Chapter (26)

Chapter 26

Capacitance and Dielectrics

Multiple Choice

1. Determine the equivalent capacitance of the combination shown when C = 12 pF.

C C

2C

C

a. 48 pF b. 12 pF c. 24 pF d. 6.0 pF e. 59 pF

2. Determine the equivalent capacitance of the combination shown when C = 15 mF.

C 2C

C

C

a. 20 mF b. 16 mF c. 12 mF d. 24 mF e. 75 mF

3. Determine the equivalent capacitance of the combination shown when C = 12 nF.

2C C

C 3C

a. 34 nF b. 17 nF c. 51 nF d. 68 nF e. 21 nF

75

76 CHAPTER 26

4. Determine the equivalent capacitance of the combination shown when C = 45 μF.

C 2C

C 2C

a. 36 μF b. 32 μF c. 34 μF d. 30 μF e. 38 μF

5. If C = 10 μF, what is the equivalent capacitance for the combination shown?

8.0 μF 6.0 μF

C

a. 7.5 μF b. 6.5 μF c. 7.0 μF d. 5.8 μF e. 13 μF

6. What is the equivalent capacitance of the combination shown?

12 μF 24 μF

20 μF

12 μF a. 29 μF b. 10 μF c. 40 μF d. 25 μF e. 6.0 μF

Capacitance and Dielectrics 77

7. What is the equivalent capacitance of the combination shown?

30 μF

30 μF

20 μF

10 μF a. 20 μF b. 90 μF c. 22 μF d. 4.6 μF e. 67 μF


2C 3C

C

6C a. 28 μF b. 36 μF c. 52 μF d. 44 μF e. 23 μF


2CC

2C

2C 2C


78 CHAPTER 26

10. Determine the energy stored in C2 when C1 = 15 μF, C2 = 10 μF, C3 = 20 μF, and V0 = 18 V.

+�

–�

V0C2 C3

C1

a. 0.72 mJ b. 0.32 mJ c. 0.50 mJ d. 0.18 mJ e. 1.60 mJ

11. Determine the energy stored in C1 when C1 = 10 μF, C2 = 12 μF, C3 = 15 μF, and V0 = 70 V.

+ –

V0

C1 C2 C3


12. Determine the energy stored by C4 when C1 = 20 μF, C2 = 10 μF, C3 = 14 μF, C4 = 30 μF, and V0 = 45 V.

C1 C4

+ –

V0

C2

C3



13. Determine the charge stored by C1 when C1 = 20 μF, C2 = 10 μF,C3 = 30 μF, and V0 = 18 V.

C1

+ –

V0

C2

C3

a. 0.37 mC b. 0.24 mC c. 0.32 mC d. 0.40 mC e. 0.50 mC

14. What is the total energy stored by C3 when C1 = 50 μF, C2 = 30 μF, C3 = 36 μF, C4 = 12 μF, and V0 = 30 V?

C4

+ –

V0

C3C2C1

a. 6.3 mJ b. 25 mJ c. 57 mJ d. 1.6 mJ e. 14 mJ

15. How much energy is stored in the 50-μF capacitor when Va – Vb = 22V?

50 μF

25 μF

25 μFa

b


80 CHAPTER 26

16. What is the total energy stored in the group of capacitors shown if the charge on the 30-μF capacitor is 0.90 mC?

30 μF

20 μF

15 μF a. 29 mJ b. 61 mJ c. 21 mJ d. 66 mJ e. 32 mJ

17. What is the potential difference across C2 when C1 = 5.0 μF, C2 = 15 μF, C3 = 30 μF, and V0 = 24 V?

C2 C3

C1

+ –��V0

a. 21 V b. 19 V c. 16 V d. 24 V e. 8.0 V


18. What total energy is stored in the group of capacitors shown if the potential difference Vab is equal to 50 V?

50 μF

20 μF

10 μF

a

b

a. 48 mJ b. 27 mJ c. 37 mJ d. 19 mJ e. 10 mJ

19. Determine the energy stored in the 60-μF capacitor.

50 V

25 μF

40 μF 60 μF


20. Determine the energy stored in the 40-μF capacitor.

50 V40 μF 60 μF

25 μF


82 CHAPTER 26

21. If VA – VB = 50 V, how much energy is stored in the 36-μF capacitor?

36 μF

72 μF

54 μF

A B

a. 50 mJ b. 28 mJ c. 13 mJ d. 8.9 mJ e. 17 mJ

22. If VA – VB = 50 V, how much energy is stored in the 54-μF capacitor?

36 μF

72 μF

54 μF

A B

a. 50 mJ b. 13 mJ c. 28 mJ d. 8.9 mJ e. 17 mJ

23. A 3.0-μF capacitor charged to 40 V and a 5.0-μF capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 3.0-μF capacitor?

a. 11 μC b. 15 μC c. 19 μC d. 26 μC e. 79 μC

24. A 6.0-μF capacitor charged to 50 V and a 4.0-μF capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected. What is the total energy stored in the 6.0-μF capacitor at equilibrium?



25. A 25-μF capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected. The final potential difference across the 25-μF capacitor is 36 V. What is the value of the capacitance of C?


26. A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other. What is the final charge on the 6.0-mF capacitor?

a. 20 mC b. 8.0 mC c. 10 mC d. 12 mC e. 230 mC

27. When a capacitor has a charge of magnitude 80 μC on each plate the potential difference across the plates is 16 V. How much energy is stored in this capacitor when the potential difference across its plates is 42 V?


28. A 15-μF capacitor and a 30-μF capacitor are connected in series, and charged to a potential difference of 50 V. What is the resulting charge on the 30-μF capacitor?

a. 0.70 mC b. 0.80 mC c. 0.50 mC d. 0.60 mC e. 0.40 mC

29. A 15-μF capacitor and a 25-μF capacitor are connected in parallel, and charged to a potential difference of 60 V. How much energy is then stored in this capacitor combination?

a. 50 mJ b. 18 mJ c. 32 mJ d. 72 mJ e. 45 mJ

84 CHAPTER 26

30. A 20-μF capacitor charged to 2.0 kV and a 40-μF capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 20-μF capacitor after the two are so connected?

a. 53 mC b. 27 mC c. 40 mC d. 80 mC e. 39 mC

31. A 15-μF capacitor is charged to 40 V and then connected across an initially uncharged 25-μF capacitor. What is the final potential difference across the 25-μF capacitor?

a. 12 V b. 18 V c. 15 V d. 21 V e. 24 V

32. A 30-μF capacitor is charged to 40 V and then connected across an initially uncharged 20-μF capacitor. What is the final potential difference across the 30-μF capacitor?

a. 15 V b. 24 V c. 18 V d. 21 V e. 40 V

33. A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60-μF capacitor. If the final potential difference across the 60-μF capacitor is 40 V, determine C.


34. A 30-μF capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C. If the final potential difference across the 30-μF capacitor is 20 V, determine C.



35. A 30-μF capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-μF capacitor. If the final potential difference across the 10-μF capacitor is 20 V, determine V0.

a. 13 V b. 27 V c. 20 V d. 29 V e. 60 V

36. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are

a. 21Q0, 2

1V0

b. Q0, 21V0

c. Q0, V0 d. Q0, 2V0 e. 2Q0, 2V0

37. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the new capacitance and the potential difference between the plates are

a. 21C0, 2

1V0

21

b. C0, V0

c. 21C0, 2V0

d. C0, 2V0 e. 2C0, 2V0

86 CHAPTER 26

38. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are

a. 21Q0, 2

1V0

b. 21Q0, V0

c. Q0, V0 d. 2Q0, V0 e. 2Q0, 2V0

39. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the capacitance of the capacitor and the magnitude of the charge on the plates are

a. 1C0, 2

1Q0 2

b. 21C0, Q0

c. C0, Q0 d. 2C0, Q0 e. 2C0, 2Q0

40. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. While it is connected to the battery the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the potential difference between them are

a. 31Q0, 3

1V0

b. Q0, 31V0

c. Q0, V0 d. 3Q0, V0 e. 3Q0, 3V0


41. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. While it is connected to the battery, the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the new capacitance are

a. 31Q0, 3

1C0

b. Q0, 31C0

c. Q0, C0 d. 3Q0, C0 e. 3Q0, 3C0

42. The equivalent capacitance of the circuit shown below is

C 2C C

a

b a. 0.2 C. b. 0.4 C. c. 1 C. d. 4 C. e. 5 C.


C 2C Ca b

a. 0.2 C. b. 0.4 C. c. 1 C. d. 4 C. e. 5 C.


2Ca

b

C C

a. 0.50 C. b. 1.0 C. c. 1.5 C. d. 2.0 C. e. 2.5 C.

88 CHAPTER 26

45. Which of the following is not a capacitance?

a. dA0ε

b. dA0κε

c. )( abk

ab

e −

d. )ln(2 abke

e. dAke 0ε

46. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitudes of the charge on the plates and the potential difference between them are

a. 03 0 31

,1

VQ .

b. 0

00 3 ,3 VQ

0 31

, VQ .

c. . 00 ,VQd. . 00 3 , VQe. .

47. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitudes of the capacitance and the potential difference between the plates are

a. 00 31

,31

VC .

b. 00 3 , VC

00 ,VC

1.

c. .

d. 00 300 3 ,3 VC

1 ,3 VC .

e. .


48. An initially uncharged parallel plate capacitor of capacitance C is charged to potential V by a battery. The battery is then disconnected. Which statement is correct?

a. There is no charge on either plate of the capacitor. b. The capacitor can be discharged by grounding any one of its two plates. c. Charge is distributed evenly over both the inner and outer surfaces of the

plates. d. The magnitude of the electric field outside the space between the plates is

approximately zero. e. The capacitance increases when the distance between the plates increases.

49. A 0.120 pF parallel-plate capacitor is charged to a potential difference of 10.0 V and then disconnected from the battery. A cosmic ray burst creates 1.00 electrons and 1.00 positive charges between the plates. If the charges do not recombine, but reach the oppositely charged plates, by how much is the potential difference between the capacitor plates reduced?

×106

×106

a. 1.33 V b. 7.34 V c. 8.67 V d. 1,330 V e. 8,670 V

50. A 0.16 pF parallel-plate capacitor is charged to 10 V. Then the battery is disconnected from the capacitor. When 1.00 ×107

+1.1 V+8.9 V

electrons are now placed on the negative plate of the capacitor, the voltage between the plates changes by

a. . −8.9 V−1.1 Vb. .

c. 0 V. d. . e. .

51. A 0.16 pF parallel-plate capacitor is charged to 10 V. Then the battery is disconnected from the capacitor. When 1.00 107 positive charges of magnitude ×e| | are now placed on the positive plate of the capacitor, the voltage between the

plates changes by

a. . −8.9 Vb. . −1.1 Vc. 0 V. d. . +1.1 V

+8.9 Ve. .

90 CHAPTER 26

52. A parallel plate capacitor is charged to voltage V and then disconnected from the battery. Leopold says that the voltage will decrease if the plates are pulled apart. Gerhardt says that the voltage will remain the same. Which one, if either, is correct, and why?

a. Gerhardt, because the maximum voltage is determined by the battery. b. Gerhardt, because the charge per unit area on the plates does not change. c. Leopold, because charge is transferred from one plate to the other when the

plates are separated. d. Leopold, because the force each plate exerts on the other decreases when the

plates are pulled apart. e. Neither, because the voltage increases when the plates are pulled apart.

53. Addition of a metal slab of thickness a between the plates of a parallel plate capacitor of plate separation d is equivalent to introducing a dielectric with dielectric constant κ between the plates. The value of κ is

a. d − a

d.

b. . dc. . d − a

dd.

ad −.

e. da

.

54. A parallel plate capacitor is connected to a battery and charged to voltage V. Leah says that the charge on the plates will decrease if the distance between the plates is increased while they are still connected to the battery. Gertie says that the charge will remain the same. Which one, if either, is correct, and why?

a. Gertie, because the maximum voltage is determined by the battery. b. Gertie, because the capacitance of the capacitor does not change. c. Leah, because the capacitance decreases when the plate separation is

increased. d. Leah, because the capacitance increases when the plate separation is

increased. e. Neither, because the charge increases when the plate separation is

increased.


Open-Ended Problems

55. Is it feasible to construct an air-filled parallel-plate capacitor that has its two plates separated by 0.10 mm and has a capacitance of 1.0 F?

56. Regarding the Earth and a cloud layer 800 m above the Earth as the “plates” of a capacitor, calculate the capacitance if the cloud layer has an area of 1.0 km2. If an electric field of 2.0 × 106 N/C makes the air break down and conduct electricity (lightning), what is the maximum charge the cloud can hold?

57. An electron is released from rest at the negative plate of a parallel plate capacitor. If the distance between the plates is 5 mm and the potential difference across the plates is 5 V, with what velocity does the electron hit the positive plate? (me = 9.1 × 10–31 kg, qe = 1.6 × 10–19 C.)

58. A 200-volt battery is connected to a 0.50-microfarad parallel-plate, air-filled capacitor. Now the battery is disconnected, with care taken not to discharge the plates. Some Pyrex glass is then inserted between the plates, completely filling up the space. What is the final potential difference between the plates? (The dielectric constant for Pyrex is κ = 5.6.)

92 CHAPTER 26


Chapter 26

Capacitance and Dielectrics

1. d

2. c

3. b

4. d

5. d

6. b

7. a

8. b

9. c

10. d

11. c

12. d

13. b

14. a

15. d

16. d

17. c

18. d

19. b

20. c

21. d

22. b

23. a

24. b

25. c

26. d

27. b

28. c

29. d

30. b

31. c

32. b

33. c

34. d

35. b

36. d

37. c

38. b

39. a

40. d

41. e

42. d

43. b

44. b

45. e

46. b

47. d

48. d

49. a

50. d

51. d

52. e

53. d

54. c

55. No. Each plate would have an area of 1.1 × 107 m2

56. 11.1 nF, 17.7 C

57. 1.33 × 106 m/s

58. 36 V

94 CHAPTER 26

Chapter (26)

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