P 8.6-20 The voltage source voltage in the circuit shown in Figure P 8.6-20 is

v_s(t) = 25u(t) – 10 V

Determine i(t) for t ≥ 0.

Figure P 8.6-20

First recognize that the two inductors are in series and can be replaced with the effective inductance. Since they are in series you merely add the two inductors

So the circuit is

Let’s do source transformations to get a Norton equivalent circuit. So transforming the voltage source and the 100 Ω gives us

Combining the parallel resistors

Now source transform the current source and the 60 Ω

Combining the two resistors as they are in series

Finally do source transformation and we have our Norton equivalent circuit

So our Norton resistance is obviously 100 Ω

In time before t = 0, the circuit will be in steady state and the inductor would be a short circuit so that the current through it would be

Long time after t = 0, again in steady state

Using the standard formula

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This page last updated on July 19, 2019