AIIMS 2018 Physics RC Circuits MCQ Question

In a series RC circuit, the voltage across the capacitor $V(t)$ as it charges is given by the formula $V(t) = V_0(1 - e^{-t/RC})$, where $V_0$ is the battery voltage, $R$ is the resistance, $C$ is the capacitance, and $t$ is time. Given that the capacitor charges from 0 to 6 V in 0.1 s with a 12 V battery, we can set up the equation $6 = 12(1 - e^{-0.1/(RC)})$, leading to $e^{-0.1/(RC)} = 0.5$. Solving for $R$ gives $R = 0.1/(C \ln(2))$, confirming option A as correct.

Options B, C, and D are incorrect because they either use the wrong logarithmic factor or incorrect time constants, leading to incorrect expressions for resistance.