Question

A capacitor $C=100\mu F$ is connected to three resistors each of resistance $1k\Omega$ and a battery of emf $9V$. The switch $S$ has been closed for long time so as to charge the capacitor. When switch $S$ is opened, the capacitor discharges with time constant

• A. $33ms$
• B. $5ms$
• C. $3.3ms$
• D. $50ms$

Answer 1

The correct option is D $50ms$

When the switch S is opened, the capacitor will discharge through the two resistors on the top.

As these resistor are in parallel so $R_{eq}=\frac{1\left(1\right)}{1+1}=1/2k\Omega$

Thus time constant , $\tau =C{R}_{eq}=100\times {10}^{-6}\times \left(1/2\right){10}^3=50ms$