Capacitors in series

Capacitors in series follow a reciprocal sum: 1/C = 1/C₁ + 1/C₂ + … Two 10 µF capacitors in series give 5 µF. The total is always smaller than the smallest, and the voltage rating of the string adds up.

Series is how you get a higher voltage rating than any single capacitor offers, and it comes with a trap. The voltage only divides evenly if the capacitors are matched and their leakage currents are similar. In practice leakage differs, the string drifts, and one capacitor ends up carrying more than its share until it fails — which then puts the full voltage across the next one. Any series string handling significant voltage needs balancing resistors across each capacitor to hold the division steady, which is why you see them on every high-voltage capacitor bank.