P8.6-4 Determine v_o(t) for t > 0 for the circuit shown in Figure P8.6-4.

Figure P 8.6-4

For time t < 0, assuming steady-state, The circuit looks like

The capacitor would be acting like an open circuit and the voltage across the capacitor is the output voltage of the op-amp since now voltage would be dropped across the 20 kΩ resistor. So now consider the current i₁ which can be written as

Solving for v₀

Now for time t > 0 when the circuit is in steady-state we have

Again knowing the capacitor will act like an open circuit after a long time and therefore the voltage across it will be the output voltage of the op-amp, we can find it from the current again.

Solving for v₀

So using the standard equation we get

The Thevenin resistance will be the 20 kΩ resistor between op-amp output and the capacitor.

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This page last updated on July 16, 2019