Answer:
Radius of the copper wire is less than the radius of aluminum wire by a factor of 0.805
Explanation:
We know that Resistance of a wire is given by
R = ρL/A
Where ρ is the resistivity of the material used, L is the length and A is the cross-sectional area of the wire.
A = πr²
R = ρL/πr²
The resistivity of copper wire is ρc = 1.72x10⁻⁸
The resistivity of aluminum wire is ρa = 2.65x10⁻⁸
If both wires has same resistance then we can compare them as
Rc = Ra
ρcL/πrc²= ρaL/πra²
Assume a 1 m length of wire
ρc/rc²= ρa/ra²
ρc/ρa = rc²/ra²
1.72x10⁻⁸/2.65x10⁻⁸ = rc²/ra²
0.649 = rc²/ra²
rc/ra = √0.649
rc/ra = 0.805
rc = 0.805ra
So that means the radius of the copper wire is less than the radius of aluminum wire by a factor of 0.805
