Question

Aluminum and copper wires of equal length are found to have the same resistance. What is the ratio of their radii

Answer 1

Answer:

R = ρ L / A       resistance of wire

ρC / ρA = [RC AC/ LC] / [RA AA/ LA} = AC / AA

Since resistance and length are the same for both wires where A is the area of the wire

ρC / ρA = rC^2 / rA^2        where r is the radius of the wire

(ρC / ρA)^1/2 = rC / rA

rC / rA = (1.72 / 2.83)^1/2

rC / rA = .780        radius of copper wire is .780 of aluminum wire