A blob of 500 grams of copper (density of copper is 8.96 grams/cm^3) is to be ma

Question

A blob of 500 grams of copper (density of copper is 8.96 grams/cm^3) is to be made into a long straight wire with a circular cross section. his means that the wire is a long thin cylinder (Volume of a cylinder is pr^2h). The wire must be at least 12 meters long to be used as part of a certain electrical circuit. What length of wire should be made from this copper in order to have minimal resistance. The formula for resistance of a wire is R= ?l/A, and the resistivity of copper is 1.72*10^-8 Ohm-meter.

Explanation / Answer

R is proportional to length/area Common sense dictates that we make the wire as short as possible to give it the maximum cross-sectional area. We want the numerator as small as possible. We want to make the denominator as large as possible. We need 12m, so we make the wire 12m long. That is the answer. Here is some filler. 500g/(8.96 g/cm^3) = 55.8 cm^3 Vol/Length = cross sectional area = 55.8cm^3/120cm = 0.465 cm^2 0.465cm^2/PI = 0.148 = r^2 r = 0.385 cm = 3.8 mm This is the radius of the wire that is 12m long and has a mass of 500g.

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