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In an RC circuit, a battery of EMF V is connected with two resistors each of resistance R in series, and a capacitor C is connected in parallel with one of the resistors. The switch is closed at t = 0. The potential difference across the capacitor as a function of time is:

1. V/2 (1 - e^(-t/RC))
2. V/2 (1 - e^(-2t/RC))
3. V/2 (1 - e^(-2t/3RC))
4. V/2 (1 - e^(-3t/RC))

Correct answer: V/2 (1 - e^(-2t/RC))

Solution

Using Thevenin's theorem with the capacitor removed: V_th = V/2 (voltage divider) and R_th = R||R = R/2. The capacitor charges to V_th with time constant tau = R_th * C = RC/2, giving V_C(t) = V/2 * (1 - e^(-t/(RC/2))) = V/2 * (1 - e^(-2t/RC)).

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