Plot the current i(t) in Fig. 8.86 if (a) R = 10 Ohm; (b) R = 1 Ohm. In which ca
ID: 1928528 • 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 (a) Obtain an expression for v C 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