Capacitors are used in electric circuits to store energy. Situations often arise where two or more capacitors are connected together in a circuit. In this topic, we will look at capacitors connected in parallel. The next topic deals with capacitors in series.
When two capacitors are connected in parallel (Figure 23.10), their combined or total capacitance Ctotal is simply the sum of their individual capacitances ${C_1}$ and ${C_2}$:

${C_{total}} = {C_1} + {C_2}$

This is because, when two capacitors are connected together, they are equivalent to a single capacitor with larger plates. The bigger the plates, the more charge that can be stored for a given voltage, and hence the greater the capacitance.

The total charge Q on two capacitors connected in parallel and charged to a potential difference V is simply given by:

$Q = {C_{total}} \times V$

For three or more capacitors connected in parallel, the equation for their total capacitance becomes:

${C_{total}} = {C_1} + {C_2} + {C_3} + ...$

Capacitors in parallel: deriving the formula

We can derive the equation for capacitors in parallel by thinking about the charge on the two capacitors.
As shown in Figure 23.11, ${C_1}$ stores charge ${Q_1}$ and ${C_2}$ stores charge ${Q_2}$. Since the p.d. across each capacitor is V, we can write:

${Q_1} = {C_1}V$ and ${Q_2} = {C_2}V$

The total charge is given by the sum of these:

$Q = {Q_1} + {Q_2} = {C_1}V + {C_2}V$

Since V is a common factor:

$Q = ({C_1} + {C_2})V$

Comparing this with $Q = {C_{total}}V$ gives the required ${C_{total}} = {C_1} + {C_2}$. It follows that for three or more capacitors connected in parallel, we have:

${C_{total}} = {C_1} + {C_2} + {C_3} + ...$

Capacitors in parallel: summary

For capacitors in parallel, the following rules apply:
- The p.d. across each capacitor is the same.
- The total charge on the capacitors is equal to the sum of the charges:

${Q_{total}} = {Q_1} + {Q_2} + {Q_3} + ...$

- The total capacitance Ctotal is given by:

${C_{total}} = {C_1} + {C_2} + {C_3} + ...$