series combination capacitance

Question

Equivalent capacitance of two capacitors C1 and C2 in series equals?

RankGuru · Accepted Answer

1. **Series Properties**: Same charge $Q$ on each capacitor; voltages add up ($V = V_1 + V_2$).
2. **Logic**: $V = Q/C_{eq} = Q/C_1 + Q/C_2$.
3. **Equation**: Dividing by $Q$: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}$.
4. **Rearranging**: $\frac{1}{C_{eq}} = \frac{C_1 + C_2}{C_1 C_2} \implies C_{eq} = \frac{C_1 C_2}{C_1 + C_2}$.
5. **Note**: The equivalent capacitance in series is always smaller than the smallest individual capacitance.

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series combination capacitance

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