Where Is the Error in This Power Transmission Calculation?

AI Thread Summary
The calculation of power loss in transmission cables shows an unrealistic figure of 139 MW, indicating an error in the resistance value used. A suggested correction points to a potential typo in the ohmic resistance, likely being 20 ohms. Typical copper cables have a resistance of around 8 ohms per kilometer, which implies an implausible distance of 2500 km from the power station to the city. This discrepancy highlights the need for accurate resistance values in power transmission calculations. Correcting these values is essential for realistic power loss assessments.
songoku
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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
 
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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.
 
Thank you very much Delta2
 
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