P 7.8-5 The switch in the circuit shown in Figure P 7.8-5 has been open for a long time before it closes at time t = 0.  Determine the values of ,  and , , the current in one of the 20 Ω resistors and in the capacitor immediately before the switch closes and the values of ,  and , , the current in that 20 Ω resistor and the capacitor immediately after the switch closes.

 

Figure P 7.8-5

 

An annotated circuit with things in steady state before the switch closes.  The capacitor would be an open circuit and we have:

 

Since capacitor acts like an open circuit the current through it is zero.

 

 

The current in the lower 20 Ω resistor can be seen by current division to be 2/3 of the total since the other two 20 Ω resistor make an effective 40 Ω resistor in parallel to this 20 Ω resistor.

 

And that makes

 

This also gives us the voltage drop across the upper 20 Ω resistor is

 

 

But this would also be

 

 

Now when the switch is thrown we have the following circuit

The left 20 Ω resistor is now shorted out so the circuit should look more like

So .  Now continuity conditions require that voltage across capacitor cannot change discontinuously, so the voltage remains

 

 

But both of the 20 Ω resistors are in parallel and they must also have this voltage across them so their currents are

 

So since

 

 

 

 

 

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This page last updated on April 14, 2019