Physics revision: EMF, internal resistance and calculating internal resistance

Internal resistance: WTF is it and why does it make everything so awkward? In our latest A level Physics revision session we’ll be looking at what EMF and internal resistance is and how to calculate them from graphs.

Electromotive force or EMF is the term given to the energy per unit charge by a source of emf such as a voltaic cell (i.e. a battery) or electrical generator. It is basically the potential difference across a power supply.

Internal resistance

If you took a 12V battery and connected a voltmeter across it you would find that the potential difference is less than 12V. This is due to internal resistance in the cells of the battery because nature isn’t as perfect as we’d like it to be.

As electrons pass through the cell energy is transferred to them from the chemical energy stored in the battery. This process and the chemicals themselves provide resistance and this is known as internal resistance.

The potential difference measured from the voltmeter is equal to the EMF of the battery (12V) minus the volts lost due to the internal resistance, Rinternal Since V = IR from Ohm’s law the potential difference of a cell or other power supply can be calculated using this formula:

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Where V is the ‘external voltage’ (reading when a voltmeter is put across the power source), E is the EMF of the power source, I is the current and rinternal is the internal resistance of the power source.

Alternatively the external voltage can be calculated by multiplying the current and total resistance of the circuit, V = IRexternal

Measuring internal resistance

To measure internal resistance you should first refer back to the above equation, V = E – Irinternal. Rearranged as V = -Ir + E and you have an equation which looks a lot like that of a straight line (y = mx + c). This is how internal resistance is measured, by applying a ‘load resistance’ (a resistor across the power source) and varying it’s resistance a range of values for V and I can be measured by a voltmeter and ammeter:

Internal resistance circuit

When plotted against one another a straight line is given with an intercept of the EMF and gradient of -r, the internal resistance:

Internal resistance from graph

Therefore we can conclude that to find the internal resistance of a power supply we measure the gradient of the line on a graph of potential difference against current.