Measurement of Capacitance and Permittivity of Air

Object

Investigate the charging and discharging characteristics of a capacitor.

Determine the dielectric permittivity of air o.

Introduction

The capacitance of a pair of parallel plates of area A is

where d is the separation between the plates.

In this experiment a parallel plate capacitor is alternatively charged up (see figure 1(a)) to a voltage VS and discharged through a resistor RA (see figure 1(b)). The charge stored by the capacitor is small, so a high frequency switching between charge and discharge is used to give a detectable current (see figures 1(a) and 1(b)).

The charge (Q) stored in the capacitor at voltage VS is given by:

Q = CVS

The charge Q is discharged f times per second (f is the switching frequency of the electronic switching box). Hence the current I is given by:

I = CVSf

and substituting then:

I VS f

Therefore:

the current I is proportional to the supply voltage VS.

the current I is proportional to the frequency f.

the current I is inversely proportional to the plate separation d.

The ammeter voltage VA across the resistor RA is related to the current by Ohm's Law. Hence:

VA = I RA

so that: VA VS f RA

Apparatus

Combined Electronic Switching Circuit and Variable DC Power Supply, two aluminium plates, 100k ammeter resistor (RA), two digital voltmeters, metre rule, various 4mm test leads, plastic spacers.

Setting up the equipment

1. Place plastic spacers at the corners of the plates to hold them apart, the spacing between the plates can be varied in fixed steps by stacking up the spacers or using the range of spacers provided. To prevent short circuits plastic spacers MUST always hold the plates apart Always switch off the power before moving the plates or spacers!

2. The frequency of the Electronic Switching Circuit is displayed on the unit and can be varied using the frequency control. The frequency display shows zero when the frequency is too high!

3. The voltage of the DC supply is measured by voltmeter VS (see Fig. 1).

4. The discharge current is measured by measuring the voltage VA across the ammeter resistance RA.

Experiment

1. For a fixed supply voltage VS and fixed frequency f, measure the ammeter voltage VA for a range of plate separations d. Plot a graph of I against 1/d. Is this graph a straight line?

2. For a given plate spacing d and fixed frequency f, double the supply voltage VS. How does the ammeter voltage VA change? Does this agree with theory?

3. With VS at about 10 volts, measure the discharge current for a range of frequencies. Plot a graph of VA versus f.

4. The gradient of the graph of ammeter voltage VA against f should be equal to VSRA. Hence calculate the Permittivity of air o. What is the absolute error in your value of o?

5. The speed of light is given by the formula where o = 4**10-7mkgC-2. What is the value of c using your result for o? What is the absolute error in your value of c?

d (10-3m)

1/d (m-1)

0.292 0.003

3420 40

0.428 0.003

2340 20

0.528 0.001

1894 4

0.733 0.001

1364 2

1.033 0.002

968 2

1.486 0.003

673 1

1.980 0.002

505.1 0.5

4.014 0.001

249.13 0.06

5.82 0.02

171.7 0.7

The first seven spacer thicknesses (0.292 - 1.980 mm) in the table above are cut from plastic card/sheet usually available in modelling shops in nominal thicknesses of 10, 20, 30, ... 80 thousanths of an inch. The last two thicknesses (4.014 & 5.82 mm) were made from some plastic & perspex sheet we had.

Mark Davison, 1997, give feedback or ask questions about this experiment.

Back to the experiment menu