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FIRST-ORDER CIRCUITS

[CHAP. 7

7.48

In the circuit of Fig. 7-49, let k ¼ 0. Ans: v ¼ et ; i ¼ 1  0:5et

Find v and i after the switch is closed at t ¼ 0.

7.49

Show that the segment of the circuit enclosed by the dashed box in the circuit of Fig. 7-49 is equivalent to an inductor with value L ¼ 1=ð1  kÞ H. Hint: Write KVL between terminals AB of the dashed box.

7.50

The switch in the circuit of Fig. 7-49 is closed at t ¼ 0. Find v at t > 0 for the following values of k: (a) 0.5, (b) 1, (c) 2. Ans: ðaÞ v ¼ et=2 ; ðbÞ v ¼ 1; ðcÞ v ¼ et

7.51

Find i, the current drawn from the battery, in Problem 7.50. Ans: ðaÞ i ¼ 1  0:5et=2 ; ðbÞ i ¼ 0:5; ðcÞ i ¼ 1  0:5et

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