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

Explanation

It is given that l. =l + 5% of `l = l (1 + 5/100)`
As on stretching the wire its volume remains constant, hence A.l= A.l.
`rArr A. = (Al)/(l.) = (Al)/(l (1 + 5/100) ) = (A)/( (1+ 5/100))`
` therefore ` New resistance `R. (rho l.)/(A.) = (rho l (1 + 5/100)^2)/(A ) = R.(1 + 5/100)^2 = R (1 + 10/100)`
` therefore ` Percentage increase in resistance `Delta R = (R. - R)/(R ) xx 100% = (R (1 + 10/100) -R)/(R ) xx 100% = 10%`