Page 167 - Schaum's Outline of Theory and Problems of Electric Circuits

FIRST-ORDER CIRCUITS
156

Fig. 7-36 [CHAP. 7

Supplementary Problems

7.25 The capacitor in the circuit shown in Fig. 7-37 has initial charge Q 0 ¼ 800 mC, with polarity as indicated. If
the switch is closed at t ¼ 0, obtain the current and charge, for t > 0.
4
Ans: i ¼ 10e 25 000t ðAÞ; q ¼ 4 10 ð1 þ e 25 000t Þ ðCÞ

Fig. 7-38
Fig. 7-37

7.26 A2-mF capacitor, with initial charge Q 0 ¼ 100 mC, is connected across a 100-
resistor at t ¼ 0. Calculate
the time in which the transient voltage across the resistor drops from 40 to 10 volts. Ans: 0:277 ms

7.27 In the RC circuit shown in Fig. 7-38, the switch is closed on position 1 at t ¼ 0 and then moved to 2 after the
passage of one time constant. Obtain the current transient for (a)0 < t < ; ðbÞ t > .
Ans: ðaÞ 0:5e 200t ðAÞ; ðbÞ 0:516e 200ðt Þ (A)

7.28 A 10-mF capacitor, with initial charge Q 0 , is connected across a resistor at t ¼ 0. Given that the power
transient for the capacitor is 800e 4000t (W), find R, Q 0 , and the initial stored energy in the capacitor.
Ans: 50
; 2000 mC; 0:20 J

7.29 A series RL circuit, with R ¼ 10
and L ¼ 1 H, has a 100-V source applied at t ¼ 0. Find the current for
t > 0. Ans: 10ð1 e 10t Þ (A)

7.30 In Fig. 7-39, the switch is closed on position 1 at t ¼ 0, then moved to 2 at t ¼ 1 ms. Find the time at which
the voltage across the resistor is zero, reversing polarity. Ans: 1:261 ms

7.31 A series RL circuit, with R ¼ 100
and L ¼ 0:2 H, has a 100-V source applied at t ¼ 0; then a second
0
0
source, of 50 V with the same polarity, is switched in at t ¼ t , replacing the first source. Find t such that
0
the current is constant at 0.5 A for t > t . Ans: 1:39 ms