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

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SUMMARY

The discussion centers on the calculation of power loss in transmission lines, specifically why power loss is expressed as I²R instead of using the general power formulas P=VI or P=I²R. A power station generates 120 kW and transmits this power over 10 km with a total resistance of 0.40 ohms at 240 V. The calculations involve determining the current in the transmission lines, voltage drop, and power loss, emphasizing the relationship between current, voltage, and resistance in electrical systems.

PREREQUISITES
  • Understanding of Ohm's Law (V=IR)
  • Familiarity with power calculations (P=VI)
  • Knowledge of electrical resistance and its impact on power loss
  • Basic concepts of electrical energy and units (Watts, Joules)
NEXT STEPS
  • Learn how to calculate current using P=VI in electrical circuits
  • Study the implications of resistance in power transmission systems
  • Explore the concept of EMF (electromotive force) in electrical engineering
  • Investigate the differences between AC and DC power transmission
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Electrical engineers, power system analysts, students studying electrical engineering, and anyone interested in understanding power loss in transmission lines.

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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