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

Answer

C

Explanation

Resistance of wire `R = (rhol)/(pi r^(2))`
volume of the wire `V = pir^(2)l or pir^(2)= V//l`
`:. R = (rhol)/(V//l) = (rhol^(2))/(V) , i.e. R prop l^(2)`
`:. (R_(2))/(R_(1)) = ((nl)/(l))^(2)= n^(2)`
`R_(2) = n^(2) R_(1) = n^(2)R`