A cylindrical metallic wire is stretched to increase its length by 5%. Calculate the percentage change in resistance.

Explanation

We know that `R = (rhol)/(A)`
But `(l_(f))/(l_(i)) -1 =5%`
`(l_(f))/(l_(i)) = (5)/(100) +1 = (105)/(100) = (21)/(20)`
On stretching volume remains same
i.e `(l_(f))/(l_(i)) = (A_(i))/(A_(f))`
From relation R`= rho (l)/(A)` we have
`(R_(f))/(R_(i))= (l_(f))/(l_(i)) xx (A_(i))/(A_(f)) = ((l_(f))/(l_(i)))^(2) = ((21)/(20))^(2)`
`:. (R_(f)-R_(i))/(R_(i)) = [((21)/(20))^(2) -l]=0.1025`
thus change in resistance 10.25 %