Energy Stored by a Capacitor (AQA A Level Physics): Revision Note

Energy stored by a capacitor

• When charging a capacitor, the power supply pushes electrons onto the negative plate and pulls them from the positive plate

  • It, therefore, does work on the electrons, and electrical energy becomes stored on the plates

• As the capacitor charges, electrons flow:

  • from the negative terminal of the power supply to the negative plate of the capacitor

  • from the positive plate of the capacitor to the positive terminal of the power supply

• At first, a small amount of charge is pushed from the negative plate to the positive plate, then gradually, this builds up

  • Adding more electrons to the negative plate at first is relatively easy since there is little repulsion

• As the charge on the negative plate increases, i.e. becomes more negatively charged, the force of repulsion between the electrons on the plate and the new electrons being pushed onto it increases

• This means a greater amount of work must be done to increase the charge on the negative plate, or in other words:

The potential difference across the capacitor increases as the amount of charge increases

• The charge $Q$ on the capacitor is directly proportional to its potential difference $V$

• The graph of charge against potential difference is, therefore, a straight line graph through the origin

• The electrical (potential) energy stored in the capacitor can be determined from the area under the potential-charge graph

• Therefore, the work done, or energy stored, by a capacitor is defined by the equation:

$E=\frac{1}{2}QV$

• Where:

  • $E$ = work done or energy stored (J)

  • $Q$ = charge (C)

  • $V$ = potential difference (V)

• Substituting the charge with the capacitance equation $Q=CV$, the energy stored can also be defined as:

$E=\frac{1}{2}C{V}^2$

• By substituting the potential $V$, the energy stored can also be defined in terms of just the charge, $Q$ and the capacitance, $C$:

$E=\frac{Q^2}{2C}$