Emf of cell is defined as the work done by the cell in flowing a unit charge throughout the whole circuit.
If w is the work done by the cell for the flow of charge q throughtout the whole circuit then
EMF of cell, E = 
Let a cell of emf E and internal resistance r be connected across an external resistance R as shown in figure.
The electrons flow from the negative terminal A to the external resistance R then towards the positive terminal B of the source (cell).
Inside the cell the electrons have to move from the positive to the negative terminal through the electrolyte.
The necessary work is done by the emf of the cell. The remaining part of the emf is used for driving the electrons in the external circuit.
Let I be the current throught the circuit and r the internal resistance of the cell.
E - Ir = V AB = IR
E = lr + IR = I (r+R)
