A copper wire is stretched so as to increase its length by 0.2%. Calculate the percentage change in the resistance of the wire.

Explanation

Resistance of a wire `R = rho (l)/(A)" "…..(i)`
where I,A are the length and area of cross - section of the wire , respectively.
When the wire is streched , the new length of the wire .
`l_(1) = l + (0.2)/(100) l = (100.2l)/(100)`
As the wire is the wire is streched , its volume remain constant .
`V_(1) = V_(1)`
`" " A_(1) = (l xx A)/(l_(1))= (l xx A)/((100.2)/(100)l) = (100 A)/(100.2)`
New resistance of the wire ,
`R_(1) =(rhol_(1))/(A_(1)) = (rho((100.2)/(100))l)/(((100)/(100.2))A) `
`rArr " " R_(1) = (rho(100.2)^(2)l)/((100)^(2)A) = ((100.2)/(100))^(2).R" "`[from Eq.(i)]
Precentage change is the resistance of the wire .
`= (((100.2)/(100))^(2) R-P)/( [((100.2)/(100))^(2) - 1]xx100)` = 0.4%
`therefore ` % Change of resistance = 0.4% .