Page 139 - Schaum's Outline of Theory and Problems of Electric Circuits

FIRST-ORDER CIRCUITS
128
t=RC [CHAP. 7
vðtÞ¼ V 0 e ; t > 0 ð3Þ
dv V 0 t=RC
iðtÞ¼ C ¼ e ; t > 0 ð4Þ
dt R
The voltage and current of the capacitor are exponentials with initial values of V 0 and V 0 =R, respecti-
vely. As time increases, voltage and current decrease to zero with a time constant of ¼ RC. See
Figs. 7-1(b) and (c).

EXAMPLE 7.1 The voltage across a 1-mF capacitor is 10 V for t < 0. At t ¼ 0, a 1-M
resistor is connected
across the capacitor terminals. Find the time constant , the voltage vðtÞ, and its value at t ¼ 5s.
6
6
¼ RC ¼ 10 ð10 Þ s ¼ 1s vðtÞ¼ 10e t ðVÞ; t > 0 vð5Þ¼ 10e 5 ¼ 0:067 V

Fig. 7-1

EXAMPLE 7.2 A5-mF capacitor with an initial voltage of 4 V is connected to a parallel combination of a 3-k
and
a 6-k
resistor (Fig. 7-2). Find the current i in the 6-k
resistor.

Fig. 7-2