The electromotive force (or EMF) is the energy given to each coulomb of charge by a source of electrical energy, e.g. a cell, battery, etc. This can also be thought of as the “actual voltage” of a voltage source and remains constant for a given source.

→ e.g. an EMF of $1.5 \space V$ means that $1.5 \space J$ of energy is given to each coulomb of charge passing through the cell .

Internal resistance is the resistance of the materials within the voltage source itself, often modelled as a resistor in series with it. It results in the effective energy a source is able to provide a circuit being less than the stated value (the EMF) due to some of the energy provided being lost to internal resistance.

An ideal source of voltage would be one with no internal resistance, so that it would produce a constant voltage at its terminals regardless of the current being drawn from it. The stated voltage of an ideal source would be the voltage that any component connected to it would have access to. However, all real voltage sources have internal resistance.

The terminal potential difference (or t.p.d.) is the voltage available from the voltage source when connected to an external load (e.g. a lamp or resistor). This is measured when the source is connected to a component that draws current. It is always less than the EMF of a source when current is drawn (t.p.d. $=$ EMF $-$ “lost volts”) and it will decrease as the current drawn increases, as shown below in the experimental graph.

The “lost volts” refer to the voltage of a source that a component connected with it does not have access to because it is dissipated due to the source’s internal resistance when current flows through the source. The “lost volts” are equal to the difference between the EMF and t.p.d. of a source.

The following relationships involve EMF ($E$), lost volts ($Ir$), t.p.d. ($V$), current ($I$), external resistance ($R$), and internal resistance ($r$), and can be used to solve problems involving those quantities.

$$ E=V+Ir $$

$$ V=IR $$

To measure the EMF of a voltage source, the current drawn should be close to zero, so a very high resistance voltmeter should be connected across the terminals of the source with no additional components connected to the circuit.

The following is the experiment to measure the internal resistance and EMF of a cell.

From these results a graph of $V$ (t.p.d.) against $I$ (current) can be used to determine the internal resistance.

The graph is a straight line with a negative gradient. To analyse this, the equation $E=V+Ir$ can be rearranged to compare with $y=mx+c$.

$$ V=E-Ir $$