Question

An electric power station is producing 210 kW of power that is to be sent to a small town located 34.0 km away. Each of the two wires that comprise the transmission line has a resistance per kilometer of length of 0.40 Ω/km. Find the power lost in heating the wires if the voltage is stepped up from 1.20 kV to 30.0 kV using an ideal transformer.

Answer 1

You probably know this equation giving the power dissipated:

P = IV

P = power, I = current, V = applied voltage

We can substitute I = V/R from Ohm's law:

P = V²/R

Given values:

V = 30.0×10³V, R = 0.40Ω/km×34.0km = 13.6Ω

Plug in and solve for P:

P = (30.0×10³)²/13.6

P = 6.62×10⁷W