## Lost Energy When Charging and Discharging Capacitors

When a charge moves through a potential difference the energy change is If the voltage is constant, then the energy change is proportional to the charge transferred. However, the voltage is not generally constant. When a capacitor is being charged the voltage is increasing. The equation obeyed by capacitors implies that the voltage is directly proportional to the charge. If we draw a graph of voltage against charge we obtain a straight line graph through the origin. Then the work done in charging the capacitor is equal to the area under the graph is The energy delivered when a capacitor is being discharged is also for the same reasons.

We can show this mathematically. For a charging capacitor at any time, and so the work done in transferring a small amount of charge through a potential difference is Then Energy is needed to charge the capacitor but when fully charged the capacitor only stores The 'missing' energy is used to overcome resistance in the charging circuit.