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
