\"A continuous electric current of 2,000 amps is to be transmitted from a genera

Question

"A continuous electric current of 2,000 amps is to be transmitted from a generator to a transformer located 220 feet away. A copper conductor can be installed for $4.8 per pound, will have an estimated life of 27 years, and can be salvaged for $1.1 per pound. Power loss from the conductor will be inversely proportional to the cross-sectional area of the conductor. The power loss in one hour may be expressed as 6.295/A kilowatt, where A is the cross-sectional area of the conductor in square inches. The cost of energy is $0.0812 per kilowatt-hour, the interest rate is 12.5%, and the density of copper is 555 pounds per cubic foot. Calculate the optimum cross-sectional area of the conductor. You should assume the conductor operates 24 hours a day, 365 days per year."

Explanation / Answer

Energy loss (kw/hr) = (6.295 / A) (24 x 365) ($0.0812) = $4477.71 /A

Material weight (pounds) = (220) * (12) * (555) * (A/123) = 770.83A

Total material cost = 770.83 x A x $4.8 = $3700 A

Capital recovery cost at 12.5%:

(3700A - $1.1 x 770.83A) (A/P, 12.5) + ($1.1 x 770.83A x 0.125)

542.44A

Total equivalent annual cost at 12.5% :

542.44A + 4709.11/A

Optimal cross-sectional area at 12.5% :

dAEC/dA = 542.44 - 4709.11/A^2 = 0

This gives A = 2.9464 square inches

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