Power lost during transmission

[songoku]

Homework Statement

A power station needs to deliver 20 MW of power to a city. This power is generated at 16 kV and then stepped up to 240 kV. The total resistance of the transmission cables is 20 kΩ. Show the power loss during transmission is 139 kW

Relevant Equations

P = V.I

$P=I^2 R$

The current in transmission cables = 20 MW / 240 kV = 250 / 3 A

Power loss in cables =(250/3)² x 20 x 10³ = 139 MW , which is not possible

Where is my mistake?

Thanks

 

[Delta2]

I think there must be a typo in the ohmic resistance of the transmission cable, most likely it is $20\Omega$. A typical copper cable has a resistance of around $8\Omega$ per km, so if we take it that the total resistance is $20000\Omega$ this means that the power station is located 2500km away from the city...Which of course doesn't look right.

 

[songoku]

Thank you very much Delta2