text: # 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