Question

What happens to resistance and resistivity when a wire is expanded?

Answer 1

If you expand the wire of length l, n times the length will become l'=nl

The cross sectional area a of the wire becomes n times less, a'=a/n

So the resistance , R =ρl'/a' = (ρ(nl))/(a/n) = n²(ρl/a) = n²R

Resistivity is the property of the material (still it is the same metal) and it is constant.

It does't change.

Answer 2

Resistance is the term which is the resisting of flowing of charges from a specific substance of any size.

Consider we have a solid substance of copper. It will have a resisting of charges from flowing through the substance.

If we change its length and area provided to drift of charge, its resistance will vary.

But the one thing that will constant for all copper substance of any shape and size is resistivity. The resistance of a substance of copper , iron , germanium will vary if we change the shape and size of that substance, but its resistivity is constant at any shape and size.

Resistivity is different in copper,Iron etc because of their nature,but if we change the shape,only resistance will change.

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Resistivity is like the density of a material that is constant and resistance is like the mass which will depend on the length area or (volume) of substance.

So resistivity remains same and resistance will vary as R=pl/A