AIIMS 2018 Physics Capacitors MCQ Question

When a parallel plate capacitor discharges through a resistor, its energy $U$ decreases according to the formula $U(t) = \frac{1}{2} C V^2 e^{-2t/RC}$. Given that the energy reduces to half in one second, we set $U(1) = \frac{1}{2} U(0)$, leading to the equation $e^{-2/RC} = \frac{1}{2}$. Solving for resistance $R$ gives $R = \frac{2}{\ln(2)}$ MΩ, which corresponds to option A.

Options B, C, and D do not satisfy the condition of energy halving in one second, as they yield different time constants that do not align with the exponential decay of the capacitor's energy.