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8.A: Capacitance (Answers)

Check Your Understanding

8.1. \(\displaystyle 1.1×10^{−3}m\)

8.3. 3.59 cm, 17.98 cm

8.4. a. 25.0 pF;

b. 9.2

8.5. a. \(\displaystyle C=0.86pF,Q_1=10pC,Q_2=3.4pC,Q_3=6.8pC\);

b. \(\displaystyle C=2.3pF,Q_1=12pC,Q_2=Q_3=16pC\);

c. \(\displaystyle C=2.3pF,Q_1=9.0pC,Q_2=18pC,Q_3=12pC,Q_4=15pC\) 

8.6. a.\(\displaystyle 4.0×10^{−13}J\); b. 9 times

8.7. a. 3.0; b. \(\displaystyle C=3.0C_0\)

8.9. a. \(\displaystyle C_0=20pF, C=42pF\);

b. \(\displaystyle Q_0=0.8nC, Q=1.7nC\);

c. \(\displaystyle V_0=V=40V\); d. \(\displaystyle U_0=16nJ, U=34nJ\)

Conceptual Questions

1. no; yes

3. false

5. no

7. \(\displaystyle 3.0μF,0.33μF\)

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. \(\displaystyle 1.1×10^{−3}m^2\)

27. 500 µC

29. 1:16

31. a. 1.07 nC;

b. 267 V, 133 V

33. \(\displaystyle 0.29μF\)

34. 500 capacitors; connected in parallel

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

37. \(\displaystyle 11.4μF\)

39. 0.89 mC; 1.78 mC; 444 V

41. \(\displaystyle 7.5μJ\)

43. a. 405 J; b. 90.0 mC

45. 1.15 J

47. a. \(\displaystyle 4.43×10^{−9}F\);

b. 0.453 V;

c. \(\displaystyle 4.53×10^{−10}J\);

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. \(\displaystyle 4.4μF\);

b. \(\displaystyle 4.0×10^{-5}C\)

61. \(\displaystyle 0.0135m^2\)

63. \(\displaystyle 0.185μJ\)

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. \(\displaystyle 75.6μC\); 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

94f7093bf8a3e77b0a91a24f4bb3e92c64acc2c3.jpg

73. a. \(\displaystyle −3.00μF\);

b. You cannot have a negative \(\displaystyle C_2\) 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. \(\displaystyle C=ε_0A/(d_1+d_2)\) 

83. proof

Contributors

Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).