Physics E & M Question about a powerline

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In summary, the high voltage powerline operates at 500000 V-rms and carries 500 A of rms current. The resistive power loss in 200 km of the powerline can be calculated using the formula P = V2/R, where V is the potential drop and R is the resistance of the cable. After correcting the formula to P = I2R, the potential drop is calculated to be 5000 V and the resistive power loss is 2.5 MW.
  • #1
Brandon Hawi
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Homework Statement


A high voltage powerline operates at a 500000 V-rms and carries an rms current of 500 A. If the resistance of the cable is 0.05Ω/km, what is the resistive power loss in 200 km of the powerline.

V = 500000 V-rms
Irms = 500 A
R/x = 0.05Ω/km
x = 200 km

Homework Equations



P = I2R
P = V2/R
P = IV

The Attempt at a Solution



I attempted to use V2/R at first, and that gave me 2.5 x 1010 Watts, however the given answer is 2.5 x 106 Watts. I get that answer when I use I2R, but I was wondering why V2/R could not be used?
EDIT: Fixed to V2/R
 
Last edited:
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  • #2
Hello and welcome to PF!

Your formula P = V/R is incorrect. Did you mistype the formula?

Even when you have the correct formula, you have to be careful. The 500,000 V of the powerline probably represents the voltage of the line relative to ground at one end of the line. It does not represent the potential drop as you go from one end of the line to the other end of the line.

You can calculate the potential drop V and then use the (corrected) power formula that involves V and R.
 
  • #3
TSny said:
Hello and welcome to PF!

Your formula P = V/R is incorrect. Did you mistype the formula?

Even when you have the correct formula, you have to be careful. The 500,000 V of the powerline probably represents the voltage of the line relative to ground at one end of the line. It does not represent the potential drop as you go from one end of the line to the other end of the line.

You can calculate the potential drop V and then use the (corrected) power formula that involves V and R.

Sorry, I meant to type V2/R. How would one then go about calculating the potential drop V?
 
  • #4
Brandon Hawi said:
Sorry, I meant to type V2/R. How would one then go about calculating the potential drop V?
You're making Georg Ohm feel neglected today.:wink:
 
  • #5
TSny said:
You're making Georg Ohm feel neglected today.:wink:

Alright then, so V = IR. So I get V = 5000 V. Then I used V2/R and got 2.5 MW as my answer. Thanks ! :smile:
 
  • #6
Looks good!
 

Related to Physics E & M Question about a powerline

1. What is the purpose of a powerline in physics?

A powerline is used to transmit electricity from a power plant to homes and businesses. It is a crucial component of the electrical grid, which allows for the distribution of electricity to various locations.

2. How does a powerline work?

A powerline works by using a series of conductors to transmit electricity over long distances. The electricity is generated at a power plant and travels through the conductors to reach its destination. Transformers are also used to regulate the voltage and ensure safe delivery of electricity.

3. What factors affect the efficiency of a powerline?

The efficiency of a powerline is affected by factors such as the distance the electricity needs to travel, the quality of the conductors, and environmental conditions. The longer the distance, the higher the resistance and the more energy is lost. Poorly maintained or damaged conductors can also decrease efficiency.

4. Can powerlines cause health problems?

There is currently no conclusive scientific evidence to suggest that powerlines cause direct health problems. However, some studies have shown a correlation between living near powerlines and increased risk of certain health issues. More research is needed to fully understand the potential health effects of powerlines.

5. How is electromagnetic radiation related to powerlines?

Powerlines produce electromagnetic radiation, which is a form of energy that travels through space. The strength of this radiation is dependent on the amount of current flowing through the powerline. High levels of electromagnetic radiation can potentially interfere with electronic devices and may have health implications, but the levels from powerlines are typically considered safe.

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