Area Under a Potential–Charge Graph (Cambridge (CIE) A Level Physics)

Area under a potential–charge graph

• When charging a capacitor, the power supply transfers electrons onto one plate, giving it a negative charge, and transfers electrons away from the other plate, giving it a positive charge

  • It therefore does work on the electrons, which increases their electric potential energy

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

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

• As the charge of the negative plate increases i.e. becomes more negatively charged, the electric repulsion between the electrons increases

  • This means a greater amount of work must be done to increase the charge on the negative plate

Charging a capacitor

As the charge on the negative plate builds up, more work needs to be done to add more charge

• The relationship between the potential difference and charge on a capacitor is:

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

• In other words, 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

• Therefore, the electric potential energy stored in the capacitor can be determined from the area under the potential-charge graph

Graph of potential difference against charge

The electric potential energy stored in the capacitor is the area under the potential-charge graph