# Practical forms of capacitor

Most capacitors are of the parallel-plate type, either as two flat plates or as a 'swiss roll' arrangement, with the plates and dielectric rolled into a cylinder (Figure 2).

## Air capacitors

The air capacitor has the advantage of being simple to make and having a precisely known capacitance with almost perfect properties at all frequencies. It has a low insulation strength, however, only about one-twentieth of that of impregnated paper.

The tuner in a radio is a variable air capacitor, consisting of two sets or plates in air overlapping each other. The overlap of the plates and hence the capacitance may be varied by moving one set of plates into the other (see Figure 1).

## Paper capacitors

The two plates are thin metal sheets, with the paper dielectric of relative permittivity about 5 between them. They are then rolled into a cylinder. The whole arrangement is packed in a cylinder of metal or plastic. The breakdown potential of the capacitor can be increased by waxing the paper.

Such capacitors are not very stable but they are cheap to make. They have capacitances between 10-3 mF and 10 mF and are suitable for applied potential differences in the frequency range 100 Hz to 100 MHz.

## Electrolytic capacitors

When an electric current is passed through a solution of aluminium borate using aluminium electrodes, a very thin layer of oxide forms on the anode. The thickness of this layer depends on the applied potential difference and on the time for which the current is passed. This oxide film is used as the dielectric in electrolytic capacitors. It may be very thin, less than 10-7m but it has a very high insulation strength of some 109 V m- 1

## Measurement of capacitance

(a) The simplest way to measure the capacitance (C) of a capacitor is to charge the capacitor to a known potential (Vo) and then allow it to discharge through a resistor of known value. Record the value of the potential difference (V) across the plates against time and then plot a graph of ln V against time.
Since V = Voe-t/RC ln V = ln Vo – t/RC and so the gradient of the ln V against t graph will be 1/RC. If R is known you can find C.

(b) Capacitance comparison using a ballistic galvanometer
If we charge up a capacitor (C) to a known potential V and then discharge it through a ballistic galvanometer the charge passed through the galvanometer is proportional to the first deflection of the instrument (q1).
That is: Q1 is proportional to q1
If the experiment is repeated with a second capacitor using the same initial potential we have:
Q2 is proportional to q2

Since Q = CV we can write Q1 = C1V1 and Q2 = C2V2; therefore C1 is proportional to q1 and C2 is proportional to q2. This gives

C1/C2 = q1/q2

and so if the value of one of the capacitors is known the capacitance of the other may be found. (Notice that this method can only compare one capacitor with another.)

(c) Capacitance comparison by the vibrating reed method
This method is based on a rapid charge and discharge process to give a very nearly constant current from the capacitor. The circuit used is shown in Figure 1.
The reed switch itself contains a springy steel strip that becomes magnetised when placed inside the coil as shown. If an a.c. signal is applied to the coil the switch vibrates backwards and forwards between the two contacts 1 and 2.

It can be seen from the diagram that when the strip is in position 1 the capacitor is being charged, and when the strip is in position 2 the capacitor is discharging through the resistor R and the microammeter. The frequency of the supply is high, usually some 400 Hz, and the use of the rectifier means that the number of discharges per second is equal to the frequency of the a.c. signal f. As long as the frequency is high enough the meter will show a steady deflection recording the average current I passing though it.
Therefore I = Qf where Q is the charge given to the capacitor each time the switch is in position 1.

Hence Q = I/f, and since C = Q/V the capacitance of the capacitor is given by the formula:

C = I/fV