A uniform wire of resistance R is uniformly compressed along its length, until its radius becomes n times the original radius. Now resistance of the wire becomes

Options

A. `R/n^(4)`
B. `R/n^(2)`
C. `R/n`
D. nR

Answer

A

Explanation

`R prop l/A rArr R prop (lA)/A^(2) prop ("Volume")/A^(2)`
`R_(1)/R_(2) = (r_(2)/r_(1))^(4) rArr R_(1)/R_(2) =[(nr)/r]^(-4) rArr R_(2) = R_(1)/4 = R/n^(4) (R_(1) =R)`