Page 201 - Schaum's Outline of Theory and Problems of Electric Circuits

HIGHER-ORDER CIRCUITS AND COMPLEX FREQUENCY
190

Fig. 8-45 [CHAP. 8

(c) ! 1 90.9 301.5 1000 10 5
A 1 0.71 0.3015 0.128 0.091

0.58 39.88 56.48 39.88 0.58
p ffiffiffiffiffi
Phase is minimum at ! ¼ 1000= 11 ¼ 301:5 rad/s
3
5
8.50 In the circuit of Fig. 8-46 find the relationship between v 2 and v 1 for (a) k ¼ 10 , (b) k ¼ 10 . In each
case find its unit-step response; that is, v 2 for v 1 ¼ uðtÞ.

6
dv 2 6 7 4 10 t
Ans: ðaÞ þ 4 10 v 2 ¼ 4 10 v 1 ; v 2 ¼ 10 1 e uðtÞ
dt

9
dv 2 8 9 4 10 t
ðbÞ þ 4 10 v 2 ¼ 4 10 v 1 ; v 2 ¼ 10 1 e uðtÞ
dt

Fig. 8-46