Page 170 - Schaum's Outline of Theory and Problems of Electric Circuits

FIRST-ORDER CIRCUITS
159
CHAP. 7]
7.44 The input voltage in the circuits of 7-45 is a weighted sum of sinusoids with the highest frequency f 0 Hz.
Assuming that RC < 1=ð360 f 0 Þ, find v 2 ðtÞ. Ans: v 2 ðtÞ v 1 ðt 2RCÞ

7.45 Find the relationship between v 2 and v 1 in the circuit of Fig. 7-46.
dv 2
Ans: v 2 þ RC ¼ 2v 1
dt

Fig. 7-47
Fig. 7-46

7.46 In the circuit of Fig. 7-47, find the differential equation relating v 2 to v 1 . Compare with the circuit of
Fig. 7-45(a) of Example 7.17.

1
dv 2 dv 1
Ans: v 2 þ RC ¼ v 1 RC
dt 2 dt
7.47 In the circuit of Fig. 7-48, find the relationship between v 2 and v 1 .

dv 2 C 1 dv 1
Ans: v 2 þ R 1 C 1 ¼ v 1 R 2 C 2
dt C 2 dt

Fig. 7-48

Fig. 7-49