The resistance of a wire is r ohm. If it is melted and stretched to n times its original length , its new resistance will be

Options

A. `R//n`
B. `n^(2)R`
C. `R//n^(2)`
D. `nR`

Answer

B

Explanation

The resistance of a wire of length l and area A and resistivity `rho` is given as `R=rhol//a`
Given, `l.=nl`
As the volume of the wire remains constant
`therefore A.l.=Al,A.=(Al)/(r)-(Al)/(nl)=(A)/(n)`
`therefore R.=(rhol.)/(A.)=(n^(2)rhol)/(A)=n^(2)R`