Combining capacitors and applications

Parallel combination

When two capacitors C1 and C2 are connected in parallel (same shared terminals), the equivalent capacitance adds up:

C_eq = C1 + C2

This is equivalent to increasing the total plate surface area: the equivalent capacitance is therefore always greater than the larger of the two.

Series combination

When C1 and C2 are connected in series (end to end), it is the inverse of the capacitances that adds up:

1/C_eq = 1/C1 + 1/C2

The equivalent capacitance is then always smaller than the smaller of the two, as with resistors in parallel.

Summary table

Combination	Formula	Effect
Parallel	C_eq = C1 + C2	Capacitance increases
Series	1/C_eq = 1/C1 + 1/C2	Capacitance decreases

Practical applications

• Camera flash: slow energy storage, instantaneous release.
• Filtering and smoothing: in a power supply, a capacitor smooths out voltage variations.
• Random-access memory (RAM): each bit is stored by the charge or absence of charge of a tiny capacitor.
• Cardiac defibrillator: a capacitor charges slowly then delivers an intense electric pulse to the heart within a few milliseconds.

Common pitfall

Do not mix up the formulas: it is in series that you use the inverse of the capacitances (as with resistors in parallel), and in parallel that capacitances add up directly (as with resistors in series). This is the opposite of the case for resistors!