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).

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.

(a) The simplest way to
measure the capacitance (C) of a capacitor is to charge the capacitor to a known potential
(V_{o}) 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 = V_{o}e^{-t/RC} ln V = ln V_{o} – 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 (q_{1}).

That is: Q_{1} is proportional to q_{1}

If the experiment is repeated with a second capacitor using the
same initial potential we have:

Q_{2} is proportional to q_{2}

Since Q = CV we can write Q_{1} =
C_{1}V_{1} and Q_{2} = C_{2}V_{2}; therefore C_{1} is proportional to q_{1} and C_{2} is proportional to q_{2}.
This gives

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: