Question
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
1.55
Ans- (2)
Solution
Ans- (2)
Sol. $\in = \lambda\mathcal{l}$
Potential gradient
$$\begin{matrix} & \epsilon_{1} = \lambda\mathcal{l}_{1} \\ & \epsilon_{2} = \lambda\mathcal{l}_{2} \\ & y = \frac{\epsilon_{1}}{\epsilon_{2}} = \frac{\mathcal{l}_{1}}{\mathcal{l}_{2}} \\ & \frac{\Delta y}{y} = \frac{\Delta\mathcal{l}_{1}}{\mathcal{l}_{1}} + \frac{\Delta\mathcal{l}_{2}}{\mathcal{l}_{2}} \\ & \frac{\Delta y}{y} = \frac{1}{200} + \frac{1}{150} \\ & \ \frac{\Delta y}{y} \times 100\left( \frac{1}{200} + \frac{1}{150} \right) \times 100 \\ & \ = \left( \frac{3 + 4}{600} \right) \times 100 \Rightarrow \frac{7}{6} = 1.16\% \end{matrix}$$
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