In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation d R d l of its resistance R with length l is d R d l ∝ 1 l . Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P . What is the length A P ?

Step-by-step solution

According to question meter bridge have non-uniform wire, where its resistance has a variation with length as d R d l ∝ 1 l d R d l = k l     . . . 1 , where k is proportionality constant Let resistance of the left part A P and right part P B of the wire is R A P   ,   R P B respectively. From balanced condition of wheat stone bridge is: P Q = R S So, from the above condition for given meter bridge is R ' R ' = R A p R p B     ⇒ R A p   =   R p B     . .