What is electro-motive force (e.m.f.)?

As you would remember from this post on complete circuit a power supply is needed in order to move charges in the circuit.

Thus if we consider that an electric current is a flow of positive charges according to the conventional definition of current, for the positive charges to move from the positive terminal to the negative terminal of the power supply they need energy. It is this energy that is supplied by the power supply to the positive charges. The positive charges can thus use this energy to move around the circuit. It is this energy that the positive charges possesses that is called electrical energy.

Fig 1

Fig 1  shows a closed circuit. If the circuit is closed then an electric current will flow as indicated from the positive terminal of the power supply to the negative terminal of the power supply.

Fig 2

In fig 2 you can see 1 c of charge leaving the positive terminal of the power supply. Now for this 1 C of charge the power supply will provide a certain amount of energy. 

Suppose that for every one coulomb of charge that leaves the power supply the power supply provides 10 J of energy. Then the electromotive force (e.m.f.)  of the power supply will be 10 Volt (V).

Hence if the e.m.f. of a dry cell is 1.5 V it means that when the dry cell is in a circuit for every 1 C of charge then the power supply will provide 1.5 J of energy.

Hence we can define the electromotive force as the energy that the power supply provide to a unit charge to move it around the circuit.

Hence if the a charge Q is moved around a circuit and the power supply supplied W amount of energy, the the e.m.f. E can be calculated as shown:

E  = W/Q

Example

If 4 C of charge  needs 10 J of energy is provided by the power supply. Calculate the e.m.f. of the power supply?

E = W/Q

= 10 /4

2.5 J