Page 131 - Schaum's Outline of Theory and Problems of Electric Circuits

[CHAP. 6
WAVEFORMS AND SIGNALS
120
The rms value of v 2 ðtÞ can also be derived directly. Because of the squaring operation, a full-rectified
p
ffiffiffi
cosine function has the same rms value as the cosine function itself, which is V m = 2.
6.15 A 100-mH inductor in series with 20-
resistor [Fig. 6-18(a)] carries a current i as shown in
Fig. 6-18(b). Find and plot the voltages across R, L, and RL.

Fig. 6-18

8 8
> 10 > 0 for t < 0
<
<
4
3
i ¼ 10ð1 10 tÞ ðAÞ and di ¼ 10 A=s for 0 < t < 10 3 s
> dt > 3
:
:
0 0 for t > 10 s
8 8
> 200 V > 0 for t < 0
<
<
3
v R ¼ Ri ¼ 200ð1 10 tÞ ðVÞ and v L ¼ L di ¼ 1000 V for 0 < t < 10 3 s
> dt > 3
:
:
0 0 for t > 10 s
Since the passive elements are in series, v RL ¼ v R þ v L and so
8
< 200 V for t < 0
5
v RL ¼ 2ð10 tÞ 800 ðVÞ for 0 < t < 10 3 s
: 3
0 for t > 10 s
The graphs of v L and v RL are given in Fig. 6-18(c) and (d), respectively. The plot of the resistor
voltage v R has the same shape as that of the current [see Fig. 6-18(b)], except for scaling by a factor of þ20 .