Plot the current i(t) in Fig. 8.86 if (a) R = 10 Ohm; (b) R = 1 Ohm. In which ca
ID: 1928525 • Letter: P
Question
Plot the current i(t) in Fig. 8.86 if (a) R = 10 Ohm; (b) R = 1 Ohm. In which case does the inductor (temporarily) store the most energy? Explain. Driven RC Circuits Obtain an expression for vC in the circuit of Fig. 8.87 valid for all values of t. (b) Sketch v C(t) over the range 0 t 4 micro s. Obtain an equation which describes the behavior of i A as labeled in Fig. 8.88 over the range of - 1 ms t 5 ms. FIGURE 8.88 The switch in the circuit of Fig. 8.89 has been closed an incredibly long time, before being thrown open at t = 0. (a) Evaluate the current labeled i x at t = 70 ms. (b) Verify your answer with an appropriate PSpice simulation.Explanation / Answer
The given figure is that of a charging RC circuit.
Now, the switch is thrown ON at t = 0. Before that it was OFF. So, at all time instants before t = 0, the current in the circuit is zero.
i(t) = 0 ; for -0.1 ms <= t < 0 ........... (i)
As soon as the switch is thrown ON, the capacitor starts charging
The equivalent resistence in the circuit = 3 + 1 = 4 k
Time constant of the circuit = = RC
= RC = (3 x 10^3) x (300 x 10^-9) = 9 x 10-4 s = 0.9 ms
The expression for the voltage across the capacitor is given by :
Vc(t) = Vo (1 - e-t/RC)
= 10 (1 - e-t/(9 x 10-4)) ; for t >= 0
i(t) = C dVc(t)/dt
= (Vo/R) e-t/RC
= (10/4k) e-t/(9 x 10-4) ; for t >= 0
i(t) = (2.5 mA) e-t/(9 x 10-4) ; for t >= 0 ........ (ii)
Final expression :
i(t) = 0 ; for -0.1 ms <= t < 0
= (2.5 mA) e-t/(9 x 10-4) ; for 0 <= t <= 5ms