The EMF or electromotive force is the energy supplied by a battery or a cell per coulomb (Q) of charge passing through it. The magnitude of emf is equal to V (potential difference) across the cell terminals when there is no current flowing through the circuit.
e = E/Q
Where, e = emf or electromotive force (V), W = Energy (Joules), and Q denotes charge (Coulombs). Both emf (electromotive force) and pd (potential difference) are measured in V (Volts)
Electromotive force (emf) formula can also be written as,
e = IR + Ir or, e = V + Ir
Where,
e is the electromotive force (Volts),
I = current (A),
R = Load resistance,
r is the internal resistance of cell measured in ohms.
Difference between EMF and Potential Difference?
The amount of energy (any form) changed into energy (electrical) per coulomb of charge is termed as EMF whereas the potential difference is the amount of energy (electrical) that is changed into other forms of energy per coulomb of charge. Cell, solar cell, battery, generator, thermocouple, dynamo, etc are examples of sources of emf.
Solved Example
Example: Find the terminal potential difference of a cell when it is connected to a 9-ohm load with cell emf = 2 Volts and resistance (internal) 1 ohm?
Sol:
Given
emf =2
External resistance = 9 ohm
Internal resistance = 1 ohm
Since I = V/R
And R = External resistance + Internal resistance = 9 + 1 = 10 Ohm
Now, I = 2/10 = 0.2 Ampere
e = V + Ir
2=V+ (0.2)1
V =2-0.2
Therefore, the external resistor gets, V = 1.8 Volts
If we draw a graph of V (terminal potential difference) Vs current (I) in the circuit, we obtain a -ve gradient straight line. Also, The intercept of the straight line on y-axis denotes the electromotive force of the cell or battery, and the graph gradient denotes the internal resistance (r) of the battery or cell.