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Capacitors
Practical capacitors usually consist of two close conducting surfaces separated by an insulator; with one of the conducting surfaces being connected to earth.

Both conducting surfaces are initially uncharged.
When an electron approaches plate a, an electron is repelled from plate b towards earth.
When an electron is put onto plate a, it will have a negative charge; plate b will have lost an electron to earth and so be left with positive charge.

As each electron approaches plate a, more electrical work has to be done, and when the electron is finally added to plate a,
the electrical work done is stored in the electric field between plates a and b.

The electric field strength, E, between the plates;

E = V/d

where V is the difference in electrical potential between the plates and d is the distance between the plates.

Capacitance, C is defined as:

where Q is the charge on one of the plates.
So the capacitance of the two metal plates:

The electric field strength at a distance d from a point charge:

( 4πd2 = the area, A, of a sphere, centred on the point charge, radius d).
This is valid for the conducting plates.

Where A is the area of overlap of the metal plates and ε0 is the permittivity of free space. (8.85×10-12Fm-1).

E.g. If two overlapping metal plates, 10cm by 10cm are separated by 1mm, calculate their capacitance.
C = 0.1×0.1×8.85×10-12/10-3 = 8.85×10-11F = 88.5pF

This is an example of a variable capacitor with a maximum capacitance of ≈2000pF

To increase the capacitance, A can be increased and d can be reduced.
Air, at STP breaks down at ≈3000Vmm-1, which limits the maximum potential difference that can be used.
This can be substantially increased by replacing the air between the plates with an insulating material,
e.g, Polystyrene, ≈60,000Vmm-1 and mica, ≈400,000Vmm-1.
Insulators, used in this way are known as dielectrics, and as well as increasing the breakdown voltage, they also increase the capacitance.
The factor by which the capacitance is increased is called the Relative permittivity and given the symbol εr.
For polystyrene is εr≈2 and mica, ≈5

The formula for the capacitance of a parallel plate capacitor with a dielectric becomes


With a dielectric, the size is significantly reduced - this having a maximum value of ≈600pF

Two parallel conducting plates have a very limited capacitance, even with a dielectric separator.
These are fixed value capacitors, with many hundreds of metal plates, separated by a polyester dielectric.
The black one has a value of 10µF (107pF)

Capacitors can also be rolled up

These capacitors have polystyrene as their dielectric.

Very large value capacitors can be made by using aluminium oxide as the dielectric, which is chemically formed directly
on the metal plates of the capacitor.
These are known as Electrolytic capacitors and require a very small current to pass through the capacitor
to maintain the aluminium oxide layer.
As a result, they are polarised and have to be connected the correct way round in a circuit.

This one has a value of 0.47F, - compare with the earth at 7.1×10-4F!



Types and uses of capacitors

Super capacitors (Ultra capacitors, Electric Double Layer Capacitors, EDLC) often use a carbon coating
on the conducting plates to massively increase the surface area.
These can have values of 100F+ and are often used in electric cars to store energy from regenerative braking.
They have huge power densities (10kW/kg)


More photographs of different types of capacitors.