The definition of emf (electromotive force)

In a circuit in which a current is present, the total rate at which energy is drawn from the source of current and dissipated in the circuit per unit current is defined as the electromotive force, (emf), in the circuit.

The emf is represented by the symbol E. From the above definition,

where P is the power dissipated in the circuit and I is the current flowing in the circuit.

The potential difference is defined as

"The potential difference between two points on a conductor is the work done per unit charge by a charge moving from a point of higher potential to that of lower potential."

Observe that potential difference is defined in terms of work and charge, whereas emf is defined in terms of power and current.

From the definition, we could define the unit of emf as the watt per ampere, which is the volt.

Both emf and potential difference have units of volts, as both are ultimately concerned with energy transformation per unit charge.

The emf of a battery:

The emf of a battery may be measured by connecting a voltmeter across its terminals. This measured potential difference is the same as the emf of the battery when it is not connected to a circuit.

In general, however, when the battery is connected to a circuit the potential difference measured by the voltmeter will be lower than the emf because of the internal resistance of the battery. Some of the energy dissipated in the circuit will be dissipated in this internal resistance.

The equivalent circuit is shown on the left, where r is the internal resistance of the battery with emf E, connected to a circuit with resistance R. The voltmeter measures the potential difference across R and not the emf of the battery which is equivalent to the potential difference across
(R + r).

Internal resistance:

Sources of electric currents, such as batteries or generators, are made of conductors. Since all conductors do have some resistance, batteries and generators will have a resistance of their own, called INTERNAL RESISTANCE, to distinguish it from the loads in a circuit, which are called EXTERNAL RESISTANCE. The internal resistance

comes into play when a current is flowing through the source, and results in a DECREASE in the measured potential difference across the source terminals. If one places a voltmeter across the terminals of a battery which is part of an open circuit, the voltage that is read is the electromotive force of the battery. How does one measure the internal resistance?

In a closed circuit, the voltmeter reading across the battery terminals is less than the battery emf. The difference is the voltage drop across the internal resistance r. If we know the current that is flowing through the circuit, let us say I, then

We see that the circuit voltage, V, is inversely proportional to the circuit current, I .