Capacitors in parallel

Two capacitors are in parallel when they are connected between the same two nodes: they therefore have the same voltage $V$ across them, imposed by the circuit.

Capacitors in parallel: the same voltage $V$ across $C_1$ and $C_2$, charges add.

Each accumulates the charge corresponding to its capacitance:

$Q_1 = C_1 V, \qquad Q_2 = C_2 V$

The total charge delivered by the circuit is shared between the two, so $Q = Q_1 + Q_2$. The equivalent capacitor must satisfy $Q = C_\text{par}\,V$, from which:

Key formula

$\ev{C_\text{par} = C_1 + C_2}$

Capacitances in parallel add directly — behaviour opposite to that of resistors (which add in series). Intuition: putting capacitors in parallel is equivalent to placing the plates side by side, increasing the surface available to store charge at the same voltage.

Links

Topics: Electric circuits Concepts: Capacitance and the capacitor

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