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

Explanation

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