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.

Question

Physics

Celeste Landry

14 September, 12:17

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.

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Gina Ortega · 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