Page 332 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 26] CAPACITANCE 317

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26.11. A total of 2 × 10 C is shifted from one terminal to the other while a storage battery is charged. The potential
difference between the terminals afterward is 12 V. The energy stored in the battery is
(a) 17 kJ (c) 24 MJ
(b) 2.4 MJ (d) 29 MJ

26.12. A storage battery is being charged at a rate of 100 W at a potential difference of 13.6 V. The rate at which charge is
being shifted between its terminals is
(a) 0.136 C/s (c) 7.35 C/s
(b) 0.54 C/s (d) 1360 C/s

26.13. A charged 50-µF capacitor is discharged through a 1.0-k resistor. The charge on the capacitor will drop to 37 percent
of its original value in
(a) 50 ns (c) 25 ms
(b) 20 ms (d) 50 ms

Supplementary Problems

26.1. Verify that RC has the dimensions of time.
26.2. A 10-µF capacitor has a potential difference of 250 V across it. What is the charge on the capacitor?

26.3. A capacitor has a charge of 0.002 C when it is connected across a 100-V battery. Find its capacitance.

26.4. What is the potential difference across a 500-pF capacitor whose charge is 0.3 µC?
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26.5. The plates of a parallel-plate capacitor have areas of 40 cm and are separated by 0.2 mm of waxed paper (K = 2.2).
Find the capacitance.

26.6. The waxed paper is removed from between the plates of the capacitor of Prob. 26.5. Find the new capacitance.
26.7. The plates of a parallel-plate capacitor of capacitance C are moved closer together until they are half their original
separation. What is the new capacitance?
26.8. The capacitance of a parallel-plate capacitor is increased from 8 to 50 µF when a sheet of glass is inserted between
its plates. What is the dielectric constant K of the glass?

26.9. Three capacitors whose capacitances are 5, 10, and 20 µF are connected in series. Find the equivalent capacitance
of the combination.

26.10. The three capacitors of Prob. 26.9 are connected in parallel. Find the equivalent capacitance of the combination.

26.11. List the capacitance that can be obtained by combining three 10-µF capacitors in all possible ways.
26.12. A 20- and a 25-pF capacitor are connected in parallel, and a potential difference of 100 V is applied to the combination.
Find the charge on each capacitor and the potential difference across it.
26.13. A 50- and a 75-pF capacitor are connected in series, and a potential difference of 250 V is applied to the combination.
Find the charge on each capacitor and the potential difference across it.
26.14. A5-µF capacitor has a potential difference of 1000 V. What is its potential energy?