P 7.8-4 The switch in the circuit shown in Figure P 7.8-4 has been closed for a long time before it opens at time t = 0.  Determine the values of , and , , the voltage across the 4 Ω resistor and the inductor immediately before the switch opens and the values of , and , the voltage across the resistor and the inductor immediately after the switch opens.

 

Figure P 7.8-4

 

Here is an annotated circuit from t<0 and in steady state

In steady state the inductor acts like a short circuit as drawn here, so the   To find  we will need to find the total current labeled  here.  To do that we need to get total resistance, so the 80 Ω and the 20 Ω resistor are in parallel and have an equivalent resistance of

 

 

So the total resistance is 4Ω + 16 Ω or 20 Ω.  So the total current in steady state before t = 0 is

So

 

That means the voltage drops over the 80 Ω and the 20 Ω resistors are 24 V-4.8 V = 19.2 V so we can find the other two currents

 

And

Check Current

As it should.

After the switch is thrown open, the circuit becomes:

Now because of continuity conditions on inductors we know

 

 

Now  since we have a simple series circuit now.  So

 

 

To find  we need to do a voltage walk around the loop.

 

 

 

 

 

 

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This page last updated on April 14, 2019