Three capacitors each of capacitance $C$ and of breakdown voltage $V$ are joined in series. The capacitance an

Question

Three capacitors each of capacitance $C$ and of breakdown voltage $V$ are joined in series. The capacitance and breakdown voltage of the combination will be:

Accepted Answer

1. **Equivalent Capacitance:** For capacitors connected in series, the reciprocal of the equivalent capacitance ($C_{eq}$) is the sum of the reciprocals of the individual capacitances [NCERT Class 12, Sec 2.14.1, Eq. 2.45].
   $$\frac{1}{C_{eq}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C}$$
   $$C_{eq} = \frac{C}{3}$$

2. **Breakdown Voltage:** In a series combination, the total potential difference (voltage) is the sum of the potential differences across each capacitor ($V_{total} = V_1 + V_2 + V_3$). Since the capacitors are identical, the voltage distributes equally. If each capacitor can withstand a maximum voltage $V$ before breaking down, the combination can withstand a total voltage of $V + V + V = 3V$.

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