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A cell sends a current through a resistance R for time t, next the same cell sends current through another resistance r for the same time t. If same amount of heat is developed in both the resistances, then the internal resistance of cell is :

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$\frac{R + r}{2}$

$\frac{R - r}{2}$

$\sqrt{(R r)}$

$\frac{\sqrt{(R r)}}{2}$

answer is C.

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Detailed Solution

${(\frac{ε}{R + x})}^{2} R . t = {(\frac{ε}{r + x})}^{2} r t$

where x is the internal resistance of the cell and $ε$ is the emf of the cell.

solving for x we get $x = \sqrt{R r}$

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