Why is power loss = I^2R instead of P=VI or P=I^2R?

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Homework Help Overview

The discussion revolves around understanding the concept of power loss in electrical transmission lines, specifically addressing why power loss is expressed as I²R instead of using the general power formulas P=VI or P=I²R. The context includes a scenario involving a power station generating 120kW and transmitting power over a distance with specific resistance.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between power, current, and resistance, questioning the reasoning behind the use of I²R for power loss. Some express confusion about the formulas and seek a deeper understanding of the underlying principles.

Discussion Status

Participants are actively engaging with the topic, with some providing insights into the relationships between voltage, current, and power. There is a mix of attempts to clarify concepts and questions about specific calculations, indicating a productive exploration of the subject.

Contextual Notes

Some participants note that the discussion is not for homework but for revision purposes. There are also indications of confusion regarding the application of formulas and the assumptions made in the problem setup.

victorhugo
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[Moderator note: Thread moved from technical section hence no template. Question text from later in the thread added to this post to make things clear]

"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

[Since question d looks an awful lot like question c, I suspect a miscopy from the original source]

Since power is in joules, i'd imagine we could get the energy in - energy out (using p=vi=i^2r).
But it doesn't work like that. My textbook states that power loss = I^2R, but why?
Could someone explain please? thank you
 
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victorhugo said:
Since power is in joules
The unit of power is Watts... :smile:
 
berkeman said:
The unit of power is Watts... :smile:
Oh... Oops.
 
so e=pt?
 
also i still don't see the process where i can get power loss by I^2R...
 
victorhugo said:
so e=pt?
Yes, Energy = Power * Time
victorhugo said:
also i still don't see the process where i can get power loss by I^2R...
Can you say more about your specific question? The energy loss in wires leading to a load is I^2 * R.
 
"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

I haven't gone over this stuff in a veryyy long time but it helps to understand it for my last course. I honestly don't get the way they do *any* of those questions, so a logical explanation to any assumed knowledge would definitely help :)
 
*btw this is not homework but me revising some basic stuff i need to know for my upcoming course*
 
You have been here long enough to know that all schoolwork-type questions go in the Homework Help forums, and use the HH Template. Sigh.
 
  • #10
berkeman said:
You have been here long enough to know that all schoolwork-type questions go in the Homework Help forums, and use the HH Template. Sigh.
Well it's been a while since i had to trouble doing homework questions so it didnt even pop into mind.
"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

a. I don't like to pick out the formulas i have and plug in the numbers I have. I want to see how the formula works. So, current being C/s, I don't see what i can do here.
same for b, c and d.
please help :frown:
 
  • #11
victorhugo said:
Well it's been a while since i had to trouble doing homework questions so it didnt even pop into mind.
"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

a. I don't like to pick out the formulas i have and plug in the numbers I have. I want to see how the formula works. So, current being C/s, I don't see what i can do here.
same for b, c and d.
please help :frown:
You are given the power input and the resistance of the transmission line. What is the current to deliver that power at that voltage? What would be the power dissipated in the wires to deliver that current?
 
  • #12
We actually get power from
$$ P = εI $$
where ε is the emf. ε is the energy per unit charge. Current is the charge passing through per unit time. Therefore, the product of them means how much energy is passing through per unit time. You also have the relation between I, ε, R. You can then find the answer you want
 
  • #13
Chan Pok Fung said:
We actually get power from
$$ P = εI $$
where ε is the emf. ε is the energy per unit charge. Current is the charge passing through per unit time. Therefore, the product of them means how much energy is passing through per unit time. You also have the relation between I, ε, R. You can then find the answer you want
That's not helpful in this question.

Quiz Question -- Why not? :smile:
 
  • #14
Chan Pok Fung said:
We actually get power from
$$ P = εI $$
where ε is the emf. ε is the energy per unit charge. Current is the charge passing through per unit time. Therefore, the product of them means how much energy is passing through per unit time. You also have the relation between I, ε, R. You can then find the answer you want
berkeman said:
That's not helpful in this question.
Actually it can help if @victorhugo considers this fundamental enough to start with. The current delivered by the power source can be extracted from the source EMF and the power it generates, both given values:
victorhugo said:
"A power station generates electric power at 120kW... If the power is transmitted at 240 V...
So the power station is putting out 120 kW with an EMF of 240 V.
 
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  • #15
In short the issue is P(w) = V(v) * I(a) Since V= I * R(ohms) we have
=( I * R ) * I = I^2R.

In this problem - for clarity it should state this is a single phase system, and V and I units in RMS values.
 

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