First slide

potentiometer

Question

In the potentiometer arrangement shown, the driving cell A has emf $ε$ and internal resistance r. The emf of the cell B is $\frac{ε}{2}$ and internal resistance 2r. The potentiometer wire CD is 100 cm long. If balance is obtained with length CJ = l, then

Moderate

A

$l = 50 cm$
B

$l > 50 cm$
C

$l < 50 cm$
D

Balance cannot be obtained

Solution

As potential gradient k in the potentiometer wire will be less than ( $ε$ /100) (v/cm) because of presence of r, so for the battery of emf ( $ε$ /2) the balance point l will be greater than 50 cm as shown.
$l = \frac{ε / 2}{k (< ε / 100)} \Rightarrow l > 50 cm$

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