In the potentiometer arrangement shown, the driving cell D has emf $ε$ and internal resistance r. The cell C, whose emf is to be measured, has emf $ε / 2$ and internal resistance 2r. The potentiometer wire is 100 cm long. If balance is obtained at the length $A J = l$ ,

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Balance cannot be obtained.

Balance will be obtained only if resistance of AB is $\geq$ r.

$l = 50 c m$

$l > 50 c m$

answer is B, C.

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Detailed Solution

Potential gradient $x = \frac{E}{r + R} \times \frac{R}{100}$
Where R = resistance of potentiometer wire.
$\frac{E}{2} = x l \Rightarrow \frac{E}{2} = \frac{E}{r + R} \times \frac{R}{100} l$ , $l = \frac{50 (r + R)}{R} \Rightarrow l > 50 c m .$
Balance length should be less than or equal to 100 cm.
$l \leq 100$
$\Rightarrow \frac{50 (r + R)}{R} \leq 100 \Rightarrow R \geq r$