What is the resistance of 2,000 feet of AWG #6 copper wire? What is the resistan

Question

What is the resistance of 2,000 feet of AWG #6 copper wire? What is the resistance of 2,000 feet of AWG #6 aluminum wire? Determine the minimum required copper wire size to power a 28VDC motor that uses 40 Amps and is 25 feet from the bus bar (nearest power source). Assume that the power wire is a single wire in free air and that the motor current load is continuous. Is there sufficient information to determine the size of aluminum wire that is required for the circuit in problem 3? (Yes or No) What is the maximum allowable voltage drop for the circuit in problem #3?

Explanation / Answer

a)

AWG #6 ==> diameter = d = 4.621 mm

==> R = 1.028 ohms/km

==> R = 1.028 * (2000 * 0.3048e-3) = 0.6266688 = 0.627 ohms

b)

R = (2.82/1.68) * (1.028) * (2000 * 0.3048e-3) = 1.0519 = 1.05 ohms

c)

R = V/i = 28/40 = 0.7 ohms

R = rho L/A = rho L/(pi r^2)

==> radius = r = sqrt(rho L/(pi R)) = sqrt(1.68e-8*(25*0.3048)/(3.1416*0.7)) = 2.41e-4 m

d)

Yes

==> radius = r = sqrt(rho L/(pi R)) = sqrt(2.82e-8*(25*0.3048)/(3.1416*0.7)) = 3.13e-4 m

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