THE PARALLEL PLATES CAPACITOR AND DIELECTRICS
Objective
The purpose of this experiment is to study some properties of the parallel plates
capacitor and the effect of placing dielectric materials between the plates of the
capacitor.
Theory
A capacitor consisting of two parallel metal plates each with an area A, and separated
by a distance d, can be shown to have a capacitance C:
C =ε
A
d
(1)
where ε is the permittivity of the material between the plates. The above equation
neglects the effect of the electric field bulging out at the edges of the plates. The
€ air is very close to that for vacuum ε0. For practical purposes we will
permittivity for
assume that the air behaves like a vacuum for this experiment. The dielectric constant
k, for a dielectric material is defined by the following equation:
k=
ε
ε0
(2)
By combining equations (1) and (2) above it can be shown that the dielectric constant
can also be found from:
€
C
k=
(3)
C0
where C0 is the capacitance of the capacitor with vacuum between the plates, and C is
the capacitance with the dielectric material between the plates, and with A and d
remaining constant.
A value of capacitance will be measured by charging the
€
capacitor to a known potential difference, then discharging it through a ballistic
galvanometer. The deflection of the galvanometer is very nearly proportional to the
charge sent through it. The sensitivity of the galvanometer will be needed in order to
convert the deflection of the galvanometer to the corresponding amount of charge. If
the response of the ballistic galvanometer is assumed to be linear, then only one
measurement of the sensitivity is needed. Having charged the capacitor to a potential
difference V, and measured the charge q, that was placed on it, the capacitance can
be found from:
C=
€
q
V
(4)
Procedure
1. Connect the apparatus as shown in the diagram below using the
standard (known) capacitor.
Charge Capacitor Power Supply Voltage Adjust Discharge Capacitor through galvanometer V G 1MΩ Resistor Capacitor Figure 1: Diagram of the electric circuit used to charge and discharge the
capacitor
2. You will be using the galvanometer to measure the charge on the capacitor
plates. This and the potential between the plates will allow you to find the
capacitance (see equation 4). Before you can do this however, you will need to
calculate the sensitivity of your galvanometer. Set the galvanometer range to
DIRECT. Charge the standard capacitor to a known potential difference (50 to
100 volts will normally be good here). Allow a few seconds for the capacitor
to charge as it is charging through a large resistance. Use the double-poledouble throw switch to discharge the capacitor through the galvanometer.
Record the maximum value of the deflection reached by the galvanometer on
the first swing. You will likely need to repeat this a few times before getting
good results. Average the maximum reading obtained for three good trials. The
charge on the capacitor (from equation 4) divided by the average deflection of
the galvanometer will determine the sensitivity of the galvanometer in micro-
coulombs per mm of deflection. This value of sensitivity is valid only on the
DIRECT range.
3. Replace the standard capacitor with the parallel plate capacitor. Carefully
bring the capacitor places together until they just touch but do not exert
significant pressure on each other.
Check that the plates are reasonably close to being parallel to each other. Read
the vernier scale that measures the plate separation, and if the reading is not
zero, use this reading to correct readings of plate separation.
4. Set the plate separation to 0.3 mm. Charge the parallel plate capacitor to
some known potential difference and determine the deflection of the
galvanometer, when the charge from the plates flow through it. Use a potential
difference that gives a reasonable deflection of the galvanometer. It is best to
start with a low value and to increase it if needed. Record the value of
deflection and of the potential difference used. (Watch for discharge).
5. Repeat step 4 for several other values of plate separation between 0.3 mm
and 10.0 mm. Choose more values at the closer spacing.
6. Take the necessary measurements to determine the area of the plates.
7. Use the measured sensitivity of the galvanometer to determine the values of
charge for each value of deflection of the galvanometer. Calculate the
capacitance for each plate separation using equation (4). Plot a graph of
capacitance C against values of 1/d. Determine the slope of your graph and
from it calculate the permittivity of air using equation (1).
8. Obtain six sheets of paper, all the same thickness, and each one larger in
area than one capacitor plate. Place one sheet of paper between the capacitor
plates and close the plates on it until it is snug but not tight. Use a suitable
potential difference to obtain a deflection on the galvanometer. Repeat this for
multiple layers of the paper up to six layers.
9. Do the necessary calculations and plot a graph of capacitance against 1/d for
the data from step 7. Use thickness of the paper for values of d as determined
using a micrometer. From the slope of the graph determine the dielectric
constant for the paper.
10. Measure the dielectric constant for the paper sheets and for at least two
other of the materials provided by comparing the value of the capacitance for
the parallel plate capacitor with and without the material filling the volume
between the plates. Use equation (3) for this and be careful to use the same
separation of the plates for readings with and without the dielectric.