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.