Electrical sources and internal resistance

An electrical cell is made from materials (metal or chemicals, for example). All materials have some resistance. Therefore, a cell must have resistance. This resistance is called the internal resistance of the cell.

A cell can be thought of as a source of electromotive force (EMF) with a resistor connected in series.

A circuit diagram containing a variable resistor, an ammeter, resistor, switch and battery with a voltmeter across the battery and resistor.

When a load resistance is connected, current flows through the cell and a voltage develops across the internal resistance. This voltage is not available to the circuit so it is called the lost volts, \(V_{L}\).

\(V_{L}\) can also be calculated as \(I r\) using Ohm's Law.

The voltage across the ends of the cell is called the terminal potential difference, \(V_{tpd}\).

\(V_{tpd}\) can also be calculated as \(I R\) where \(R\) is the load resistance.

Voltage is a measure of energy, and energy is always conserved. So the EMF \(E\) of a cell is equal to the sum of its terminal potential difference, \(V_{tpd}\), and the lost volts, \({V_L}\).

This gives rise to the equation \(E= {V_{tpd}} + {V_L}\)

This equation can be written in different forms, eg \(E= I(R + r)\). To solve problems on internal resistance it should be remembered that such circuits involve using a series circuit with the internal resistance and the load.