P 8.3-11 The voltage v(t) in the circuit shown in Figure P 8.3-11 is given by

Determine the values of R₁, R₂, and C.

Figure P 8.3-11

The voltage across the capacitor is the same as the voltage across R₂ since they are wired in parallel. The voltage across the capacitor has the standard form:

Consider time a long time after the switch is thrown. The capacitor is an open circuit and the circuit looks like

The voltage across the capacitor is the voltage across R₂ and can be found by adding voltages around the loop.

Solving for v_C

Since we have a simple series circuit we can use voltage division and

Solving for

Now because the voltage cannot change instantaneously on a capacitor, consider the situation just after the switch is thrown, the circuit is unchanged so the sum of voltages remains

So the sum of voltages around the closed loop is

Solving for v_C

So now consider t = 0

The circuit just before the switch is thrown looks like

Now again consider voltage division

Now use value for and Solve for

After the switch is thrown the circuit looks like

The Thevenin resistance for the capacitor is the 4 Ω and R₂ are in parallel so

From the time constant relations

Solving for C

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This page last updated on July 2, 2019