Page 328 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 26] CAPACITANCE 313

SOLVED PROBLEM 26.13
A 100-µF capacitor is to have an energy content of 50 J to operate a flashlamp. (a) What voltage is
required to charge the capacitor? (b) How much charge passes through the flashlamp?
2
1
(a) Since W = CV ,
2

2W (2)(50 J)
V = = = 1000 V
C 10 −4 F
3
(b) Q = CV = (10 −4 F)(10 V) = 0.1C
CHARGING A CAPACITOR
When a capacitor is being charged in a circuit such as that of Fig. 26-6, at any moment the voltage Q/C across
it is in the opposite direction to the battery voltage V and thus tends to oppose the flow of additional charge. For
this reason a capacitor does not acquire its final charge the instant it is connected to a battery or other source of
emf. The net potential difference when the charge on the capacitor is Q is V − (Q/C), and the current is then
Q V − (Q/C)
I = =
t R
As Q increases, its rate of increase I = Q/ t decreases. Figure 26-7 shows how Q, measured in percent of
final change, varies with time when a capacitor is being charged; the switch of Fig. 26-6 is closed at t = 0.
The product RC of the resistance R in the circuit and the capacitance C governs the rate at which the
capacitor reaches its ultimate charge of Q 0 = CV. The product RC is called the time constant T of the circuit.
After a time equal to T, the charge on the capacitor is 63 percent of its final value.

Fig. 26-6

Fig. 26-7