Two batteries having same emf E but having different internal resistances r₁ and r₂(<r₁) are connected in series to an external resistance R as shown in figure. For this situation mark out the correct statement(s).

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For all values of R potential difference across both the batteries would be zero

Only one value of R exist for which potential difference across battery having internal resistance r₂ is zero

No value of R exist for which potential difference across any of the battery is zero

Only one value of R exist for which potential difference across battery having internal resistance r₁ is zero

answer is A.

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Detailed Solution

Current in the circuit is, $I = \frac{2 E}{r_{1} + r_{2} + R}$

Potential difference across the battery having internal resistance $r_{1}$ is,

$V_{1} = E - {Ir}_{1} = \frac{E (r_{2} + R - r_{1})}{r_{1} + r_{2} + R}$

Potential difference across the battery having internal resistance $r_{2}$ is,

$V_{2} = E - {Ir}_{2} = \frac{E (r_{1} + R - r_{2})}{r_{1} + r_{2} + R}$

If $V_{1} = 0, then R = r_{1} - r_{2} > 0 as r_{1} > r_{2}$

If $V_{2} = 0, then R = r_{2} - r_{1} < 0$ which is not possible.

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