Question

A conducting wire has a resistance of 20 ohm. Its length is now stretched to increase by 2 %. Calculate the resulting value of the resistance of the wire.

Answer 1

R=20Ω

Let length of conducting wire is l

l'= l+(2/100)l=l+0.02l = 1.02l

Volume of wire = cross sectional Area (A) X length (l)

Cross sectional area for stretched wire A' = V/l'=(Axl)/1.02xl)=A/1.02

R'= (ρl')/A'= (ρx1.02l)/(A/1.02)

                 =(1.02x1.02)(ρl/a)

                 =1.0404xR

                 =1.0404x20

                 =20.808Ω