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# A $4 \mu F$ capacitor and a 2.5MW resistor are connected in series with a 12V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor.

$\begin {array} {1 1} (A)\;20\: In(2) & \quad (B)\;In(2) \\ (C)\;5\: In(2) & \quad (D)\;10\: In(2) \end {array}$

Required Condition : $V_C = 3V_R = 3(V-V_C)$ where V is the applied voltage
$V_C =\large\frac{3}{4}$ $V$
$\Rightarrow V(1 – e^{\large\frac{-t}{\tau}} ) =\large\frac{3}{4}$ $V$
$\Rightarrow e^{\large\frac{-t}{\tau}} = \large\frac{1}{4}$
$\tau= CR = 10s$
Hence, $t = 20 ln(2)$
Ans : (A)

edited Sep 22, 2014