t represents:

A) the time constant

B) the time it takes for C to lose the fraction 1/e of its initial charge

C) the time it takes for C to lose the fraction (1 – 1/e) of its initial charge

D) the time it takes for C to lose essentially all of its initial charge

E) none of the above

Difficulty: E

Section: 27-4

Learning Objective 27.4.4

68. A charged capacitor is being discharged through a resistor. At the end of one time constant the charge has been reduced by (1 – 1/e) = 63% of its initial value. At the end of two time constants the charge has been reduced by what percent of its initial value?

A) 82%

B) 86%

C) 100%

D) between 90% and 100%

E) need to know more data to answer the question

Difficulty: M

Section: 27-4

Learning Objective 27.4.5

69. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open.

The values of the emf , resistance and R, and capacitance C for each for the circuits are

Rank the circuits according to the current just after switch S is closed least to greatest.

A) 1, 2, 3, 4

B) 4, 3, 2, 1

C) 4, 2, 3, 1

D) 4, 2, 1, 3

E) 3, 1, 2, 4

Difficulty: M

Section: 27-4

Learning Objective 27.4.6

70. In the circuit shown, the capacitor is initially uncharged, and V = 10 V. At time t = 0, switch S is closed. If  denotes the time constant, the approximate current through the 3  resistor when

t = /10 is:

A) 0.50 A

B) 0.75 A

C) 1.0 A

D) 1.5 A

E) 3.0 A

Difficulty: M

Section: 27-4

Learning Objective 27.4.6

71. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open.

The values of the emf , resistance R, and the capacitance C for each of the circuits are

Rank the circuits according to the time after switch S is closed for the capacitors to reach half their final charges, least to greatest.

A) 1, 2, 3, 4

B) 2, 4, 3, 1

C) 1, 3, 4, 2

D) 4, 2, 1, 3

E) 3, 1, 2, 4

Difficulty: M

Section: 27-4

Learning Objective 27.4.7

72. In the circuit shown, both resistors have the same value R. Suppose switch S is initially closed and capacitor C is charged. When switch S is then opened, the circuit has a time constant _a. Conversely, suppose S is initially open and capacitor C is uncharged. When switch S is then closed, the circuit has a time constant _b. The ratio _a/_b is:

A) 0.5

B) 0.67

C) 1

D) 1.5

E) 2

Difficulty: M

Section: 27-4

Learning Objective 27.4.7

73. A certain capacitor, in series with a 720- resistor, is being charged. At the end of 10 ms its charge is half the final value. The capacitance is about:

A) 9.6 F

B) 14 F

C) 20 F

D) 7.2 F

E) 10 F

Difficulty: M

Section: 27-4

Learning Objective 27.4.7

74. An initially uncharged capacitor C is connected in series with resistor R. This combination is then connected to a battery of emf V₀. Sufficient time elapses so that a steady state is reached. Which of the following statements is NOT true?

A) The time constant is independent of V₀

B) The final charge on C is independent of R

C) The total energy dissipated by R is independent of R

D) The total energy dissipated by R is independent of V₀

E) The initial current (just after the battery was connected) is independent of C

Difficulty: E

Section: 27-4

Learning Objective 27.4.8