If a conducing wire is stretched to make itself twice longer then what change in the resistance of the wire will be seen if its resistivity and volume remain unchanged ?

Explanation

Let the initial resistance of the wire `R=rho(l)/(A)` and final resistance `R.=(l.)/(A)` Here l.=2l.
As `A.l.=Al therefore (A.)/(A)=(l)/(l.)=(1)/(2)`
`therefore (R.)/(R )=((rho l.)/(A.))/((rho l)/(A))=(l.)/(l).(A)/(A.)=2xx2=4 therefore R.=4R`
`therefore` Resistance of the wire will be four times its previous value.