Electric power transformer problem

[MIA6]

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.

 

[alphysicist]

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.

 

[Moetasim]

I can explain that the formula P=I^2R is derived from Ohm's Law, which states that the power (P) dissipated in a circuit is equal to the current (I) squared multiplied by the resistance (R). This formula is applicable to any type of electric circuit, including transmission lines. In this case, the power loss in the transmission lines is calculated by using the current (I) and resistance (R) values, as they directly affect the amount of power dissipated.

It is important to note that the power loss in the transmission lines is not the same as the power output from the power plant. The power output is the amount of power that is actually being used by the town, while the power loss is the amount of power that is lost during transmission due to resistance in the lines. So, in order to find the total power loss, we need to use the formula P=I^2R, rather than subtracting the power output from the power input.

I hope this explanation helps to clarify any confusion regarding the calculation of power loss in this scenario. It is important to use the correct formula and understand the underlying principles in order to accurately analyze and solve problems related to electric circuits.