The length of a potentiometer wire is `l`. A cell of emf `E` is balanced at a length l/3 from the positive end of the wire. If the length of the wire is increased by l/2. At what distance will the same cell give a balance point.

Answer

5

Explanation

Let `E_(0)` be the pot diff applied across the total length `l(= 10cm)` of potentiometer wire
Potential gradient in the first case `= (E_(0))/(l)`
As per question, `E = (l)/(3)((E_(0))/(l)) = (E_(0))/(3)`….(i)
potential gradient in the second case `= (E_(0))/(3l//2) = (2E_(0))/(3l)`
If `x` is the desired length of potentiometer to balance the emf `E` of the cell, then
`E = x xx (2E_(0))/(3l)`......(iii)
From (i) and (ii) we have
`(E_(0))/(3) = x xx (2E_(0))/(3l)`
or `x = (l)/(2)= (10)/(2) = 5 cm`