Electrostatics: What power equations to use?

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Discussion Overview

The discussion revolves around the application of different power equations in the context of electrical circuits, specifically focusing on the equations P=IV, P=I²R, and P=V²/R. Participants explore the conditions under which these equations yield consistent results, particularly in relation to power loss in transmission lines.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant notes discrepancies in results when using different power equations for calculating power loss, specifically finding P=I²R to be correct while the others yield different answers.
  • Another participant argues that all equations should be equivalent when applied correctly, referencing Ohm's Law to demonstrate how to derive the equations from one another.
  • A third participant emphasizes the importance of defining the voltage correctly when using the equations, suggesting that the choice of voltage can lead to different results.
  • One participant provides a specific example involving an electric power company and questions the application of the equations in that scenario, noting that the results differ based on the equation used.
  • Another participant suggests that the confusion may stem from misunderstanding the definitions of voltage in the context of the equations, particularly in relation to the load and transmission lines.
  • A later reply indicates that the use of P=I²R is the most convenient for calculating power line losses, implying that this equation is preferred in practical applications.

Areas of Agreement / Disagreement

Participants generally agree that the equations should yield the same results under proper conditions, but there remains disagreement on the definitions and applications of voltage in different contexts, leading to unresolved discrepancies in their calculations.

Contextual Notes

Participants highlight the potential for confusion arising from the definitions of voltage and the specific setup of problems, indicating that assumptions about the circuit configuration may affect the outcomes of the equations used.

hihowareu
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I was wondering what the different power equations are used for...

P=IV, P=I2R, and P=V2/R

I was solving for power loss and I noticed that using P=I2R gave me the right answer but the other two gave me different answers
 
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They should all be equivalent. Take Ohm's Law (V=IR). If you plug in V from Ohm's Law into your first equation you get P=I^2R. If you take Ohm's Law in the form I=V/R and plug it into your first equation you get P=V^2/R. I would guess the difference was a result of the problem setup, i.e. what you define V, I, and R to be. If you show the problem I might be able to help more.
 
hihowareu said:
I was wondering what the different power equations are used for...

P=IV, P=I2R, and P=V2/R

I was solving for power loss and I noticed that using P=I2R gave me the right answer but the other two gave me different answers

I agree they should give the the same answer for resistors. Maybe you can give us details so we can understand exactly what you are doing. There is of course the question of which V you are using with the other two equations. If you don't use the right voltage, things will not check out.

The more general of these equations is P=IV because you can apply this to nonlinear devices more easily. But, for a linear resistor there is no ambiguity and all three equations are valid.
 
Thanks for the replies

for example: An electric power company decides to ship 30 000 W of power at 20 000V over 2.5 [tex]\Omega[/tex] transmission lines. How much power is lost over the lines.

I got the right answer by using is P=IV to get I. Then using P=I2R to get the power lost.

But if I use P=V2/R I get a completely different number.
 
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In your first definition V is the voltage supplied from the generator, which is the voltage across the wire AND the voltage across the load. Solving for I gives you the correct current to use in P=I^2R.

In your second definition V is still the voltage supplied to the load and wire. That would be the power dissipated from a (load+wire) of resistance R. To make this correct you would need to find the voltage across ONLY the wire, which is not the same as the voltage supplied by the generator.

Hope this helps.
 
The above answer sounds like the most likely mistake. It is a common mistake. The formula P=I^2*R is the most conenient for power line losses.
 

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