7.4.3

# Energy Stored by a Capacitor

Test yourself

## Energy of a Capacitor - QV Graphs

The work done on a charge (Q) in moving through a potential difference of ΔV is equal to QΔV. This helps to find the energy stored by a capacitor.

### Transporting charge

• Imagine a parallel plate capacitor that has a potential difference of V. The definition of capacitance says that Q = CV.
• By transporting a tiny amount of charge, ΔQ, from the negative plate to the positive plate, the potential difference is approximately constant.

### Area under graph

• The increase in energy stored is equal to the energy gained by the charge, i.e. VΔQ. This is equal to the area shaded on the graph.
• This means that the total energy stored will equal the area of the triangle: ½QV.

## Capacitor Equations

Capacitors are easy to handle if you know what equation to use.

### Capacitance

• Definition of capacitance:
• $C=\frac{Q}{V}$
• Capacitance of a parallel plate:
• $C=A{{\epsilon}_0}{{\epsilon}_r}/d$

### Energy

• The energy stored in a capacitor is:
• $E=\frac{1}{2}QV$
• By using the definition of capacitance, you can rearrange to get:
• $E=\frac{1}{2}CV^2$
• $E=\frac{1}{2}\frac{Q^2}{C}$