Internal Resistance Formula

Internal resistance refers to the opposition to the flow of current offered by the cells and batteries themselves resulting in the generation of heat. Internal resistance is measured in Ohms. The relationship between internal resistance (r) and emf (e) of cell s given by.

e = I (r + R)

Where, e = EMF i.e. electromotive force (Volts), I = current (A), R = Load resistance, and r is the internal resistance of cell measured in ohms.

On rearranging the above equation we get;

e = IR + Ir  or, e = V + Ir

In the above equation, V is the potential difference (terminal) across the cell when the current (I) is flowing through the circuit.

Note: The emf (e) of a cell is always greater than the potential difference (terminal) across the cell

Example: 1 The potential difference across the cell when no current flows through the circuit is 3 V. When the current I = 0.37 Ampere is flowing, the terminal potential difference falls to 2.8 Volts. Determine the internal resistance (r) of the cell?

Solution:

e = V + Ir

Or, e – V = Ir

Or, (e – V)/I = r

Therefore, r = (3.0 – 2.8)/0.37 = 0.54 Ohm.

Due to the Internal Resistance of the cell, the electrons moving through the cell turns some of the electrical energy to heat energy. Therefore, the potential difference available to the rest of the circuit is:

V = E (EMF of cell) – Ir (the p.d. across the internal resistor)