A continuous electric current of 2,000 amps is to be transmitted from a generato

Question

A continuous electric current of 2,000 amps is to be transmitted from a generator to a transformer located 170 feet away. A copper conductor can be installed for $5.8 per pound, will have an estimated life of 27 years, and can be salvaged for $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 6.531/A kilowatt, where A is the cross-sectional area of the conductor in square inches. The cost of energy is $0.0897 per kilowatt-hour, the interest rate is 10.6%, 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

This is the good question.

To solve it we will find the cost equation in terms of Area and then for optimum area the cost is minimum.

Hence we will find minima.

Now Cost for installation is

Density =555ponds / cubic foot

Volume = 170A cubic foot

Cost C1= 170A×5.8$ - 170A×1$

=416A $

Cost for energy=C2 = (6.531/A )×0.0897 $ for 1 hour

For 1 year

=( 6.531×.0897×24×365)/A +10.6%

=5675.8/A $

Total cost C = C1+C2

For optimum area dc/dA =0

Solving we get

A=3.69 square- feet

Please rate my answer if you like it. I will further help you in comments if you need. But this is the correct solution.

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