CAPACITORS

1. What are capacitors?

Capacitors are devices that are able to store electric charges. Consider two plates of a conducting material, separated by an insulator (or a vacuum), and connected to a battery as shown (A above). Electrons from the negative terminal of the battery will accumulate on one plate (which will acquire a negative charge) while electrons will be drawn away from the other plate (which thereby becomes positively charged). As the plates become charged, the electric potential difference between the plates will increase until it is equal to the voltage of the battery.

If we then disconnect the battery, the plates, that is, the capacitor, will remain charged (B above), since there is no path for the negative charges to flow to the positively charged plate. If we then close the circuit (C), negative charges will flow to the positively charged plate via the circuit, the capacitor will be discharged and the electric potential between the plates will be zero (C).

2. Capacitance

The CAPACITANCE, C of a capacitor with plates with cross-sectional area, A (), and separated (in a vacuum) by a distance d , is given by

We see that the capacitance is is the ratio of the charge Q on each plate to the potential difference, V. In a vacuum, the capacitance depends on the geometry of the system (the area of the plates and the distance between them, but not on the charge. εo (pronounced "epsilon zero") is a fundamental physical constant known as the PERMITTIVITY OF FREE SPACE, with value 8.85x10-12 C2·N-1·m-2 ()

The unit of capacitance is the FARAD, F, which is the charge in coulombs which a capacitor will accept for the potential across it to change 1 volt: 1 F = 1C·V-1 = 1 C2·N-1m-1, named in honour of the 19th century British scientist Michael Faraday. The farad is actually a very large capacitance, and so capacitors normally come in capacitances of the order of microfarads (F, 1 F = 1x10-6 F) or picofarads (pF, 1 pF = 1x10-12 F).

Using the farad as a unit, εo has a value of 8.85x10-12 F·m-1.

The picture on the left shows a 16 F capacitor used as part of the alternator circuit in a motor car.


3. Dielectrics

In the above discussion, we have mentioned that the space between the plates has to be an insulator (or a vacuum). The nature of the insulator, called a DIELECTRIC has a marked effect on the capacitance of a given capacitor. In the presence of a dielectric, the capacitance is increased by a factor K, the DIELECTRIC CONSTANT of the insulator (). The values of the dielectric constants of some substances are shown here on the right (for a vacuum, K = 1). Note that K is a dimensionless number, and so has no units. For practical purposes, the dielectric constant for dry air may be taken as 1.

The effect of the dielectric will be to increase the capacitance, decrease the field and decrease the potential difference between the plates.

Dielectric Temperature
C
K
Vacuum
Air (dry, at 1 atm)
Glass
Water

Plastics
Titanium dioxide
Paper
Barium titanate

20
25
25
80
20
20
20
25
1.00000
1.0006
5-10
78
61
3-20
100
3.5
~2000

The capacitance of a capacitor where the plates are separated by a dielectric of thickness, d, and dielectric constant, K, will therefore be given by:

The factor o is known as the PERMITTIVITY of the dielectric material.

To summarize, the capacitance of a capacitor, will depend on

3.1 The breakdown voltage:

A charged capacitor acts as if it were a very high resistance in a circuit, preventing a flow of charges and hence a current though the circuit. If, however the potential difference applied to the plates is high enough, a spark will pass through the insulator. For solid insulators, the spark will burn a hole through it and allow current to pass through. The voltage at which this occurs is called the BREAKDOWN VOLTAGE of the insulator (). Various insulators behave differently in this respect. One can define a quantity known as the DIELECTRIC STRENGTH, Emax, usually measured in megavolts per meter (MV·m-1), that provides measure of a dielectric material's resistance to breakdown.
Dielectric Emax(MV·m-1)
Air
Window glass
Polystyrene
Water
Teflon
Neoprene rubber
L.D. Polyethylene film
0.4 - 3.0
9.8-13.8
19.7
65-70
87-173
16-28
300

A capacitor will therefore have a maximum voltage below which it can be safely operated. This is called the VOLTAGE RATING of that capacitor. For example, a capacitor with a voltage rating of 600 V will not experience failure if the potential difference across it is kept below 600 V.

Why do dielectrics increase the capacitance of a capacitor?

(Click here for a discussion)

4. Additional questions


















The behaviour of dielectrics

When a dielectric is inserted between the plates of a capacitor, the charges on the plates cause the molecules of the dielectric to become polarized. Each molecule becomes a DIPOLE, and these dipoles align themselves in the electric field. Within the dielectric, the charges on the dipole cancel out, the positive ends of the dipoles seeking the negative ends. At the surface of the plates however, there will be a net negative charge due to the dielectric near the surface of the positive plate, and a net positive charge near the surface of the negative plate.

This will set up an electric field, E' that will be opposite to the field, E, created by the battery in a vacuum. The sum of these fields will be the effective field, Eeff = E - E'. Since the separation of the charges is proportional to E, the field E' will also be proportional to E. Hence Eeff = E/K, where K is the permittivity, which is always greater than 1. The effective field in the presence of the dielectric will consequently be less than the field in vacuum.

In the presence of the dielectric, the capacitance of a parallel plate capacitor whose plates are separated by a distance d is C = Q/V, where V = Eeffd

This gives C = Q/Eeffd = KQ/Ed = Kε0A/d. The capacitance of the parallel plate capacitor thus increases by the factor K. In short, the presence of a dielectric between the plates of a parallel plate capacitor increases the capacitance by decreasing the net electric field/opposing electric field set up by the voltage source.