physics notes

Electromotive force or EMF is the term given to the energy per unit charge by a source of emf such as a voltaic cell or electrical generator. It is basically the potential difference across a cell or other 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. As electrons pass through the cell energy is transferred to them from the chemical energy stored in the cell. 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, R_internal Since V = IR from Ohm's law the potential difference of a cell or other power supply can be calculated using this formula:


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 r_internal 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 = IR_external

Measuring internal resistance

To measure internal resistance you should first refer back to the above equation, V = E - Ir_internal. 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:

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