In the potentiometer, when the cell in the secondary circuit is shunted with 4 resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with 12 resistance, the balance is shifted to a length of 180 cm. The internal resistance of cell is _ _ _ _

Step-by-step solution

In a potentiometer, the internal resistance r of a cell is given by the formula r = R ( l₀ l - 1 ) , where l₀ is the balancing length in open circuit, l is the balancing length when shunted with resistance R . This can be rewritten as l₀ l = 1 + r R or l = l₀ 1 + r/R . Case 1: R₁ = 4 and l₁ = 120 cm. 120 = l₀ 1 + r/4 = 4l₀ 4 + r ... (i) Case 2: R₂ = 12 and l₂ = 180 cm. 180 = l₀ 1 + r/12 = 12l₀ 12 + r ... (ii) Dividing equation (ii) by (i): 180 120 = 12l₀ 12 + r 4 + r 4l₀ 3 2 = 3(4 + r) 12 + r 1 2 = 4 + r 12 + r 12