# Capacitance

Definition:

Capacitance is regarding the storage of charge, and the measure of such storage can be determined by C = Q/V. So we can define capacitance as the amount of charge stored per unit potential difference

Capacitance is a ratio of the amount of charge on a body to the potential between it and another body.

Capacitance similar to the water timers / clocks...

This is probably one of the more difficult concepts on the LC. You mention the analogy with water at a height this is correct but often misinterpreted.

It is the gravitational field that creates the gravitational potential energy and as water moves from high to low it experiences a force and work can be done. This does not always have to be potential to kinetic - for example in a hydro-electric station water does work in turning a turbine. It does have some kinetic energy otherwise it would not flow but most of the potential energy is converted to electrical energy. This is also basis of the famous experiment by Joule converting mechanical energy to thermal energy.

How does this help? Well in a circuit there is an electric field through the circuit and charges feel a force and move if free to do so. As they move from high to low electrical potential they lose their electrical potential energy and this must be converted to another form. Circuits are often drawn with the positive along the top and the negative labeled as zero volts along the bottom - I presume this is to strengthen the analogy with gravitational potential energy.

In the case of the capacitor the battery does work in placing charges on the plates against the repulsion of the charge on the plates. This charge on the plates creates a field and a PD between the plates. When this PD is equal to the that of the battery current will stop. When the capacitor is removed charges try to get from one plate to the other and can follow any path and so when you short circuit the capacitor it discharges

While this all makes sense to me students still find it difficult and of course the analogy is complicated by the fact that there are two types of charge.

David Hobson

Unit of capacitance.

1 Farad = 1 Coulomb per Volt

History of capacitors

http://science.howstuffworks.com/electricity1.htm

Parallel plate capacitor.

The Capacitance of a parallel plate capacitor is proportional to the permitivity of the material about the capacitor, the Area unto which the two plates overlap perpendicular to the plate, and inversely proportional to the distance between the parallel plates.

Appropriate calculations.

for combinations of capacitors http://www.lon-capa.org/~mmp/kap19/RR480app.htm

When the capacitors are arranged in series it is like that we add the gaps together to form one large gapped capacitor. As you should know at this point in a parallel plate capacitor a larger gap leads to a smaller capacitance.

When the capacitors are arrange in a parallel fashion it is quite analogous to having one parallel plate capacitor just with a greater area, so the total charge per volt storage increases with this greater area.

for some applet to demonstrate this effect

http://www.lon-capa.org/~mmp/kap19/RR480app.htm

Use of C = Ae/d

Demonstration that capacitance depends on the common area, the distance between the plates, and the nature of the dielectric.

Appropriate calculations.

‘Permittivity’ is actually an unfortunate term – it should be called ‘unpermittivity’ or something more helpful, because the higher the value of , the less will be the force between the two charges

To Show Energy is stored in a capacitor.

Method:

• Set up the apparatus as shown.

• Allow the capacitor to build up a charge.

• Disconnect it from the generator

• Bring a conducting wire from each plate to the bulb

Energy stored in a Capacitor

Energy stored in a Capacitor can be shown to be given by the following equation.

Capacitors – conduct a.c. but not d.c.

Appropriate calculations.

Charge capacitor – discharge through lamp or low-voltage d.c. motor.

Demonstration.

http://www.lon-capa.org/~mmp/kap23/RC/app.htm

Give a use for Capacitors

Be sure to tell them why a capacitor is required?

Common uses of capacitors:

Sun, Sep 9, 10:21 PM

to lcphysics

Hi folks

Just wondering if anyone can give me a simple enough explanation as to how a capacitor can be used to tune radios. Thanks in advance.

### John Toner

Sun, Sep 9, 11:20 PM

to lcphysics

Hi Noreen,

I can try, though someone - I have no doubt - will do a better job.

Firstly, the short answer is "variable capacitors" which are capacitors with moving plates. As you rotate the tuning knob you slide one plate over another, changing their shared area. This changes the capacitance. But that doesn't answer HOW a capacitor changes the tuning.

Start by thinking of the resonance tubes we use for measuring the speed of sound in air. There are a few different factors we could change to alter the resonant frequency of the tube: its length, its diameter, the density of the gas inside etc.

If we set the resonance tube up and input a jumble of sounds of different frequencies into it at the same time, the tube will resonate any only one of those frequencies (forget harmonics for now).

Now look at a radio. It has an antenna that will pick up radio signals of different frequencies at the same time so to pick up only a specific frequency, we connect it to a circuit that resonates at that particular frequency only, like the resonance tube.

Like the resonance tube, there are some factors we could change to do this: the inductance, the resistance, the capacitance. Most radios have a main inductor to set the band (like 88 MHz to 108 MHz for normal FM). But to do more fine tuning you can change the resistance or the capacitance. Resistance drifts due to heating etc (that's why I imagine it's not used... I could be corrected). So the other option is capacitance and that's what's used.

It should be noted that moving your hand close to a capacitor actually slightly changes its capacitance because you're effectively bringing an earthed object into proximity. This is why, particularly in cheap radios, you can perfectly tune in the radio station but then moving your hand away makes it slightly drift off tuning again. The phenomenon is called "hand capacitance".

I hope that helps.

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• flash guns

• smoothing

• filtering.

Capicitor and Inductance circuits by wally