Plot the current i(t) in Fig. 8.86 if (a) R = 1 ohm. In which case does the indu
ID: 1800168 • Letter: P
Question
Plot the current i(t) in Fig. 8.86 if (a) R = 1 ohm. In which case does the inductor (temporarily) store the most energy? Explain. Obtain an expression for vC(t) in the circuit of Fig. 8.87 valid for all values of t. (b) Sketch vC(t) over the range 0 le t le 4 mu s. Obtain an equation which describes the behavior of iA as labeled in Fie 8.88 over the range of -1 ms le t le 5 ms. The switch in the circuit of Fig. 8.89 has been closed an incredibly long Uinc before being thrown open at t = 0. (a) Evaluate the current labeled ix at t = 70 ms. (b) Verify your answer with an appropriate PSpice simulation.Explanation / Answer
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Assuming the capactior is initially uncharged
the current iA will be 0 for -1ms <= t <= 0 .
iA = 0 , -1ms <= t <= 0 .
Now at t = 0 ,the switch closes and the current starts flowing.
The Time constant of the circuit is
= (Req) C = 4k (300 nF) = 1.2 ms.
Writing KVL gives
10V - (iA(t))(Req) - Vc(t) = 0 and
for capacitor we have Q(t) = C Vc(t) which on differentiation
gives iA(t) = C dVc(t) / dt .
Using these equations to solve we end up with
Vc(t) = 10V (1 - e-t/ReqC )
Now
iA(t) = C dVc(t) / dt = (2.5 mA) e-t/ for 0 <= t <= 5ms