Proof of the Formula for the Capacitance of a Parallel Plate Capacitor
Apparatus:
EHT power supply, coulombmeter, two metal plates on insulating handles, 50cm ruler, two clamp stands with bosses and clamps, crocodile clip, long wires.
Procedure:
1. Assemble the apparatus shown above.
Ensure:
(a) that the positive flying lead is connected to the lower positive terminal (the one that protects YOU with a 50M¦ resistor).
(b) that the negative terminal of the power supply is connected to the Earth terminal.
2. Place the capacitor plates facing each other so that they are
apart.
3. Adjust the output of the EHT (Extra High Tension) supply so that its voltmeter reads 2000V.
4. Charge the capacitor by momentarily touching the unearthed (right-hand) plate with the flying lead.
5. Measure the charge stored in the following way:
(a) Reset the coulomb-meter by pressing the red button, the meter should now read 0 nanocoulombs (nC). [
]
(b) Move the meter towards the right-hand plate, touch the plate with the collecting (metal) cap. The meter should now read the charge
stored by the capacitor.
6. Repeat stages 2 to 5 for five further plate separations d between 0.5 cm and 6.0 cm.
7. Calculate
and tabulate this along with
and
8. Plot a graph ofagainst
9. Measure the gradient
of your graph.
10. Measure the area
of one of the plates.
11. The capacitance
of a parallel plate capacitor is given by:
&
where:
= the permittivity of the space between the plates.
12. Show that the two equations above can be used to obtain the expression:
13. Use the above expression and the value of your graph’s gradient
to calculate the permittivity,
[Hint:
is the equation of a straight line graph through the origin.]
