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Series Combination of Cells

Two cells of ...

Question

Two cells of the same emf $e$ but difference internal resistances $r_{1}$ and $r_{2}$ are connected in series with an external resistance $R$ . The potential drop across the first cell is found to be zero. The external resistance $R$ is

r_{1} - r_{2}

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r_{1} / r_{2}

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r_{1} r_{2}

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r_{1} + r_{2}

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Solution

The correct option is A $r_{1} - r_{2}$
$i = \frac{2 e}{r_{1} + r_{2} + R}$
Potential across first cell $= Δ V = e - i r_{1} = e - (\frac{2 e}{r_{1} + r_{2} + R}) = e [\frac{r_{1} + r_{2} + R - 2 r_{1}}{r_{1} + r_{2} + R}] = e [\frac{r_{2} + R - r_{1}}{r_{1} + r_{2} + R}]$
As given in the question, $Δ V = 0$
$⟹ r_{2} + R + r_{1} = 0$
$⟹ R = r_{1} - r_{2}$

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