In a potentiometer experiment, when the cell is shunted with a 4 Ω resistor, the balancing length is 120 cm.

When the same cell is shunted with a 12 Ω resistor, the balancing length becomes 180 cm.

Find the internal resistance of the cell.

Solution:

For a potentiometer:

V ∝ balancing length

Therefore:

V₁/V₂ = 120/180 = 2/3

Terminal voltage formula:

V = ER/(R+r)

For 4 Ω:

V₁ = 4E/(4+r)

For 12 Ω:

V₂ = 12E/(12+r)

Using ratio:

[4/(4+r)] ÷ [12/(12+r)] = 2/3

4(12+r) = 8(4+r)

48 + 4r = 32 + 8r

16 = 4r

r = 4 Ω

Answer:

4 Ω