Combination of capacitors

Series: capacitors joined end to end. Every capacitor carries the same charge Q, because the joined inner plates are an isolated conductor with zero net charge.

In series the voltages add: V = Q/C₁ + Q/C₂ + …, so 1/C = 1/C₁ + 1/C₂ + … + 1/Cₙ.

The series combination is smaller than the smallest capacitor in it, and the smallest capacitor takes the largest share of the voltage.

Parallel: all capacitors share the same potential difference V, and each takes its own charge Qᵢ = CᵢV.

In parallel the charges add, Q = Q₁ + Q₂ + …, so C = C₁ + C₂ + … + Cₙ.

Worked value: three 10 μF capacitors in series (10/3 μF) in parallel with a fourth 10 μF give 13.3 μF. On 500 V the series three each hold 1.7 × 10⁻³ C and the fourth holds 5.0 × 10⁻³ C.

The capacitor rules are the reverse of the resistor rules: series capacitors combine like parallel resistors.