P 8.6-22 The voltage source voltage in the circuit shown in Figure P 8.6-22 is

v_s(t) = 10 + 40u(t) V

Determine v(t) for t ≥ 0.

Figure P 8.6-22

The two capacitors are in series so we can replace the pair with an effective capacitor

So in steady-state when the capacitor is acting like an open circuit we just have the voltage across the 40 Ω resistor which we can find by simple voltage division

The Thevenin resistance can be found by deactivating the power source

Adding the 5 Ω resistors we have

So we have two resistors in parallel

Now we need steady state voltage before t = 0

And steady-state long after t = 0

Using the standard formula

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This page last updated on July 19, 2019