# The charge and discharge of a capacitor

It is important to study what happens while a capacitor is charging and discharging. It is the ability to control and predict the rate at which a capacitor charges and discharges that makes capacitors really useful in electronic timing circuits.

When a voltage is placed across the capacitor the potential cannot rise to the applied value instantaneously. As the charge on the terminals builds up to its final value it tends to repel the addition of further charge.
The rate at which a capacitor can be charged or discharged depends on:
(a) the capacitance of the capacitor) and
(b) the resistance of the circuit through which it is being charged or is discharging.
This fact makes the capacitor a very useful if not vital component in the timing circuits of many devices from clocks to computers.

In the section headed Capacitors 1 we compared a charged capacitor to a bucket with water in it. Now, if a hole is made in the bottom of the bucket the water will run out. Similarly, if the capacitor plates are connected together via an external resistor, electrons will flow round the circuit, neutralise some of the charge on the other plate and reduce the potential difference across the plates. The same ideas also apply to charging the capacitor.

During charging electrons flow from the negative terminal of the power supply to one plate of the capacitor and from the other plate to the positive terminal of the power supply.

When the switch is closed, and charging starts, the rate of flow of charge is large (i.e. a big current) and this decreases as time goes by and the plates become more charged so "resisting" any further charging. You should realise that the addition of a resistor in the circuit in series with the capacitor ONLY affects the TIME it takes for the capacitor to become fully charge and NOT the EVENTUAL POTENTIAL DIFFERENCE ACROSS IT – this is always the same and equal to the potential difference across the supply. (Figure 1)

Those of you who have a flash lamp built into your camera will know that it takes a few seconds to charge - this is because the energy for the flash is being transferred to, and stored in, the capacitor inside the flash unit and this takes time to become fully charged.

If we consider the example of a capacitor connected to an indicator lamp you should realise that if a capacitor was used to light it then the lamp would get slowly dimmer as the capacitor discharges as the potential difference across it falls and the current flowing gets less.

## What happens when a capacitor is charging and discharging?

Charging

As soon as the switch is closed in position 1 the battery is connected across the capacitor, current flows and the potential difference across the capacitor begins to rise but, as more and more charge builds up on the capacitor plates, the current and the rate of rise of potential difference both fall. (See Figure 3). Finally no further current will flow when the p.d. across the capacitor equals that of the supply voltage Vo.
The capacitor is then fully charged.

Discharging

As soon as the switch is put in position 2 a 'large' current starts to flow and the potential difference across the capacitor drops. (Figure 4). As charge flows from one plate to the other through the resistor the charge is neutralised and so the current falls and the rate of decrease of potential difference also falls.

Eventually the charge on the plates is zero and the current and potential difference are also zero - the capacitor is fully discharged. Note that the value of the resistor does not affect the final potential difference across the capacitor – only the time that it takes to reach that value.

The bigger the resistor the longer the time taken.

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS CD