Question

In the circuit shown in figure, when the switch is closed, the capacitor charges with a time constant

• A. $RC$
• B. $2RC$
• C. $\frac{1}{2}RC$
• D. $RC\log 2$

Answer 1

Answer: (A)

$RC$

The resistance in the middle plays no part in the charging process of

C, as it does not alter either the potential difference across the

RC combination or the current through it.

When the switch is closed, the resistance of the middle will not play any role during the charging capacitor. The capacitor will be charging through top resistor R in the circuit.
Charge at instant $t$ is $q\left(t\right)=q_0(1-e^{-t/RC})$.
Thus, time constant $\tau =RC$.