# Capacitors

The combination of any two conductors separated by an insulator is called a capacitor. A capacitor is a device that can be made to store electric charge and you can compare it with a bucket used to store water.
In general a bigger capacitor can store more charge than a smaller one. The two conductors usually carry an equal and opposite charge such that the net charge on the capacitor as a whole is zero. If a capacitor is state as having a charge Q it means that the conductor at the higher potential has a charge + Q and that at the lower potential a charge - Q.

The charge can then be released later.

Capacitors are used in a variety of situations:
(a) in a camera flash lamp - to store charge
(b) in timing devices - to release the charge at a certain rate
(c) as tuners - variable capacitors in a radio
(d) in a rectified output from a power supply
(e) in switches - to slow down current change and so reduce sparking
(f) in computer memory banks - to store information

Practical capacitors come in three basic forms:
(a) as part of an integrated circuit
(b) as two parallel plates (described more fully later)
(c) as a cylinder made of a pair of rolled up plates

All capacitors have an insulator between the plates and this insulator may be air or another gas, waxed paper or an electrolyte. This insulating material is called a dielectric.

In just the same way that a certain volume of water can be stored in two different shaped beakers (see Figure 1(a)) the same amount of charge may be stored in two different capacitors (see Figure 1(b)). The water pressure at the base of one container is higher than the other and similarly the potential difference across one capacitor is greater than that across the other.

You have to be careful when handling capacitors as you cannot be sure that they are not still charged. One that is storing a large charge at a high potential can give you a nasty shock!

The simplest

type of capacitor is a pair of metal plates with air between them. If they are connected to a cell as shown in Figure 2 no steady current will flow because of the insulator (air), between the plates. However currents that change with time are possible. The following diagrams explain what happens when the capacitor is charged.

When the switch is closed, electrons flow from plate A to the cell and from the cell to plate B.

Eventually a charge Q is stored on each plate and the capacitor is said to be fully charged.
Notice that both plates have the same size of charge although they are of opposite sign.

The addition of a resistor (R) in the circuit (Figure 3) does not affect the final potential difference across the capacitor. However it will slow down the time it takes the capacitor to become fully charged because the current in the circuit during charging will be less.

We will return to charging later to look at the factors which affect the rate at which capacitors can be charged and discharged in much greater detail including a mathematical treatment.

The ability to store charge is called the capacitance of the capacitor.

Capacitance is measured in farads (F)

The capacitance of a capacitor is related to the potential difference across it (V) and the charge on each of its plates (Q) by the formula:

Capacitance (C) = Charge (Q)/Potential difference (V)

A capacitor has a capacitance of one farad if the potential across it rises by one volt when a charge of one coulomb is placed on it.

A farad is actually a very large unit. A pair of plates 1mm apart in a vacuum would have need to have an area of 1.13x108m2 if the capacitance was to be 1 farad. This means two square plates with sides about 11.3 km (6.5 miles) long! Most of the capacitors that you will meet will have capacitances of microfarads (µF, 10-6F), nanofarads ( nF, 10-9F) or picofarads (pF, 10-12F). The capacitance of the Earth is about 4F.

Example problems
1. A capacitor of capacitance 2000 mF has a voltage of 12V across its plates. What is the charge stored on each of the plates?

Q = CV = 2000x10-6x12 = 2.4x10-2 C

2. A capacitance of 2000 mF is charged using a steady current of 0.1mA for 60s. What voltage does it gain?

Charge = current x time = 0.1x10-3x60 = 6x10-3C
Voltage = Charge/Capacitance = 6x10-3/2000x10-6 = 3V

Electrolytic capacitors have capacitances greater than 1 mF, they are polarised and must always be connected the right way round in the circuit otherwise they will explode! Smaller value capacitors can be unpolarised and may be connected either way round. The symbols for the two types of capacitor are shown in Figure 4.

Student investigation
Investigate how the material between the plates of a parallel plate capacitor affects its capacitance. Hang two metal plates vertically about 5mm apart, charge them up using a low voltage supply and then disconnect them from the power supply.

Very carefully lower a sheet of the material between the plates and measure the variation in p.d between the plates using a high resistance voltmeter or oscilloscope. How does the p.d. and capacitance change?

Problems
1. Calculate the capacitance of the following capacitors:
(a) 12V storing 0.05C (b) 6V storing 10-4C (c) 3V storing 10-6C

2. What charges are stored on the following:
(a) 12V 2000 mF (b) 6V 200 pF (c) 3V 4700 mF (d) 6V 1000 mF

3. A thunder cloud and the ground can be considered to be a parallel plate capacitor. When a spark jumps between the cloud and the ground you get a lightning flash. A certain thunder cloud carries a charge of 5x10-2C and the potential between it and the ground is 100kV. What is the capacitance of this 'natural' capacitor?

4. How long would it take to charge a 1000 mF capacitor to 10V using a steady current of 150 mA?