# Emf

As you'll have noticed voltage can also be referred to as potential difference. There is a further term used to describe for voltage, emf, or electromotive force.

**Definition for emf (note this is similar to the definition for
a volt)**

Two points in a circuit have an emf of one volt if one joule of energy
is transferred when one coulomb of charge passes from one point to another.

Combination of cells

When cells are combined the total emf can be calculated quite simply. If one cell have a pd of 1V then four cells have a pd of 4V. However if the cells are arranged as follows:

Then the total voltage = 1V x 3 – 1V = 2V

This is because one of the cells is facing the wrong direction and thus has cancelled out one of the other three cells emf. Really it’s just common sense!

Internal resistance

Circuits are not as perfect as you have thus far been led to believe, a cell will often have internal resistance due to the chemicals which comprise them and this is where emf comes in useful. The internal resistance of a cell is given as 'r' and the cells emf as 'E'.

When a cell is delivering no current then the pd = emf

Take the following circuit

By taking V = IR it is possible to deduce

E = I(R + r)

Therefore the terminal potential difference of the cell is equal to:

emf – lost volts due to internal resistance = pd of cell

**Measuring E and r**

A measure for E and r can be obtained using a voltmeter and a variable
resistor.

This circuit relies on the fact that the voltmeters resistance is infinite in order to take a current of zero. This is theoretically impossible but digital voltmeters do have resistances equal to millions of ohms.

When V is plotted against I

E is the y-intercept because “when a cell is delivering no current then the pd = emf”. The gradient is equal to -r.

**Kirchhoff's Laws**

The principals described can be given via the following two laws:

**Kirchhoff's first law **

The sum of the currents flowing in to any point in a circuit = sum of
the current flowing out of that point.

This law is based on the conservation of charge. It, similar to energy, cannot be created or destroyed, it can only be transferred.

**Kirchhoff's second law **

Sum of emf = sum of the potential differences