# 9.1.A: Capacitance (Answers)

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## 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

**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 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).