Two cells of same emf but different internal resistances $r_{1}$ and $r_{2}$ are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is

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$r_{1}$

$r_{2}$

$r_{1} - r_{2}$

$r_{2} - r_{1}$

answer is A.

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Detailed Solution

$I = \frac{2 E}{R + r_{1} + r_{2}} ... (i)$
But $V_{A} - V_{B} = E - I r_{2} = 0$
$\Rightarrow I = \frac{E}{r_{2}} .... (i i)$
Comparing values of I from (i) and (ii)
$\frac{E}{r_{2}} = \frac{2 E}{R + r_{1} + r_{2}} \Rightarrow R = r_{2} - r_{1}$

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