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Two cells with same e.m.f. ‘E’ and different internal resistances $r_{1} and r_{2}$ are connected in series to an external resistance ‘R’. The value of R so that the p.d. across the first cell be zero is

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$\sqrt{r_{1} r_{2}}$

$r_{1} - r_{2}$

$\frac{r_{1} + r_{2}}{2}$

$(r_{1} + r_{2})$

answer is B.

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Detailed Solution

$i = \frac{E_{1} + E_{2}}{R + r_{1} + r_{2}} = \frac{2 E}{R + r_{1} + r_{2}}$

$V_{1} = E_{1} - i r_{1} = 0 \Rightarrow i = \frac{E}{r_{1}} = \frac{2 E}{R + r_{1} + r}$

$R + r_{1} + r_{2} = 2 r_{1}$

$R = r_{1} - r_{2}$

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