Suppose that you wish to fabricate a uniform wire out of 0.800 g of copper. If t

Question

Suppose that you wish to fabricate a uniform wire out of 0.800 g of copper. If the wire is to have a resistance R = 0.600 ?, and if all of the copper is to be used.

Explanation / Answer

Resistivity of copper = 1.7 × 10-8 ohm.m and density = 8.94 g/cm3 = 8940 kg/m^3 R = PL/A => 0.6 = 1.7 × 10-8 x L / A find V = mass / density = 0.0008 kg / 8940 = 8.95 x 10^-8 m^3 = A x L => A = 8.95 x 10^-8 / L so 0.6 = 1.7 × 10-8 x L^2 / 8.95 x 10^-8 = 0.19 L^2 so L^2 = 3.16 => L = 1.78 m --------------------------------------… from the relation : A = 8.95 x 10^-8 / L => A = 6.17 x 10^-8 m^2 = pi (r^2) => r^2 = 1.45 x 10^-8 => r = 1.19x 10^-4 m = 119 µm so dameter = 2r = 238 µm

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