Q. A $4\mu F$ capacitor, a resistance of $2.5\ m\Omega$ is in series with 12 V battery. Find the the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given ln (2)=0.693]
A) 13.86 s
B) 6.93 s
C) 7 s
D) 14 s
Explanation
(a) Given, $\ \ \ \ \ \ \ V_{C} = 3V_{R} = 3(V - V_{C})$
Here, V is the applied potential.
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\ \ \ \ \ V}_{C} = \frac{3}{4}\ $V
Or $V\left( 1 - e^{- t/\tau_{C}} \right) = \frac{3}{4}\ $V
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ e^{- t/\tau_{C}} = \frac{1}{4}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
Here, $\tau_{C} = CR = 10s$
Substituting this value of $\tau_{C}$ in Eq.(i) and solving for t, we get
$t = 1\ \ 3.8\ \ \ 6s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.