Electric Circuits: E.m.f.

The term electromotive force (emf) is used to describe the energy provided by a cell or power supply per coulomb of charge passing through it.
It is important to note that emf is not a force, despite the name. It is a form of energy and is measured in volts.
Although ‘force’ appears in the term, it is not a type of force. Rather, ‘force’ in this context refers to the ‘forcing’ or driving of charge around the circuit.
The symbol for emf is ε.

Any device that converts other forms of energy into electrical energy acts as a source of emf.
Common sources of emf include batteries and cells which convert chemical energy into electrical energy, and generators that convert mechanical energy into electrical energy.

A real battery or cell is not a perfect emf. It has some small but significant internal resistance, often denoted by the symbol r.
The internal resistance is owing to the resistance of the chemicals and the connectors inside the cell or battery.
When current flows from a cell or battery, energy is dissipated within the cell itself due to its internal resistance, causing heating.
The ‘lost volts’ is the potential difference across the internal resistance, which is lost inside the cell.

The total energy transferred by the cell is divided between the external circuit and the internal circuit.
This can be expressed as ε = Ir + I(R) where ε is the emf, Ir is the lost volts in the internal resistance, and I(R) is the potential difference across the external load.
If no current is drawn from the battery (I=0), then the potential difference across the terminals of the cell is equal to the emf. This is because no energy is being dissipated in the internal resistance.

The terminal potential difference (V) is the potential difference across the terminals of the cell or battery.
The equation V = ε - Ir can be used to determine the terminal potential difference. This equation is obtained by rearranging the energy transfer equation above. It represents that some energy per unit charge (Ir) is used up inside the source.
As the current being supplied by the source increases, the potential difference across the terminals reduces. This is due to the increased energy loss in the internal resistance of the source.