Capacitors in series

Two capacitors are in series when they are connected one after the other along the same branch. The internal conductor between the two is isolated: the charge arriving on one plate repels an equal charge on the facing plate of its neighbour. The key property follows: the two capacitors carry the same charge $Q$.

The voltages across each are then:

$V_1 = \frac{Q}{C_1}, \qquad V_2 = \frac{Q}{C_2}$

The total voltage imposed by the circuit is the sum of the two drops:

$V = V_1 + V_2 = Q\left(\frac{1}{C_1} + \frac{1}{C_2}\right)$

Imposing $V = Q / C_\text{ser}$ gives the reciprocal rule:

Key formula

$\ev{\frac{1}{C_\text{ser}} = \frac{1}{C_1} + \frac{1}{C_2}}$

The reciprocals of capacitances in series add — just as resistors do in parallel. The equivalent series capacitance is therefore always smaller than the smallest one: adding capacitors in series is equivalent to moving the plates further apart, reducing the overall capacitance.

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Topics: Electric circuits Concepts: Capacitance and the capacitor

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