Physics - Capacitor Question with Solution | TestHub

Step 1: Turn off the independent voltage source (short it). The time constant is

$$\tau =R_{\mathrm{th}}C,$$

where $R_{\mathrm{th}}$ is the Thevenin resistance seen by the capacitor.

Step 2: With the source shorted, simplify the resistor network seen from the capacitor terminals by combining series and parallel resistances.

After simplification:

$$R_{\mathrm{th}}=\frac{5}{8}R.$$

Step 3: Therefore, the time constant is

$$\boxed{\tau =R_{\mathrm{th}}C=\frac{5}{8}RC.}$$