If a copper wire is stretched to make it `0.1%` longer what is the percentage change in its resistance?

Options

A. decrease by 0.05%
B. increase by 0.05%
C. increase by 0.2%
D. decrease by 0.2%

Answer

C

Explanation

The resistance of a wire is directly proportional to the length `(l)` of it & inversely proportinal to the area (A) of it.
`R prop (l)/(A)`
Let, `R_(1) = rho (l_(1))/(A_(1)) " " `(`rho` is the resistivity)
Since, the wire is stretched by 0.1% the length will increase by the same and area would decrease. because the volume will remain the same.
`l_(1)A_(1) = l_(2) A_(2)`
so, `A_(2) = (A_(1))/( 1.001) " "(l_(1) = 1.001 l_(1))`
let `R_(1) = rho (l_(1))/(A_(1))`
and `R_(2) = rho (l_(2))/(A_(2))`
`R_(2)= rho (1.001l_(1))/((A_(1))/(1.001)) =(1.001)^(2) rho (l_(1))/(A)`
`R_(2) = 1.002 R_(1) or 0.2%` increase