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.
Figure 2
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 2).
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
Aluminium foil
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 F and 10 F
and are suitable for applied potential differences in the
frequency range 100 Hz to 100 MHz.
Figure 2
Paper soaked in dielectric
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.
1
(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 (1).
That is: Q1  1
If the experiment is repeated with a second capacitor using the same initial potential we
have:
Q 2  2
Since Q = CV we can write Q1 = C1V1 and Q2 = C2V2; therefore C1  1 and C2 2. This
gives
C1/ C2 = 1/2
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.
1
2
400 Hz
a.c
V
A
Figure 3
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
C = I/fV
2