Power Loss in 400kV Cable Carrying 1GW of Power

In summary: Thanks for the help!In summary, the question asks for the power loss in a cable carrying 1GW of power with a line resistance of 5 ohms. The correct equation to use is P=I^2/R, where I=P/V. After substituting the values, the power loss is calculated to be 1.25x10^6 W. The mistake made was dividing instead of multiplying when substituting the values into the equation.
  • #1
JordanHood
9
0

Homework Statement


A 400kV line is carrying 1GW of power and experiences a line resistance of 5 ohms. What is the power loss in the cable due to resistive losses?

Homework Equations

The Attempt at a Solution


You are given 4 potential answers to this question
a) 3.2x10^7 W
b) 78 W
c) 5000 W
d) 2x10^8 W

I have tried using I=P/V and then substituting this value into P=I^2/R but this doesn't seem to give any of the answers. Can anyone help me out?
 
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  • #2
You might want to check your equation relating power and current.
 
  • #3
I suspect you are probably using the LINE resistance, when you should be using the line resistance plus the load resistance, to computer the current. Since you did not bother to post any work, I'm just guessing here. Please post your work when you ask such questions. How can we tell where you've gone wrong when we don't see what you did?
 
  • #4
I used I=P/V to get 1x10^9/400x10^3 = 2500A. I then substituted this into Power loss= I^2/R to get 2500^2/5 = 1.25x10^6 W.
 
  • #5
JordanHood said:
I used I=P/V to get 1x10^9/400x10^3 = 2500A. I then substituted this into Power loss= I^2/R to get 2500^2/5 = 1.25x10^6 W.
So you are agreeing with me; you made exactly the mistake I thought you probably had made. Think about it.
 
  • #6
phinds said:
So you are agreeing with me; you made exactly the mistake I thought you probably had made. Think about it.
ah yes, gosh that was stupid P=i^2*R not divided like I was doing
 

1. What is the cause of power loss in 400kV cables carrying 1GW of power?

The main cause of power loss in cables is resistance. As the current flows through the cable, it encounters resistance which leads to a voltage drop. This voltage drop results in power loss.

2. How does distance affect power loss in 400kV cables carrying 1GW of power?

The longer the distance the power has to travel, the higher the power loss will be. This is because the resistance in the cable increases with distance, leading to a higher voltage drop and thus, more power loss.

3. What can be done to reduce power loss in 400kV cables carrying 1GW of power?

One way to reduce power loss is to use conductors with lower resistance. This can be achieved by using thicker cables or materials with higher conductivity. Additionally, using transformers at regular intervals along the cable can help to compensate for the power loss.

4. How does temperature affect power loss in 400kV cables carrying 1GW of power?

Temperature can also impact power loss in cables. As the temperature increases, the resistance of the cable also increases, leading to more power loss. It is important to consider the temperature of the environment when designing and installing power cables.

5. What are the consequences of power loss in 400kV cables carrying 1GW of power?

The most immediate consequence of power loss is a decrease in the efficiency of the power transmission. This can result in a decrease in the amount of power reaching the destination and potential disruptions in the power supply. Additionally, power loss can also lead to increased costs and environmental impacts, as more power needs to be generated to compensate for the loss.

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