Page 333 - Schaum's Outline of Theory and Problems of Applied Physics

318 CAPACITANCE [CHAP. 26

26.15. (a) What potential difference must be applied across a 10-µF capacitor if it is to have an energy content of 1 J?
(b) What is the charge on the capacitor under these circumstances?

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26.16. The dielectric between the plates of a certain 80-µF capacitor has a resistance of 10 . If the capacitor is charged
and then disconnected, how long will it take for the charge on the capacitor to fall to 37 percent of its original value?
26.17. A5-µF capacitor is connected to a 100-V battery through a circuit whose resistance is 800 . (a) What is the time
constant of this arrangement? (b) What is the initial current that flows when the battery is connected? (c) What is
the final charge on the capacitor?

26.18. Find the charge on the capacitor of Prob. 26.17 at 0.001, 0.005, and 0.01 s after the connection to the battery is made.
26.19. The resistance of the dielectric between the plates of the capacitor of Prob. 26.17 is 10 . If the capacitor is
disconnected from the battery, find the charge remaining on it 30 s, 1 min, and 10 min later.

Answers to Multiple-Choice Questions

26.1. (c) 26.6. (b) 26.11. (b)
26.2. (a) 26.7. (b) 26.12. (c)

26.3. (c) 26.8. (d) 26.13. (d)

26.4. (c) 26.9. (c)
26.5. (c) 26.10. (b)

Answers to Supplementary Problems

26.1. From their definitions, R = V/I = V t/Q and C = Q/V. Hence RC = (V t/Q)(Q/V ) = t.
26.2. 0.0025 C 26.11. 3.33 µF; 6.67 µF; 15 µF; 30 µF

26.3. 20 µF 26.12. Q 1 = 2 × 10 −9 C; Q 2 = 2.5 × 10 −9 C; V 1 = V 2 = 100 V

26.4. 600 V 26.13. Q 1 = Q 2 = 7.5 × 10 −9 C; V 1 = 150 V; V 2 = 100 V
26.5. 3.9 pF 26.14. 2.5 J

26.6. 5.9 pF 26.15. (a) 447 V (b)4.47 × 10 −3 C

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26.7. 2C 26.16. 8 × 10 s = 22.2h
26.8. 6.25 26.17. (a) 0.004 s (b) 0.125 A (c) 5 × 10 −4 C
26.9. 2.86 µF 26.18. 1.106 × 10 −4 C; 3.567 × 10 −4 C; 4.590 × 10 −4 C

26.10. 35 µF 26.19. 2.744 × 10 −4 C; 1.506 × 10 −4 C; 3.072 × 10 −9 C