The length of a wire of cylindrical cross section is increased by 100%. Find out the percentage change is the resistance,taking into account the consequent decrease in the diameter of the wire.

Explanation

Initial length=l, final length, `l^'=l+1times100/100=2l`.
If V be the volume,area of cross section `A=V/l`
`therefore` Final area of cross section , `A^'=V/(2l)`
From the formula `R=rho1/A` we get,
`R/(R')=l/(l').(A')/A=l/(2t).(V//2l)/(V//l)=1/4`
`therefore R'=4R=R+3R=R+300/100R`
i.e., percentage change in resistance=300%.