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CHAP. 7]

FIRST-ORDER CIRCUITS

131

Fig. 7-5

Fig. 7-6 Assume the switch S has been closed for a long time. The inductor current is then constant and its voltage is zero. The circuit at t ¼ 0 is shown in Fig. 7-6(b) with ið0 Þ ¼ 12=4 ¼ 3 A. After the battery is disconnected, at t > 0, the circuit will be as shown in Fig. 7-6(c). For t > 0, the current decreases exponentially from 3 A to zero. The time constant of the circuit is L=R ¼ ð1=100Þ s. Using the results of Example 7.3, for t > 0, the inductor current and voltage are, respectively, iðtÞ ¼ 3e100t vðtÞ ¼ Lðdi=dtÞ ¼ 30e100t iðtÞ and vðtÞ are plotted in Figs. 7-6(d) and (e), respectively.

ðVÞ

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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