The length of a potentiometer wire is 1 . A cell of emf E is balanced at length 1 / 3 from the positive end of the wire. If the length of the wire is increased by 1 / 2 . Then, at what distance will the same cell give a balance point?

Step-by-step solution

Let x be the desired length. Potential gradient in the first case = E₀ l E= ( 1 3 ) ( E₀ 1 )= E₀ 3 ...(i) Potential gradient in the second case. = E₀ 31 / 2 = 2 E₀ 31 E=(x) 2 E₀ 31 ...(ii) From Eqs. (i) and (ii), we get E₀ 3 = ( 2 E₀ 31 ) x x= 1 2