P 8.3-5 The circuit shown in Figure P 8.3-5 is at steady state before the switch opens at time

t = 0. Determine the voltage, vo(t), for t > 0.

 

Answer: vo(t) = 10 – 5e–12.5t V for t > 0

 

P8_3_5

Figure P 8.3-5

 

For a capacitor, The solution looks like:

 

 

For  the circuit in steady-state looks like

Using the rules of ideal Op-Amps, the voltage across the capacitor is seen to be the same as the voltage at the op-amp output since the if the capacitor is an open circuit, there is no voltage dropped across the 20 kΩ resistor so

 

 

After the switch opens the circuit becomes and we have added annotation to it.

We can see can be found from

 

 

must be the same as since no current can go into the inverting input, so the voltage drop across the 20 kΩ resistor sitting in the negative feedback position must also be 5 V.  Therefore, Vb must be 10 V, so the long term open circuit voltage across the capacitor is

 

 

Now since the load part is from the output of the op-amp, the Thevenin resistance is just the single 20 kΩ resistor between output of op-amp and the capacitor, so the time constant becomes

 

Putting these values into our standard form yields

 

simplifying

 

 

 

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This page last updated on June 28, 2019