A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf $ε$ and internal resistance r. A cell C having emf $ε / 2$ and internal resistance 3r is connected in the secondary circuit. The length AJ at which the galvanometer as shown in figure shows no deflection is

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$\frac{11}{12} L$

$\frac{11}{24} L$

$\frac{5}{12} L$

$\frac{13}{24} L$

answer is C.

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Detailed Solution

Potential gradient across wire is $\frac{12 E}{13 L}$
For null deflection $\frac{12 E}{13 L} \times l = E / 2$

$l = \frac{13 L}{24}$

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