Processing math: 100%
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Physics LibreTexts

4.A: Capacitance (Answers)

( \newcommand{\kernel}{\mathrm{null}\,}\)

Check Your Understanding

8.1. 1.1×103m

8.3. 3.59 cm, 17.98 cm

8.4. a. 25.0 pF;

b. 9.2

8.5. a. C=0.86pF,Q1=10pC,Q2=3.4pC,Q3=6.8pC;

b. C=2.3pF,Q1=12pC,Q2=Q3=16pC;

c. C=2.3pF,Q1=9.0pC,Q2=18pC,Q3=12pC,Q4=15pC

8.6. a.4.0×1013J; b. 9 times

8.7. a. 3.0; b. C=3.0C0

8.9. a. C0=20pF,C=42pF;

b. Q0=0.8nC,Q=1.7nC;

c. V0=V=40V; d. U0=16nJ,U=34nJ

Conceptual Questions

1. no; yes

3. false

5. no

7. 3.0μF,0.33μF

9. answers may vary

11. Dielectric strength is a critical value of an electrical field above which an insulator starts to conduct; a dielectric constant is the ratio of the electrical field in vacuum to the net electrical field in a material.

13. Water is a good solvent.

15. When energy of thermal motion is large (high temperature), an electrical field must be large too in order to keep electric dipoles aligned with it.

17. answers may vary

Problems

19. 21.6 mC

21. 1.55 V

23. 25.0 nF

25. 1.1×103m2

27. 500 µC

29. 1:16

31. a. 1.07 nC;

b. 267 V, 133 V

33. 0.29μF

34. 500 capacitors; connected in parallel

35. 3.08μF (series) and 13.0μ (parallel)

37. 11.4μF

39. 0.89 mC; 1.78 mC; 444 V

41. 7.5μJ

43. a. 405 J; b. 90.0 mC

45. 1.15 J

47. a. 4.43×109F;

b. 0.453 V;

c. 4.53×1010J;

d. no

49. 0.7 mJ

51. a. 7.1 pF;

b. 42 pF

53. a. before 3.00 V; after 0.600 V;

b. before 1500 V/m; after 300 V/m

55. a. 3.91;

b. 22.8 V

57. a. 37 nC;

b. 0.4 MV/m;

c. 19 nC

59. a. 4.4μF;

b. 4.0×105C

61. 0.0135m2

63. 0.185μJ

Additional Problems

65. a. 0.277 nF;

b. 27.7 nC;

c. 50 kV/m

67. a. 0.065 F;

b. 23,000 C;

c. 4.0 GJ

69. a. 75.6μC; b. 10.8 V

71. a. 0.13 J;

b. no, because of resistive heating in connecting wires that is always present, but the circuit schematic does not indicate resistors

Figure shows a closed circuit with a battery of 400 volts. The positive terminal of the battery is connected to a capacitor of 3 micro Farads, followed by a combination of two capacitors in parallel with each other, followed by a fourth capacitor of value 6 micro Farads, which in turn is connected to the negative terminal of the battery. The capacitors in parallel to each other have values 6 micro Farad and 3 micro Farad.

73. a. 3.00μF;

b. You cannot have a negative C2 capacitance.

c. The assumption that they were hooked up in parallel, rather than in series, is incorrect. A parallel connection always produces a greater capacitance, while here a smaller capacitance was assumed. This could only happen if the capacitors are connected in series.

75. a. 14.2 kV;

b. The voltage is unreasonably large, more than 100 times the breakdown voltage of nylon.

c. The assumed charge is unreasonably large and cannot be stored in a capacitor of these dimensions.

Challenge Problems

77. a. 89.6 pF;

b. 6.09 kV/m;

c. 4.47 kV/m;

d. no

79. a. 421 J;

b. 53.9 mF

81. C=ε0A/(d1+d2)

83. proof

Contributors and Attributions

Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).


This page titled 4.A: Capacitance (Answers) is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

Support Center

How can we help?