Determine the voltage vL across the inductor in Figure P5.38 for all time. Assume DC steady-state conditions for t < 0. Also assume:
Vs = 15V, L = 200 mH, RS = 1?, and R1 = 20 k?.
Analysis:
There are two cases that must be considered: t<0 and t>0. For t<0, the circuit is in a steady-state condition, as per the problem statement. Furthermore, inductors act as short-circuits under steady-state conditions. Therefore, the voltage across the inductor is:
For t>0, realize that the inductor is no longer connected to a source and is discharging. The equation for voltage across a discharging inductor is:
where R_eq is the equivalent resistance of the circuit and I_0 is the current of the inductor before being discharged.
First, determine I_0. Because the circuit was in DC steady-state at t<0, the current through L is the current through R_S, i. Using Ohm’s law provides:
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