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A cell supplies a current $I_{1}$ through a resistance $R_{1}$ and a current $I_{2}$ through a resistance $R_{2}$ . The internal resistance of a cell is

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$\frac{(i_{1} + i_{2})}{i_{1} - i_{2}} R_{1} R_{2}$

$\frac{(i_{1} R_{2} + i_{2} R_{1})}{i_{1} - i_{2}}$

$\frac{(i_{2} R_{2} - i_{1} R_{1})}{i_{1} - i_{2}}$

$R_{2} - R_{1}$

answer is D.

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Detailed Solution

$E = i_{1} (R_{1} + r) = i_{2} (R_{2} + r)$

$On solving, r = \frac{i_{2} R_{2} - i_{1} R_{1}}{(i_{1} - i_{2})}$

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