# Potential difference and e.m.f.

##### Demonstration

Opening up discussion of the difference between potential difference (p.d.) and electromotive force (e.m.f.).

#### Apparatus and materials

12-volt battery or power supply

Lamps (12 V 6 W) in holders, 2

Ammeter, 0-1 A

Voltmeter, 0-15 V

Demonstration meters OPTIONAL

#### Procedure

a Connect the battery, ammeter and lamps in series as shown. Arrange them in positions to match the circuit diagram. b Support the voltmeter below the battery and connect it first across lamp 1, then across the ammeter, then across lamp 2, then across the three together (between P and Q). Note the potential difference in each case.

c Hold the voltmeter above the battery - a purely didactic move - and connect it across the battery. Ask for a new interpretation (e.m.f.).

d With a very fast group it may be worth repeating this demonstration with a supply possessing internal resistance - e.g. a low-voltage d.c. supply with a 100 Ω resistor in series hidden in a box.

The voltmeter is connected to terminals on the outside of the box. More lamps can be added in parallel to increase the current and so reduce the terminal potential difference.

#### Teaching notes

1 Encourage students to think, as follows:

Potential differences are electrical pressure differences between the ends of some part of a circuit where electrical energy is transferred to a lamp or other component.

Voltmeters are devices to measure energy transfer for each coulomb passing through that part of the circuit.

2 When you apply the voltmeter across the battery, it is effectively the same as applying a voltmeter across the rest of the outside circuit. What happens if there is only the battery and no outside circuit? The voltmeter gives a reading and, if the voltmeter is a good one (very high resistance), then it may read slightly higher than when the battery is connected across a circuit. When the battery is disconnected from the circuit the voltmeter is reading the energy transfer from chemical to electrical in the cell. We call that the e.m.f. of the battery. It is the 'uphill push' which the battery can give to a coulomb before it slides downhill in the rest of the circuit.

Some energy is needed to transfer the coulomb through the battery. This is measured as the difference between the e.m.f. of the battery when no current is flowing, and the potential difference between the terminals of the battery when it is connected to a circuit and a charge is flowing. The bigger the internal resistance then the bigger the energy 'loss' in the battery.

3 Part d is an extension to the experiment. Use a battery with artificially increased internal resistance concealed in a box. Add more and more lamps in parallel, and note the potential difference between the terminals. As the current increases through the cell, the terminal potential difference (p.d.) falls.

4 Car batteries have a very low internal resistance and so high currents can be taken from them. However, when you start a car with the lights switched on, then the lights dim. This is because the starter motor takes a current of more than 100 amps, and so the amount of energy needed to pass this current through the battery is high. The potential difference between the terminals of the 12 V battery drops to as low as 4 V and so the lights are dim. Power supplies, especially school ones, have a high internal resistance and as more and more current is taken from the power supply then the potential difference at the terminals drops. This is why it is wise to monitor the terminal potential difference (p.d.) with a voltmeter even though there is a scale marked on the power supply.

5 There are many terms used in electrical energy discussions and they all have historical roots.

Cavendish, Watson: the idea of an 'electrical pressure'
Volta: electric tension, electromotive force (e.m.f.) used now in L.T., H.T., and E.H.T. supplies
Poisson, Green: electric potential
Lagrange, Gauss: potential energy

The definition of the volt now comes from the Josephson junction. When there is a steady direct current and a sinusoidal alternating current of frequency, f, then the average potential difference = nhf/2e across the junction.

This experiment was safety-checked in January 2007