The figure shows an RC circuit with a parallel plate capacitor. Before switching on the circuit, plate A of the capacitor has a charge - Q 0 while plate B has no net charge. If at t = 0 , the switch is closed then after how much time (in seconds) will the net charge on plate A becomes zero?[Given: C = 1 μF , Q 0 = 1 mC , ε = 1000 V and R = 2 × 10 6 ln 3 Ω ]

Step-by-step solution

Let at any time t the charge that flows from the plate B to plate A is q and the instantaneous current is I . 2 q - Q 0 2 C + I R - ε = 0 ⇒ R d q d t = - 2 q + 2 ε C + Q 0 2 C ⇒ d q 2 ε C + Q 0 - 2 q = d t 2 R C Now for the charge on plate A to be zero q = Q 0 . ∫ 0 Q 0 d q 2 ε C + Q 0 - 2 q = ∫ 0 t d t 2 R C ⇒ t = R C ln 2 ε C + Q 0 2 ε C - Q 0 = 2 s