Difference between e.m.f. and voltage (potential difference)

In 10th standard, you might have studied the concept of e.m.f…! But that was not covered in details. Actually in practice, the potential difference and e.m.f. of a cell or battery or any electrical source are different.

The potential difference is ALWAYS LESS than the e.m.f. This happens because internal resistance (r) of any real battery/source is GREATER than zero.

This resistance is invisible, but it is present inside the cell due to following reasons –

• In a battery or cell it is due to the resistance of electrolyte material.
• In a generator, it is due to the resistance of copper wires used in armature.
• In rectifier circuits, it is due to some critical resistance of electronic devices.

We shall understand about this using a simple circuit given below.

The PD of the battery is 12V. This is because the voltage drop across internal resistance (r) is zero. Now we connect a load resistor of 10Ω  across the output terminals as shown in figure. Due to this, current will flow in the circuit.

E = VR + Vr … according to KVL
E = VR + (I.r) … (1)
i.e. VR = E – (I.r) … (2)
Now to find out the current (I) in the circuit –
I = (12V/(total resistance of circuit)) = 12V/15Ω = 0.8A
Putting this value in equation (2), we get –
VR = 12V – (0.8A × 5Ω) = 8V

The above calculations show that the P.D. across load resistor is 8V. This is the actual output voltage of the battery, which is less than its e.m.f., because some voltage-drop is is developed or lost across internal resistance (r). Hence, we can draw following conclusions –

• Without load, the potential difference and e.m.f. of battery are EQUAL as the internal voltage drop within the battery is zero.
• However, when external load is connected across the two terminals of the battery, the output potential of the battery is ALWAYS LESS than its e.m.f.
• As the current through the external load resistor increases, the potential difference of the battery proportionally decreases.