P8.3-21 The circuit in Figure P8.3-21 at steady state before the switch closes. Determine an equation that represents the capacitor voltage after the switch closes.

Figure P 8.3-21

Before the switch closes and the circuit has come to steady state we have

Since the circuit is open, the voltage across the capacitor will be the voltage source so

After the switch is closed and the circuit again reaches steady state we would now have

The open circuit voltage of the capacitor is the voltage across the 40 Ω resistor which we can get from simple voltage division

Thevenin resistance is the two resistors in parallel so

so

The standard equation is

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