Calculate Power & Fraction Lost in High-Voltage Transmission Line

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AI Thread Summary
The discussion focuses on calculating power loss and the fraction of power lost in a high-voltage transmission line with a resistance of 0.28 ohms/km, carrying a current of 990 A over 162 km. The power loss due to resistance was correctly calculated using the formula P = I^2 * R, resulting in approximately 44.46 MW. To find the fraction of power lost, the total power transmitted (calculated as P = I * V) is needed, which is 733.8 MW. The user struggled with the second part of the problem but received guidance on using the correct formulas. The conversation highlights the importance of understanding both power loss and total power in high-voltage transmission systems.
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Homework Statement


A high-voltage transmission line with a resistance of 0.28 /km carries a current of 990 A. The line is at a potential of 740 kV at the power station and carries the current to a city located 162 km from the station.
(a) What is the power loss due to resistance in the line?
W

(b) What fraction of the transmitted power does this loss represent?
%



Homework Equations



Power= change in V^2/R

where v is potential difference and R is resistance

Power = I^2*R

where I is current



The Attempt at a Solution



I got part a correct. I used the equation p=I^2*R and got 44457336
I can't figure out how to get the second part though
I tried using p=v^2/R with 740,000 as the V and .28(162) as the R to no avail

any suggestions?
 
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If you notice, V/R does not give a current of 990 A. The concept gets a little more complicated with a transformer. I*V (990A*740kV) is the provided power. I^2*R is the power lost to resistance.
 
Hi goWlfpack! :smile:
goWlfpack said:
any suggestions?

p = IV? :wink:
 
got it! thanks guys! :)
 
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