n conducting wires of same dimension but having resitives 1,2,3,…..n are connected In series . The equivalent resistivity of the combination is

Options

A. `(n+(n+1))/(2)`
B. `(n+1)/(2)`
C. `(n+2)/(2n)`
D. `(2n)/(n+1)`

Answer

C

Explanation

For meter bridge , balancing condition is given as , Rightarrow `(P)/(Q) = (l_1)/(100)-(i_1)`
Rightarrow `(30)/(P+Q) = (37.5)/(100-37.5)`
`(30)/(P+Q)= 0.6`
`Rightarrow P+Q =50`
`Rightarrow (30)/((PQ)/(P+Q))= (71.4)(100-71.4)`
Rightarrow `30(P+Q)/(PQ)= 2.497`
`30(50)/(PQ)= 2.497` (therefore Formequation (1))
`PQ = 600. 721`
From equation (1) and (2) , We get ,
`P = 30Omega`. `Q=20Omega`