Capacitors store energy

A capacitor consists of two conducting plates separated by an insulating dielectric. When connected to a battery, charge builds up on the plates, storing energy.

Key Points:

• Work is done by the battery to move negative charge from one plate to the other, separating positive and negative charges.
• This work gets stored as potential energy in the electric field between the plates.
• Flicking a switch discharges this stored energy through an external circuit, like a light bulb.

Calculating energy stored in a capacitor

The energy stored by a capacitor equals the work done to charge it up. This can be represented by the area under a potential difference vs charge graph.

The energy stored in a capacitor is given by:

1. $W=\frac{1}{2}C{V}^2$
2. $W=\frac{1}{2}QV$
3. $W=\frac{1}{2}\frac{Q^2}{C}$

Where:

• W = energy stored (J)
• C = capacitance (F)
• V = voltage across capacitor (V)
• Q = charge stored (C)

Worked example - Calculating the energy stored in a capacitor

Calculate the energy stored by a capacitor with a capacitance of 0.01 Farads and a voltage of 12 Volts.

Step 1: Formula

$W=\frac{1}{2}{\text{C V}}^2$

Step 2: Substitution and correct evaluation

$W=\frac{1}{2}\times 0.01\times {12}^2=0.72\text{ J}$

What are capacitors used for?

Capacitors have the following key properties:

• Store relatively small amounts of energy
• Can discharge energy very quickly
• Controllable charge storage and release

These make capacitors useful for:

• Camera flashes - releasing energy rapidly
• Backup power supplies - storing charge to release when needed
• Smoothing potential difference fluctuations - charging up then discharging