Capacitors in Series - Capacitors & Stored Charge Step by Step

Series capacitors share charge, so per-farad reciprocals add. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Series capacitors share charge

Series capacitors sit in one chain, so the same charge is stored on each ideal capacitor.

Q_a = Q_b

Add per-farad reciprocals

Use per-farad reciprocal magnitudes for the two capacitances: 3 farads and 6 farads.

\text{per-farad total} = \tfrac{1}{3} + \tfrac{1}{6} = \tfrac{1}{2}

Invert the reciprocal total

A per-farad total of one half means the equivalent capacitance is 2 farads.

C_{\text{eq}} = 2\ \text{F}

Series equivalent is smaller than either part

Each row uses one chain. Equal charge is the structural reason reciprocals add, so the equivalent capacitance is reduced.

\begin{array}{c|c|c}C_a&C_b&C_{\text{eq}}\\2\ \text{F}&2\ \text{F}&1\ \text{F}\\3\ \text{F}&6\ \text{F}&2\ \text{F}\\4\ \text{F}&4\ \text{F}&2\ \text{F}\\\end{array}