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WAVEFORMS AND SIGNALS

[CHAP. 6

The rms value of v2 ðtÞ can also be derived directly. Because of the squaring p operation, a full-rectified ffiffiffi cosine function has the same rms value as the cosine function itself, which is Vm = 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 > < 10 i ¼ 10ð1  103 tÞ ðAÞ > : 0 8 > < 200 V vR ¼ Ri ¼ 200ð1  103 tÞ ðVÞ > : 0

and

and

8 for t < 0 >0 di < 4 for 0 < t < 103 s ¼ 10 A=s dt > : 0 for t > 103 s 8 for t < 0 >0 di < vL ¼ L ¼ 1000 V for 0 < t < 103 s dt > : 0 for t > 103 s

Since the passive elements are in series, vRL ¼ vR þ vL and so

vRL

8 < 200 V ¼ 2ð105 tÞ  800 : 0

ðVÞ

for t < 0 for 0 < t < 103 s for t > 103 s

The graphs of vL and vRL are given in Fig. 6-18(c) and (d), respectively. The plot of the resistor voltage vR has the same shape as that of the current [see Fig. 6-18(b)], except for scaling by a factor of þ20.

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