P 8.3-8 The circuit shown in Figure P 8.3-8 is at steady state before the switch opens at time

t = 0. The input to the circuit is the voltage of the voltage source, Vs. This voltage source is a dc voltage source; that is, Vs is a constant. The output of this circuit is the voltage across the capacitor, vo(t). The output voltage is given by

 

 

Determine the values of the input voltage, Vs, the capacitance, C, and the resistance, R.

 

P8_3_8

Figure P 8.3-8

 

For a capacitor, The solution looks like:

 

 

Before switch opens at t = 0, the steady state circuit looks like

At steady state, the capacitor is an open circuit.  So there is no current through the 10 Ω horizontal resistor and thus, no voltage drop across it.  So the voltage across the capacitor, v0, is the same as the voltage across the vertical 10 Ω resistor as well as the voltage of the power source vs.

 

 

So

At t = 0

 

Now we let the switch open and the circuit becomes

Once again after a long time t = ∞, the capacitor is an open circuit and the voltage across the capacitor as well again the voltage across the vertical 10 Ω is

 

 

By voltage division we can write

 

 

Now solve for R

 

 

Finally we have

So

We need to find Rt.  Deactivating the power source, we have the 40 Ω  and 10 Ω in parallel which then are in series with the 10 Ω.

 

 

Therefore

 

 

 

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This page last updated on July 2, 2019