Answer :
The diameter of the required aluminum wire in place of copper wire is 0.772 mm.
We know, the resistance of the wire is given by,
R = pL/A
Where,
R is resistance,
p is the resistivity of the material,
L so the length of the wire,
A is the area of the wire.
The resistivity p₁ of copper is 1.6 x 10⁻⁸Ω.
The resistivity p₂ of copper is 2.65 x 10⁻⁸Ω.
The length of both the copper as well as the aluminum wire is L.
Let us say the area of copper wire is A₁ and that of aluminum is A₂.
So, for same resistance,
p₁L/A₁ = p₂L/A₂
p₁/A₁ = p₂/A₂
Area = πD²/4
So, we can write,
p₁/D₁² = p₂/D₂²
Putting the values,
1.6 x 10⁻⁸/(0.6)² = 2.65 x 10⁻⁸/D²
D₂ = 0.772 mm.
The diameter of the aluminum wire required is 0.772mm.
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Complete Question - A circuit calls for a 0.500 mm-diameter copper wire to be stretched between two points. You don't have any copper wire, but you do have aluminum wire in a wide variety of diameters.
a) What diameter aluminum wire will provide the same resistance?
