I.P.Chambers Electronics

Digital Coulombmeter Experiments

This section contains descriptions and explanations of a number of standard experiments and investigations which can be performed using the Digital Coulombmeter. These cover the theory of charge sharing, charging by induction, Faraday's ice pails experiment, charge 'spooning', capacitance investigations and experiments involving CR time constants.

Permission is granted for these pages to be downloaded and copied as necessary. We welcome any comments or suggestions on any matter relating to these experiments.

In the Digital Coulombmeter, an integrated high impedance voltmeter with a liquid crystal display is used to measure the potential difference across a capacitor of known capacitance (4.7µF) internally connected to the input terminals as shown in fig. 1. It is a direct-reading instrument which enables quantitative work on electrical charge to be carried out at an early stage of learning and without the need for a separate indicating device. The Digital Coulombmeter has a range 0 to 1999nC.

As the potential difference across each capacitor is the same and using charge = capacitance x voltage we can see:

It can be seen, therefore, that if Cb is much larger than Ca then most of the charge which is initially on A is transferred to B when the two capacitors are connected together in parallel.

In electrostatics experiments, the capacitance of charged objects is generally low and when they are connected to the coulombmeter, almost all the charge is transferred. The high input capacitance of the coulombmeter (4.7µF) is much greater than that of a conventional electrometer d.c. amplifier set in the charge measuring mode and enables accurate measurements of charge to be made from external capacitances of up to approximately 0.22µF.

Negatively charge a polythene rod by rubbing and hold it about 50mm from the charge plate. The coulombmeter will indicate a negative charge. Remove the rod and the meter reading will fall to zero. If the rod is well charged and brought close to the charge plate, one or two small sparks may be seen (and heard) and charge will be transferred to the charge plate leaving a permanent reading on the meter when the rod is removed. The experiment can be repeated using an acetate rod and, in this case, a positive charge will be transferred to the coulombmeter. With either rod, the quantitative results obtained using the coulombmeter enable the effectiveness of different charging materials and methods to be investigated.

A detailed description of the way in which the charge flows in the above experiments may be desired by older pupils. In this instance, the following explanation may suffice.

When the negatively charged polythene rod is held near the charge plate of the coulombmeter, a charge separation is induced as indicated in fig. 4. Electrons from the charge plate are repelled onto one plate of the internal capacitor leaving the charge plate positively charged. These electrons in turn repel an equal number of electrons from the other plate to earth. This leaves a charge of -Q on one plate of the capacitor and +Q on the other plate. The coulombmeter will indicate the value -Q. A negative sign is shown because the capacitor plate connected to the positive socket of the coulombmeter has become negatively charged.

If the polythene rod is removed, electron flow occurs in the opposite direction to return all parts of the circuit to the uncharged state.

When the rod is well charged and brought close to the charge plate so that sparks occur, then negative charge is transferred from the rod to the charge plate and the internal capacitor. By counting the number of sparks and noting the final reading on the coulombmeter when the rod is taken well away from it, the charge transferred by each spark can be calculated.

Use the flying lead to short-circuit the input sockets of the coulombmeter and zero the meter reading as in fig. 6. Take away the short-circuit connection as in fig. 7 and the coulombmeter reading will remain zero.

Remove the rod. Most of the charge on the charge plate will be induced onto one plate of the internal capacitor of the coulombmeter since the capacitance of the charge plate is much lower than that of the coulombmeter.

An equal and opposite charge Q is attracted from earth so that the coulombmeter indicates the induced charge -Q on the positive plate as shown in fig. 8.

Next, move one of the insulating slabs to separate the cans as shown in fig. 10. Remove the charged rod so that the charge on each can is only free to move over the surface of the can that it is on, as in fig. 11.

Determine the polarity of the charge by touching each can in turn with the charge plate of the coulombmeter. When touching the first can, the induced charge is measured by the coulombmeter. On touching the second can the reading of the coulombmeter will return to zero showing that the charge on the first can was equal and opposite to the charge on the second can.

Alternatively, the reading may be zeroed by short-circuiting the sockets of the coulombmeter after touching the first can. This enables the polarity and magnitude of the charge on each can to be determined.

As in all electrostatics work, but in this experiment in particular, it is important to ensure that all insulators used are clean and dry. If this is not so, the small charges that exist on the cans will quickly discharge to earth.

Short across the sockets of the coulombmeter to zero the reading. With the EHT supply set to approximately 4kV, 'spoon' charge from the positive socket of the EHT supply to the coulombmeter charge plate using an electrophorus. It will be seen that an equal quantity of charge is transferred in each operation.

More charge can be transferred by filling the spoon more full, i.e. by increasing the output voltage of the EHT supply or using a larger 'spoon'. Conversely, less charge can be transferred by decreasing the EHT output voltage or using a smaller 'spoon'.

The capacitance of the electrophorus can be calculated from the readings taken.

Typically, with the EHT supply set to 5kV, a charge of approximately 10nC will be induced onto the electrophorus.

Using Quantity of charge = capacitance x voltage gives:

Charge the capacitor by connecting the upper plate to the positive socket of the EHT supply set to approximately 1kV. Zero the coulombmeter reading and then measure the charge on the capacitor by discharging it into the coulombmeter.

For a capacitor with parallel plates 0.3m x 0.3m, separated by a 1mm air space, the charge transferred is 800nC. Hence:

where:

C is the capacitance of the capacitor = 800pF

D is the separation of the plates = 0.001m

A is the effective plate area = 0.3m square

so:

In this experiment, as before, it is important that the insulating spacers of the parallel plate capacitor are clean and dry. Dirty and/or damp insulators can cause the capacitor to discharge as soon as it is connected to the EHT supply. This effect can be demonstrated by performing the experiment with clean, dry insulators and then repeating the experiment after breathing heavily on the insulators in situ.

In addition, the relationship between capacitance and effective plate area can be investigated. Alter the effective plate area by arranging only partial overlap of the plates, keeping the same plate separation. Plot a graph of charge on the capacitor against effective plate area to show how the relationship between the two varies.

The separation of the plates may be altered by increasing the number of insulating spacers between them. Plotting a graph of capacitance against plate separation will verify that the two are inversely proportional to one another.

Using the circuit of fig. 15, charge the coulombmeter with, for example, a charged rod as described earlier. Discharge the external capacitor by shorting across it's terminals. Note the coulombmeter reading, Q1. Connect the external capacitor to the coulombmeter and record the new meter reading, Q2.

Then, the charge on the external capacitor = Q1 - Q2

and the charge on the coulombmeter capacitor = Q2

The potential difference across both capacitors is the same, so

Where Cint = internal capacitance of the coulombmeter

and Cext = external capacitance

The external capacitor should have a capacitance of between 1 and 10µF. Generally, the values of electrolytic capacitors are known only within a wide tolerance range and this type are, therefore, unsuitable for this experiment. However, any plastic-insulated type capacitor would suffice.

In a typical experiment, using an external capacitance of 2.2µF, charge readings were obtained as follows:

Q1 = 249nC, Q2 = 169nC

Cint = 4.6µF

The coulombmeter capacitor can be discharged through the resistor using the circuit of fig. 17. A graph of the charge on the coulombmeter capacitor against time can be plotted as in fig. 18 and the time constant can be determined by drawing a tangent to the curve at the point where the capacitor just starts to discharge. Where this tangent crosses the time axis gives the value of the time constant, CR, of the circuit. From a knowledge of the value of the resistor, R, the capacitance of the internal capacitor of the coulombmeter can be calculated.