While finding internal resistance of a cell, a student observes that the balance length is 2m when cell is shunted by 5Ω resistance and balance length is 3m when cell is shunted by 10Ω resistance. Internal resistance of cell is.

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While finding internal resistance of a cell, a student observes that the balance length is 2m when cell is shunted by $5 Ω$ resistance and balance length is 3m when cell is shunted by $10 Ω$ resistance. Internal resistance of cell is.

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$1.5 Ω$

$1 Ω$

$10 Ω$

$15 Ω$

answer is B.

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Detailed Solution

We know

$l \propto \frac{ER}{R + r}$

$\Rightarrow \frac{l_{1}}{l_{2}} = \frac{R_{1}}{R_{2}} \times \frac{R_{2} + r}{R_{1} + r}$

$\Rightarrow \frac{2}{3} = \frac{5}{10} (\frac{10 + r}{5 + r})$

$\Rightarrow \frac{4}{3} = \frac{10 + r}{5 + r}$

$20 + 4 r = 30 + 3 r \Rightarrow r = 10 Ω$

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