In the potentiometer arrangement shown, the driving cell `A` has emf `epsilon` and internal resistance `r`. The emf of the cell `B` is `(epsilon)/(2)` and internal resistance `2r`. The potentiometer wire `CD` is `100 cm` long. If balance is obtained with length `CJ = l`, then

Options

A. `l = 50 cm`
B. `l gt 50 cm`
C. `l lt 50 cm`
D. Balance cannot be obtained

Answer

B

Explanation

(b) As potential gradient `k` in the potentiometer wire will be less than `(epsilon//100)` `(v//cm)` because of presence of `r`. So for the battery of emf `(epsilon//2)` the balance point `l` will be greater than `50 cm` as shown.
`l = (epsilon//2)/(k(lt epsilon//100)) implies l gt 50 cm`