P 8.3-13 The circuit shown in Figure P 8.3-13 is at steady state when the switch opens at time t = 0. Determine v(t) for t ≥ 0.

 

P8_3_13

Figure P 8.3-13

 

For a capacitor, The solution looks like:

 

 

The circuit at steady state before the switch opens looks like

 can be found by doing a voltage node equation.  Assume the bottom of the circuit is ground, we have two fixed nodes of 6 V and 36 V and then the node above the vertical

60 kΩ resistor and the + plate of the capacitor are the same so just call it  and we can write

 

Multiply equation by 60 kΩ

 

 

 

 

So v(0) = 12 V! 

 

Now after the switch opens the circuit becomes as shown after it reaches steady state.

This time we can do simple voltage division is the  is the voltage across the 60 kΩ resistor

 

The  Thevenin resistance is the two resistors in parallel so

 

So plugging into our solution

 

 

 

 

 

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This page last updated on July 3, 2019