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Electricity and Magnetism

2EM

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The Internal Resistance of a Cell or Battery
(Introductory Observations)

When we measure the voltage of a battery we say we are measuring the terminal potential difference of the battery.
1. The battery (cell) in the diagram on the right is not supplying any current (assuming that the voltmeter has infinite resistance). The terminal potential difference measured under these circumstances is called the emf, E, of the battery (cell). E = ________ Volts
2. The same battery is now supplying a current of ________ Amps. The terminal potential difference, V, is now V = ________ Volts
3. The same battery is now supplying a current of ________ Amps. The terminal potential difference, V, is now V = ________ Volts

Conclusions

When a battery is not supplying any current, its terminal potential difference is equal to its __________.

As the current flowing through a battery increases, its terminal potential difference ____________.

The difference between the emf and the terminal potential difference is referred to as the "lost voltage". The lost voltage represents energy converted to ________ by the ___________________________.

Experiment to Measure the Internal Resistance of a Battery

As illustrated by the introductory observations, the terminal potential difference, V, of a battery is given by
......

V = emf – lost voltage

V = E - Ir

The aim of the experiment is to measure the internal resistance of a battery by plotting a characteristic of the battery. (See expt. 1EM for a definition the word "characteristic".)

In the following circuit a bulb is included simply to limit the maximum current.

If the equation above is rearranged, we have V = (-r) I + E and so we see that the battery characteristic (plotted with V on the vertical axis) should be a straight line of negative slope. Hence we can use the graph to find the internal resistance.

The internal resistance of a battery is not constant but increases as the battery is used. For this reason do not leave the circuit connected longer than is necessary to take the readings.