6.1.2 Energy

Okay so this whole section is basically about how to use graphs with capacitors...then a little bit on what capacitors are useful for.

The amount of energy stored in a capacitor depends on the value of the capacitance and the initial p.d. across it.

When an electron moves from an emf source (e.g a power pack/battery) on to the capacitor plate, it will experience a repulsive force from the electrons that have already been deposited onto the plate since they have the same charge. This means that work has to be done to push the electron onto the plate. This work is supplied by the battery. Basically the energy stored in a capacitor comes from the battery/power supply.

We can determine the energy stored in a capacitor using a graph of p.d. against charge (for a capacitor, duh). This gives a triangular like shape and the work done is the work under this graph. The work done on the charges is the same as the energy stored in the capacitor (this is potential/stored energy)...

area under graph = area of shaded triangle = W = 0.5VQ

If we use Q = V C we can work out a few more variations of this equation...

W =  0.5Q^2/C = 0.5 V^2C

Uses of capacitors
So it's all very good that we know all about capacitors, but why are they actually useful? Well, capacitors release the stored energy very quickly which generates a high output power. This is useful in (for example)...

• camera flashes
• back up power for computers
• emergency lighting if the mains supply cuts out

Okay so the spec technically doesn't say we need to know about smoothing capacitors but I think it's useful to know so here we go...

Mains electricity is AC (supply voltage changes rapidly from positive to negative changing the direction of current). If there is a diode in the circuit it will only allow current flowing in one direction. Without a capacitor output voltage will consist of positive cycles only - with a capacitor the output voltage is smoothed out and is almost completely DC (direct current) with a constant value. By making the time constant of the circuit much greater than the period of the alternating voltage the 'ripple' in output voltage can be kept small. It is important that the time constant be much greater than the period of the input alternating voltage else the output voltage would not be very smooth.

NOTE: the 'ripple' is the difference between the maximum and minimum output voltage