Page 169 - Schaum's Outline of Theory and Problems of Electric Circuits

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Fig. 7-42 FIRST-ORDER CIRCUITS Fig. 7-43 [CHAP. 7

þ
7.40 For the RL circuit shown in Fig. 7-43, find the current i L at the following times: (a) 1 ms, (b)0 ,
(c) 0.3 ms, (d) 1. Ans: ðaÞ 2:00 A; ðbÞ 2:00 A; ðcÞ 2:78 A; ðdÞ 3:00 A
7.41 A series RC circuit, with R ¼ 2k
and C ¼ 40 mF, has two voltage sources in series with each other,
v 1 ¼ 50 V and v 2 ¼ 100uðtÞ (V). Find (a) the capacitor voltage at t ¼ ,(b) the time at which the capa-
citor voltage is zero and reversing polarity. Ans: ðaÞ 13:2V; ðbÞ 55:5ms

7.42 Find the unit-impulse response of the circuit of Fig. 7-44; i.e., v 2 for v 1 ¼ ðtÞ (a unit-area narrow voltage
pulse).

R 2 1 t=ðR 1 CÞ
Ans: v 2 ¼ ðtÞ e uðtÞ
R 1 R 1 C

Fig. 7-44

7.43 In the circuits of Fig. 7-45, RC ¼ 5 10 7 and v 1 ðtÞ¼ 10 þ cos ð1000tÞþ 3 cos ð2000tÞ. Find v 2 ðtÞ.
6
6
Assume tan when < 18. Ans: v 2 ðtÞ 10 þ cos ½1000ðt 10 ފ þ 3 cos ½2000ðt 10 ފ ¼
6
v 1 ðt 10 Þ

Fig. 7-45