Capacitors in Parallel

fact

When two capacitors are in parallel we can replace them with a single equivalent capacitor whose capacitance is given by:

$C_{eq} = C_1 + C_2$

fact

Adding capacitors in parallel increases the equivalent capacitance.

fact

If three or more capacitors are in parallel we reduce them two at a time just like with resistors.

fact

Capacitors in parallel have the same voltage across them which means the charge on each capacitor is determined by its capacitance and the voltage across them all:

$Q_1 = C_1 \times V$

example

Find the charge on capacitor $C_2$ in the circuit below.

We can see that the voltage across both

$C_1$ and

$C_2$ is 10V since they're in parallel. So we can just apply our usual formula to find charge:

$Q = C V$ where

$Q$ is charge,

$C$ is capacitance and

$V$ is voltage. So

$Q = 10\mu$ F

$\times 10$ V

$= 100\mu$ C of charge.

practice problems

Find the equivalent capacitance C of the three parallel capacitors $C_1$, $C_2$ and $C_3$

C =

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