If the switch in the circuit shown in Figure P5.64 is closed at t = 0 and:
VS = 12V C = 130?F
R1 = 2.3k? R2 = 7k?
L = 30mH
determine the current iL through the inductor and the voltage vC across the capacitor as t ??.
Analysis:
As t ?? , the circuit will return to DC steady state conditions (practically after about 5 time constants.) In the long-term DC steady state the inductor may be modeled as a short circuit and the capacitor as an open circuit. Therefore, in this case, the voltage across the capacitor must be equal to the voltage across R2. Furthermore, the current through the inductor and R2 is simply VS/(R1 + R2).
All answers are positive indicating that the directions of the currents and polarities of the voltages assumed initially are correct. (You did do that, didn't you?)
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