# What exactly is terminal potential difference?

I'm a bit confused on what terminal potential difference actually is. When doing calculations on circuit based questions I get stuck.

• Do you understand what's meant by the potential difference between two points in space? – The Photon Oct 20 '17 at 4:57

I'd guess that you have in mind the pd between the terminals of a cell, battery or electrical supply. The terminal pd, $V_\text{term}$ is simply the pd that a voltmeter reads if connected across the cell's terminals.

Suppose you connect a 'load' resistor $R_\text{load}$ across the cell's terminals. Then $V_\text{term}$ is also the pd across the load resistor. The cell behaves as a source of emf in series with an internal resistance r, which (as a first approximation) is constant. So $V_\text{term}$ is the pd across the source of emf in series with an internal resistance, which is the same pd as the pd across the load resistance. We have a simple series circuit (source of emf, r and $R_\text{load}$).

For an ideal cell (voltage source) the terminal pd does not change as the current delivered by the cell varies and stays at the emf of the cell $\mathcal E$ as shown in diagram $1$.

For a real cell, when an experiment is performed, the terminal pd drops as the current delivered by the cell increases as shown in diagram $2$.

Since a straight line graph can be drawn through most of the points the reak cell can be modelled as an ideal cell of emf $\mathcal E$ and source/internal resistance $r$ as shown in diagram $3$.
That internal resistance is not an actual resistor within the cell but rather a "virtual" resistor within the cell which mimics the behaviour of the internal constituent parts of the cell.
Note that one of the data points in red is not on the straight line graph.
That is to reflect the fact that as the current through the cell becomes large the model of an ideal cell in series with a fixed resistor breaks down.

Diagram $4$ shows that the model can be extended to a cell which has a current driven through it from its positive terminal to its negative terminal by an external source.
This is what would happen when a cell is being charged.
In this case the terminal pd will be larger than the emf of the cell.

So in general terms when you model a real voltage source you can think of it as an ideal voltage source and a series resistor.
The voltage across both the ideal voltage source and the series resistor is called the terminal pd and the relationship between them is $V=\mathcal E -Ir$.

It is the potential difference that you would get at the output of a source.