Question

The figure shows an experimental plot for discharging of a capacitor in an RC circuit. The time constant $\tau$ of this circuit lies between :

• A. 150 sec and 200 sec
• B. 0 and 50 sec
• C. 50 sec and 100 sec
• D. 100 sec and 150 sec

Answer 1

The correct option is D 100 sec and 150 sec

For discharging of an RC circuit,

$V=V_0{e}^{\frac{-t}{\tau }}$

So, when $V=\frac{V_0}{2}$,

$ln\frac{1}{2}=\frac{-t}{\tau }$

$\tau =\frac{t}{ln2}$

From graph we can say that at $t=100sec$, $V=\frac{V_0}{2}$

$\tau =\frac{100}{ln2}$

$\tau =144.3$