Calculate Power & Fraction Lost in High-Voltage Transmission Line

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In summary, the conversation discusses a high-voltage transmission line with a resistance of 0.28 /km and a current of 990 A. The line is at a potential of 740 kV and carries the current to a city 162 km away. The power loss due to resistance is calculated using the equation P=I^2*R, resulting in a value of 44457336 W. To find the fraction of transmitted power represented by this loss, the equation P=IV is used, where I*V is the provided power of 990A*740kV. This results in a power loss percentage of 0.33%.
  • #1
goWlfpack
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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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  • #2
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.
 
  • #3
Hi goWlfpack! :smile:
goWlfpack said:
any suggestions?

p = IV? :wink:
 
  • #4
got it! thanks guys! :)
 

Related to Calculate Power & Fraction Lost in High-Voltage Transmission Line

1. What is power loss in a high-voltage transmission line?

Power loss in a high-voltage transmission line is the amount of energy that is dissipated in the form of heat due to the resistance of the line. This energy loss can lead to a decrease in the efficiency of the line and ultimately result in financial losses.

2. How is power loss calculated in a high-voltage transmission line?

The power loss in a high-voltage transmission line can be calculated using the formula P = I^2 * R, where P is the power loss, I is the current flowing through the line, and R is the resistance of the line. This formula is based on Ohm's law, which states that the amount of current flowing through a conductor is directly proportional to the resistance of the conductor.

3. What factors affect power loss in a high-voltage transmission line?

There are several factors that can affect power loss in a high-voltage transmission line, including the length of the line, the type of conductor used, the temperature of the line, and the voltage level. Higher voltages and lower temperatures generally result in lower power losses, while longer lines and materials with higher resistance can lead to higher power losses.

4. How does power loss affect the efficiency of a high-voltage transmission line?

The power loss in a high-voltage transmission line can significantly affect its efficiency. As more energy is lost due to resistance, less energy reaches its intended destination, resulting in a decrease in efficiency. This can also lead to a decrease in the voltage level of the line, which can further impact its efficiency.

5. How can power loss be reduced in a high-voltage transmission line?

There are several ways to reduce power loss in a high-voltage transmission line. One method is to use materials with lower resistance, such as aluminum or copper. Additionally, implementing measures to improve the cooling and insulation of the line can also help reduce power loss. Increasing the voltage level can also decrease power loss, as long as the line is designed to handle the higher voltage. Regular maintenance and repairs can also help reduce power loss in a transmission line.

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