A capacitor C_1 is charged to a potential difference V. The charging battery is then removed and the capacitor is connected to an uncharged capacitor C_2. The potential difference across the combination is ?

A capacitor C_1 is charged to a potential difference V. The charging battery is then removed and the capacitor is connected to an uncharged capacitor C_2. The potential difference across the combination is ?

(a) \( \frac{V C_1}{C_1 + C_2} \)

(b) \( \frac{V}{1 + \frac{C_2}{C_1}} \)

(c) \( \frac{V}{1 + \frac{C_1}{C_2}} \)

(d) \( \frac{V C_2}{C_1 + C_2} \)

Answer :  (a) \( \frac{V C_1}{C_1 + C_2} \)

\( q_{\text{before}} = q_{\text{after}} \)

\( q_1 + q_2 = q_1' + q_2' \)

\( C_1 V_1 + C_2 V_2 = C_1 V_f + C_2 V_f \)

\( C_1 V = (C_1 + C_2) V_f \)