# Electric power transformer problem

An average of 120 kW of electric power is sent to a small town from a power plant 10 km away. The transmission lines have a total resistance of 0.40 ohms. Calculate the power loss if the power is transmitted at 240 V.
The solution is I=P/V=500 A, then the power loss in the lines, P(loss)=I^2R=(500A)^2*0.04ohms=100kW
Here I don't understand why Ploss=I^2*R? I mean is that supposed to be power output, so then in order to find the power loss, we need to use Power input 120kW-output 100kW, then 20 is the power loss?!! Because when I see 'loss', it's like a common sense to use subtraction, but how come here is not? thanks for help.

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alphysicist
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It's called power loss because the 100kW is due to the heating of the wire because of the wire's resistance; that heat is lost to the air (and therefore not available for use).

Since you mentioned subtraction, to see how subtraction could be involved: If the 120kW is what the power plant generates, then we have

120kW - generated by power plant
100kW - lost as heat in the wire between the power plant and the city
20kW - power available to the city

so if you somehow knew ahead of the time the power available to the city then you could subtract that from the power generated by the power plant to find the power loss.