The radius of a conducting wire is doubled. What will be the ratio of its new specific resistance to the old one?

The equation for the resistance R is: R=ρ * (l/A), where, ρ is electrical resistivity, l is the length of the conductor, and A is the surface area.

The initial surface area is:

A=r²π, then when we double the radius we get:

A₁ = (2*r) ²π=4*r²π=4*A

Initial resistance is: R=ρ * (l/A).

When we double the radius, resistance is: R₁=ρ*{ l / (4*A) }

The ratio of the new resistance to the old one:

R₁/R=[ρ * (l/A) ] / [ ρ * { l / (4*A) } ] = ρ, l and A cancel out and we get:

R₁/R = (1/1) / (1/4) = 4/1