Question

A power station delivers 510 kw of power at 12,000 v to a factory through wires of total resistance of 2.5 ω. how much less power is wasted if the electricity is delivered at 47,000 v rather than 12,000 v?

Answer 1

The currents (Amperes) in the two cases are calculated as power/voltage:

510000W / 12000V = 42.5 A
510000W / 47000V = 10.85 A

And that the power wasted in the two cases is calculated as current^2 x resistance:

(42.5 A)^2 (2.5 Ohms) = 4,515.625 W
(10.85 A)^2 (2.5 Ohms) = 294.30625 W

So the amount of power saved is the difference:
4,515.625 - 294.30625 = 4221.32 Watts

This is the main reason why distribution grids aim to operate at the highest voltages possible.