P 8.3-9 The circuit shown in Figure P 8.3-9 is at steady state before the switch closes at time

t = 0. The input to the circuit is the voltage of the voltage source, 24 V. The output of this circuit, the voltage across the 3-Ω resistor, is given by

Determine the value of the inductance, L, and of the resistances, R₁ and R₂.

Figure P 8.3-9

This is a simple series circuit. The only effect of the switch is whether or not R₁ is in the circuit or not. The standard form for the current through the inductor is found from

The voltage across the 3 Ω resistor is found from

Solving for

Comparing with the standard form we have

Now for the time before t = 0 the steady state circuit looks like

So we can solve for

At t = 0

So

Now at t = ∞, the switch is thrown and the circuit looks like

With the inductor acting a short in steady state, we have

So at t = ∞,

Solving for

Plug that in and find

Finally using the time constants we have

So

And

The Thevenin resistance is for the t > 0 time, so it is just R₂ and the 3 Ω resistor in series, so

And

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This page last updated on July 2, 2019