To compare EMF of two cells using potentiometer the balancing...

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

\_\_\_\_

Options

A1.65
B1.45
C1.75
D1.16

Correct answer

D. 1.16

Step-by-step solution

\epsilon = \lambda \ell

(Potential gradient)

\epsilon_1 = \lambda \ell_1

\epsilon_2 = \lambda \ell_2

y = \frac{\epsilon_1}{\epsilon_2} = \frac{\ell_1}{\ell_2}

\frac{\Delta y}{y} = \frac{\Delta \ell_1}{\ell_1} + \frac{\Delta \ell_2}{\ell_2}

\frac{\Delta y}{y} = \frac{1}{200} + \frac{1}{150}

\frac{\Delta y}{y} \times 100 = \left(\frac{1}{200} + \frac{1}{150}\right) \times 100 = \left(\frac{3+4}{600}\right) \times 100 = \frac{7}{6} = 1.16\%

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