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24 September, 07:17

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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  1. 24 September, 10:30
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    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
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