Capacitors in Series and Parallel

In parallel — the capacitances add:

C_total = C₁ + C₂ + C₃ + …

Each capacitor has the same potential difference across it, since they share the same two nodes. The charges add, so the combination stores more charge for the same voltage — which is exactly what a larger capacitance means.

In series — the reciprocals add:

1 / C_total = 1 / C₁ + 1 / C₂ + 1 / C₃ + …

Each capacitor carries the same charge, because the charge pushed off one plate must arrive on the next. The potential differences add to the supply voltage.

The rules are the opposite way round to resistors — this catches almost everyone. Resistors add in series; capacitors add in parallel. Remember it through the physics rather than the formula: putting capacitors side by side is equivalent to making one big capacitor with a larger plate area, which increases capacitance.

Example: two 100 μF capacitors in parallel give 200 μF. In series they give 50 μF — less than either one alone. Series always reduces the total below the smallest individual capacitance, since connecting them in a chain is like increasing the plate separation.

Which quantity is shared is the key to every question — in parallel, V is common; in series, Q is common. Identify that first and the rest follows from Q = CV applied to each capacitor.

Series voltage division — because the charge is the same throughout, V = Q/C means the smallest capacitor takes the largest share of the voltage. This is the reverse of the intuition people carry over from resistors in parallel, and it matters: the smallest capacitor in a series chain is the one most at risk of breakdown.