P 7.7-8 The circuit shown in Figure P 7.7-8 is at steady state before the switch closes. The inductor currents are both zero before the switch closes (i₁(0) = i₂(0) = 0).

The voltage is given by

(a) Determine the inductor currents, i₁(t) and i₂(t), for t ≥ 0.

(b) Determine the energy stored by each inductor 200 ms after the switch closes.

The parallel inductors can be replaced by an equivalent inductor.

(c) Determine the current in the equivalent inductor, directed downward, for

(d) Determine the energy stored in the equivalent inductor 200 ms after the switch closes.

Figure P 7.7-8

(a) Determine the inductor currents, i₁(t) and i₂(t), for t ≥ 0.

Since we know v(t), we can get i₂ from

We are told =0, so

Now since the other inductor is in parallel it sees the same voltage so

Again we were told =0, so

(b) Determine the energy stored by each inductor 200 ms after the switch closes.

Use expression

so

and

Now let t = 0.200s

The parallel inductors can be replaced by an equivalent inductor.

The inductors are in parallel so

(c) Determine the current in the equivalent inductor, directed downward, for

Again (0) = 0, so

As would be expected.

(d) Determine the energy stored in the equivalent inductor 200 ms after the switch closes.

So at 0.2 s

As it should!

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This page last updated on April 13, 2019