Question

An electric power station that operates at 25 kV and uses a 20:1 step-up ideal transformer is producing 310 MW (Mega-Watt) of power that is to be sent to a big city which is located 280 km away with only 2.0% loss. What is the resistance of the TWO wires that are being used?

Answer 1

Input voltage is 25 kV

Output voltage of the step-up transformer

V = 25 x 10³ x 20

V = 500 x 10³ V

Because of this voltage a current will be produced in the wires, ideally the current when there is no power loss would be

VI = P

500 x 10³ x I = 310 x10⁶

I = 620 A

When this current flows through the wires, 2% of the power will be disspated bacause of the resistance

I²R = 0.02 x 310 x 10⁶

620² x R = 6.2 x 10⁶

R = 16.13 ohm

This is the combined resistance of the two wires

( remember the resistance of one wire is 16.13 /2 = 8.065 ohm)