Electromotive Force (e.m.f.) and Potential Difference (p.d.)

Picture two plastic bottles. One is filled with water almost to the top, the other only a little way up. If you join them near the bottom with a tube, which way does the water go? It always flows from the bottle with the higher water level to the one with the lower level. The flow does not last for ever, though. As soon as the two levels become equal, the water stops.

What would make the water flow again? Someone would have to lift the water from the low bottle back into the high one. In a house this job is done by a water pump. As long as the pump keeps sending water up, water keeps flowing through the pipe. An electric circuit works the same way. A cell or battery keeps charge flowing round the circuit, just as a pump keeps water flowing round the pipes.

The work a water pump does and the work a cell does to push charge round a circuit match each other closely. In the table below, the left column is about water and the right column is about charge. Read each row across.

For water to flow through a pipe, one end must be joined to water in a high place and the other end must lie lower. Water held up high stores potential energy. As it runs down, that energy changes into other forms and does work: put a turbine in its path and the turbine spins. In a circuit, as charge passes through the connecting wire and a load such as a bulb, its energy changes into kinetic energy, heat, light or other forms. The thing that makes this work happen is the electric source, such as a battery.

The positive terminal of a battery is at higher potential and the negative terminal is at lower potential. So to get a current in a circuit, one end of the load must be joined to the high potential terminal of the source and the other end to the low potential terminal. If both ends of a bulb were joined to the same terminal, there would be no difference in potential and the bulb would not light.

Charge needs energy to move through a conductor. Electric sources such as generators, batteries and solar panels supply that energy by changing some other form of energy into electrical energy. A solar panel changes light energy, a generator changes kinetic energy, and a battery changes chemical energy into electrical energy.

Inside a battery a chemical reaction takes place. It makes one terminal the positive terminal, at high potential, and the other the negative terminal, at low potential. Once the two terminals are joined by a conductor, the energy produced this way drives charge all the way round the circuit. The amount of energy the source gives to one coulomb of charge to take it once round the whole circuit is the e.m.f. of that source.

Despite its name, e.m.f. is not a force. It is energy per coulomb. A dry cell, for example, has 1.5 V printed on it. This means the cell gives 1.5 J of energy to every 1 C of charge it sends round the circuit.

The e.m.f. sets up a potential difference (p.d.) between the two ends of the load in the circuit. Suppose end A of a bulb is joined to the positive terminal of a battery and end B to the negative terminal. Now A is at a higher potential than B, so positive charge flows from A to B. Because of this potential difference, electrical energy changes into other forms, such as heat and light, as charge passes through the load.

In words, the potential difference equals the energy converted divided by the charge that flows. Using symbols, \( V \) is the potential difference, \( W \) is the energy converted in joules and \( Q \) is the charge in coulombs.

\[ V = \frac{W}{Q} \]

Energy is measured in joules (J) and charge in coulombs (C), so potential difference is measured in joules per coulomb. This unit is called the volt (V).

\[ 1\ \text{V} = 1\ \text{J/C} \]

Both e.m.f. and potential difference are measured with a voltmeter. Both are worked out as energy per coulomb, so both have the same SI unit, the volt.

• To measure e.m.f.: when no charge is flowing in the outside circuit, the potential difference across the battery's terminals equals its e.m.f. So the voltmeter is joined directly across the two terminals of the battery.
• To measure p.d.: the voltmeter is joined across the two ends of the load, so that it is in parallel with the load.

When current flows through a circuit with a load, some energy is used up inside the battery itself. So while current is flowing, the potential difference between the battery's terminals is always less than its e.m.f.

For example, a battery of e.m.f. 3 V may show a potential difference of only 2.5 V between the ends A and B of a bulb while current flows. This means the battery gives 3 J of energy to each coulomb of charge, but only 2.5 J of it turns into heat and light in the bulb outside. The other 0.5 J is used up inside the battery.

Both quantities are measured in volts and both are read on a voltmeter. The difference lies in what they describe: e.m.f. tells you what the source gives, while p.d. tells you what is spent in one part of the circuit. Without a source there is no p.d., which is why e.m.f. is the cause and p.d. is its effect.