Question

The time constant of the network shown in the figure is 

• A. $CR$
• B. $2CR$
• C. $CR/4$
• D. $CR/2$

Hint:

For time constant calculations, always first reduce the circuit to its equivalent resistance and equivalent capacitance as seen by the source.

Answer 1

The Correct Option is A

Step 1: Identify the resistive network.
The circuit consists of two resistors of value $R$ connected in parallel.
The equivalent resistance of two equal resistors in parallel is
\[ R_{\text{eq}} = \frac{R \cdot R}{R + R} = \frac{R}{2} \]
Step 2: Identify the capacitive network.
The circuit also consists of two capacitors of value $C$ connected in parallel.
The equivalent capacitance of two capacitors in parallel is
\[ C_{\text{eq}} = C + C = 2C \]
Step 3: Write the expression for time constant.
The time constant of an RC network is given by
\[ \tau = R_{\text{eq}} \times C_{\text{eq}} \]
Step 4: Substitute the equivalent values.
\[ \tau = \left(\frac{R}{2}\right) \times (2C) \]
\[ \tau = RC \]
Step 5: Conclusion.
Hence, the time constant of the given network is
\[ \boxed{CR} \]