Capacitors in Series - Electric Fields, Electrostatics & Capacitors Step by Step

This capacitors-in-series lesson treats shared charge as the reason ideal reciprocal capacitances add in one chain. The 3 F and 6 F row gives a 2 F equivalent exactly only for the stated ideal series topology. Real capacitors have tolerance, leakage, dielectric absorption, ESR and ESL, voltage limits, calibration limits, finite precision, and measurement uncertainty.

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}