An electric power station that operates at 35 kV and uses a 10:1 step-up ideal t

Question

An electric power station that operates at 35 kV and uses a 10:1 step-up ideal transformer is producing 210 MW (Mega-Watt) of power that is to be sent to a big city which is located 160 km away with only 4% loss. Each of the two wires are made of copper (resistivity = 1.68 × 10-8 .m). What is the diameter of the wires?

(My work is in the picture above, but it is wrong. Apparently, because you do not know the voltage across the wires, you need to find the current so that Plost=I^2*R. I also know that you need to take into account that there are two wires, but I'm not sure how to solve this problem even with this information. Please help, thank you!!!)

Explanation / Answer

Vp / Vs = Np / Ns

=> 35000 / Vs = 10 / 1

=> Vs = 3500 V

Power = V*I

=> 210*106 = (3500)*I

=> I = 60000 A

Current through each wire = i = 30000 A

Power loss = 4% of 210MW = 8400000 W

8400000 = 2* (i2)* R

=> 8400000 = 2*(300002)*( 1.68*10-8*160000/r2)

=> r = 0.42 metres

diameter = 0.84 metres

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