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Potentiometer

A Leclanche c...

Question

A Leclanche cell gets balanced on the wire of potentiometer at 280 cm. If a Daniel cell is joined in series with Leclanche cell, then the balance point is obtained at 480 cm. Compare the e.m.f. of two cells.

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Solution

Given: $E_{1} = ρ l_{1}$
$E_{1} + E_{2} = ρ l_{2}$
Formula used for solution
$\frac{E_{1}}{E_{2}} = \frac{l_{1}}{l_{2}}$
$\frac{E_{1} + E_{2}}{E_{1}} = \frac{ρ l_{2}}{ρ l_{1}} = \frac{l_{2}}{l_{1}}$
$1 + \frac{E_{2}}{E_{1}} = \frac{l_{2}}{l_{1}}$
$\frac{E_{2}}{E_{1}} = \frac{l_{2}}{l_{1}} - 1 = \frac{l_{2} - l_{1}}{l_{1}}$
$∴ \frac{E_{1}}{E_{2}} = \frac{l_{1}}{l_{2} - l_{1}} = \frac{280}{480 - 280} = \frac{280}{200}$
$E_{1} : E_{2} = 7 : 5$

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