Answer :
The diameter of the copper wire if its resistance is to be the same as that of an equal length of aluminum wire with diameter 1.94 mm is 1.568mm
what is resistance?
The obstruction to current flow in an electrical circuit is measured by resistance. The Greek letter omega Ω represents resistance, which is measured in ohms.
what is resistivity?
The term "resistivity" refers to a quality that quantifies how much an object resists having current flow through it. It is a feature of the material itself, independent of the size or form of the sample, and is typically temperature dependent, though it could also be pressure-dependent.
by formula we have ;
R=ρL/A =ρL/πd²/4
where
R = resistance
ρ= resistivity
L = length ; and
A = area of cross section = πd²/4
we know that,
ρ₁ of aluminum = 2.63×10⁻⁸Ωm ; d₁ is diameter of aluminum
ρ₂ of copper=1.72×10⁻⁸Ωm ; d₂ is diameter of copper
given: L of copper= L of aluminum
also, R of copper= R of aluminum
on cancelling the equal terms we get,
ρ₁/d₁²=ρ₂/d₂²
here d₂=d₁[tex]\sqrt\frac{resistivity of copper}{resistivity of aluminum}[/tex]
d₂=1.94[tex]\sqrt \frac{1.72}{2.63}[/tex]
d₂=1.568mm
Hence the diameter of copper wire is 1.568mm
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