A material 'B' has twice the specific resistance of 'A'. A circular wire made of 'B' has twice the diameter of a wire made of 'A'. Then for the two wires to have the same resistance, the ratio `l_(B)//l_(A)` of their respective lengths must be

Options

A. 2
B. 1
C. `(1)/(2)`
D. `(1)/(4)`

Answer

A

Explanation

Resistance of a wire, `R=(rhol)/(piD^(2)//4)=(4rhol)/(piD^(2))`
Given, `rho_(B)=2rho_(A),D_(B)=2D_(A)`
Then, for `R_(A)` to be equal to `R_(B)`
Then, for `R_(A)` to be equal to `R_(B)`
`(4rho_(A)l_(A))/(piD_(A)^(2))=(4rho_(B)l_(B))/(piD_(B)^(2))=(4xx2rho_(A)l_(B))/(pi(2D_(A))^(2))implies(l_(B))/(l_(A))=(2)/(1)`