The formula for resistance of the wire is
R=Where
′= specific resistance of the wire
⇒R∝⇒R∝(∵A=πr2)∴=×..........(i)
Given,
l1=l,l2=2l,r1=r,r−2=2r,R2=R
Substituting these values in Eq.(i),we have
=×=2&R2=Therefore,resistance will be halved
Now the specification resistance of the wire does nt depend on the geometry of the wire hence it remains unchanged.
Aliter
⇒R2=,specific resistance doesn't depend upon length and radius