P8.3-16. Consider the circuit shown in Figure P8.3-16.

a) Determine the time constant, t, and the steady state capacitor voltage when the switch is open.

 

b) Determine the time constant, t, and the steady state capacitor voltage when the switch is closed.

 

ckt1

Figure P 8.3-16

 

a) Determine the time constant, t, and the steady state capacitor voltage when the switch is open.

 

When the switch is open the circuit looks like

Time constant is of course

 

So we need the Thevenin resistance.  Deactivating the power source, the resistors are basically two resistors in parallel, so

 

 

 

The steady state capacitor voltage is the same as the voltage across the 120 Ω resistor.  We can find that by doing voltage division

 

 

b) Determine the time constant, t, and the steady state capacitor voltage when the switch is closed.

 

When the switch is closed the circuit looks like

The two 60 Ω resistors are in parallel and the circuit can be simplified to

Since

 

Again the time constant is of course

 

So we need the Thevenin resistance.  Deactivating the power source, the resistors are basically two resistors in parallel, so

 

 

 

The steady state capacitor voltage is the same as the voltage across the 120 Ω resistor.  We can find that by doing voltage division

 

 

When Switch is open:

When Switch is closed

 

 

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This page last updated on July 8, 2019