To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm. The least count of scale is 1 cm. The percentage error in the ratio of EMFs is______

For a potentiometer:

E₁ / E₂ = l₁ / l₂

Given:
l₁ = 200 cm
l₂ = 150 cm
least count = ±1 cm → absolute error in each length = 1 cm

step 1: relative error in ratio

$$\frac{\Delta(E_1/E_2)}{E_1/E_2}=\frac{\Delta l_1}{l_1}+\frac{\Delta l_2}{l_2}=\frac{1}{200}+\frac{1}{150}$$

step 2: calculate

$$\frac{1}{200}=0.005$$

$$\frac{1}{150}\approx0.00667$$

sum:

0.005 + 0.00667 = 0.01167

step 3: percentage error

$$0.01167\times100\approx1.17\%$$