# What is the Power Loss in a Transformer?

• annamal
In summary: Ok I admit I am not aware of the full analysis of the power loss in a transmission line (which might be a bit complicated, since the current varies along the transmission line, there is the the skin effect which increases the ohmic resistance e.t.c) but I 've seen this simplification that ##P_{loss}=I^2R## in many books, where ##I## the current at the end of the transmission line and ##R## its total ohmic resistance.In summary, the power loss in a transmission line is calculated to be I^2R.

#### annamal

Homework Statement
A transformer on a utility pole steps the rms down from 12kV to 240V. If the input current to the transformer is 2 A, what would the power loss have been if there were no transformer
Relevant Equations
##I_S = \frac{N_P}{N_S}I_P##
##P_{loss} = I_S^2R##
##\frac{N_S}{N_P} = \frac{240}{12\times 10^3} = \frac{1}{50}##
##I_S = \frac{N_P}{N_S}I_P = \frac{N_P}{N_S}I_P = 50\times 2 = 100## Amps
##P_{loss} = I_S^2R##, but I don't know how to find R

Sorry I don't completely understand the asked question. What does it mean by if there were no transformer because taking it literally, if there is no transformer, there is no problem at all lol.

alan123hk
Btw, the equation you using to calculate ##I_S## it holds only in the case of an ideal transformer, so the power loss is zero in that case.

What? Are they asking about the power lost to the magnetizing inductance of the transformer, i.e. assuming there is no load.

I am getting really fed up with instructors that ask students to answer really poorly worded questions. Of course you had to ask for help, I would too.

In any case, did you really describe the original question exactly as asked?

Still, I'll say zero. Zero power loss in a component that doesn't exist. The transformer that isn't connected will have zero voltage, zero current, and zero power dissipation.

Or maybe they're asking what the power loss is when you put 12KV into a 240V distribution network. I don't know, but I'll guess that it doesn't last for very long.

vela, alan123hk and Delta2
If you think it is poorly worded, it is the last part (part d) of this problem

The phrase "if there were no transformer, the power would be sent at 240 V to work for these houses" was omitted from your original post. It was crucial to an understanding of the situation. The entire thread was derailed because you failed to post a complete statement of the problem you wanted solved.

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nasu and DaveE
OK, that makes sense. I have no idea where R=6000Ω came from, maybe earlier in the text?

annamal said:
but I don't know how to find R
##R=\frac{V}{I}##

DaveE said:
OK, that makes sense. I have no idea where R=6000Ω came from, maybe earlier in the text?
You have 12 000 volts across the primary coil, which carries a current of 2.0 amps.

Mister T said:
You have 12 000 volts across the primary coil, which carries a current of 2.0 amps.
They are asking for the power loss in the transmission line. Not the power delivered to the load.

Mister T said:
You have 12 000 volts across the primary coil, which carries a current of 2.0 amps.
The resistance should be 200 ohms though...

@annamal, From now on, please post problem statements exactly as they are and not according to your own interpretation.

Because these two are not necessarily the same, for example here, the problem asks for the power loss in the transmission line while you asked for the power loss in the transformer, and the phrase "if there were no transformer" is accompanied by "and the power would be sent at 240V to homes" which is critical for our understanding.

nasu
I guess the book implies here that when the power is sent directly @ 240V to house, then the power loss in the transmission line is still much bigger even if we shortened the length of the transmission line (hence its resistance drops from 6000 to 200 Ohm). Or I can't make any other usefull interpretation.

The solution given to part c is clearly nonsense. There is not enough info to determine an answer. The calculated 24,000W is the power consumed by the transformer plus load, i.e. everything except the transmission line.
@annamal , please cite the source of the question.

Delta2
No I don't find it complete nonsense, 2A is the current in the transmission line that feeds the primary. 6000ohm might be the total ohmic resistance of a typical power transmission line ...

Delta2 said:
No I don't find it complete nonsense, 2A is the current in the transmission line that feeds the primary. 6000ohm might be the total ohmic resistance of a typical power transmission line ...
It could be, but we are not told it is. What we are told is that the transmission line feeds 2A into the transformer at 12kW, so it is supplying 24kW.

DaveE
haruspex said:
It could be, but we are not told it is. What we are told is that the transmission line feeds 2A into the transformer at 12kW, so it is supplying 24kW.
Ok I admit I am not aware of the full analysis of the power loss in a transmission line (which might be a bit complicated, since the current varies along the transmission line, there is the the skin effect which increases the ohmic resistance e.t.c) but I 've seen this simplification that ##P_{loss}=I^2R## in many books, where ##I## the current at the end of the transmission line and ##R## its total ohmic resistance.

Not sure but I think ##I^2R## is a good lower bound for the power loss in the transmission line.

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Delta2 said:
@annamal, From now on, please post problem statements exactly as they are and not according to your own interpretation.

Because these two are not necessarily the same, for example here, the problem asks for the power loss in the transmission line while you asked for the power loss in the transformer, and the phrase "if there were no transformer" is accompanied by "and the power would be sent at 240V to homes" which is critical for our understanding.
I couldn't because if you notice in the word problem, there is no explicit question asked for it, but the question is answered

Delta2
annamal said:
I couldn't because if you notice in the word problem, there is no explicit question asked for it, but the question is answered
Yes I understand that, but still you could have mention that it is the power loss in the transmission line, and not in the transformer.

Delta2 said:
Yes I understand that, but still you could have mention that it is the power loss in the transmission line, and not in the transformer.
In my original post, I don't mention if it is the power loss in the transmission line or transformer. I just say "what would the power loss have been if there were no transformer"

annamal said:
In my original post, I don't mention if it is the power loss in the transmission line or transformer. I just say "what would the power loss have been if there were no transformer"
Ok but your solution attempt indicates that you are looking for the power loss in the secondary of the transformer.

Parts C and D are a bit hard to understand in my humble opinion.

In part C, 6000 ohms seems to be the ohmic resistance of the transmission line, but it is strange why this value is exactly equal to the input impedance ##~\frac {12kV}{2A} ~##of the transformer ?

In addition, part D does not explain how the value of 200 ohms is obtained. This is not the ohmic resistance of the transmission line in part C, nor the ohmic resistance inside the transformer. It is really difficult to guess what it is.

Delta2
Delta2 said:
Ok I admit I am not aware of the full analysis of the power loss in a transmission line (which might be a bit complicated, since the current varies along the transmission line, there is the the skin effect which increases the ohmic resistance e.t.c) but I 've seen this simplification that ##P_{loss}=I^2R## in many books, where ##I## the current at the end of the transmission line and ##R## its total ohmic resistance.

Not sure but I think ##I^2R## is a good lower bound for the power loss in the transmission line.
It's really not so much about your formulas R=V/I or P=I2R, we all know those. It's all about which voltage, what resistance and where did it come from.

The key phrase here is "power loss" There is no reasonable interpretation of this problem that would mix that up with the power sourced or delivered to the load. If you can't see that distinction, perhaps you should be asking questions instead of providing solutions. The options are simple in this case:

1) There isn't the necessary information given to answer this question. We can't know who is responsible, we just know that it isn't there.
2) The line resistance is given as 6000Ω, or 200Ω in a subtle manner with no explanation about why.

DaveE said:
2) The line resistance is given as 6000Ω, or 200Ω in a subtle manner with no explanation about why.
Yes I think that's exactly the problem here. I tried to find more info in the accompanying text that explains the physics of an Ideal(!?) transformer and says some things about power distribution network but couldn't find anything there either.

DaveE said:
The line resistance is given as 6000Ω, or 200Ω in a subtle manner with no explanation about why.
This may be a subtle way, but it may not be suitable for the average beginner because they may not be able to tell if the question contains all the information needed to find the answer. They may think the values are calculated based on some given data, so they may be confused.

Delta2
Delta2 said:
I 've seen this simplification that ##P_{loss}=I^2R## in many books, where ##I## the current at the end of the transmission line and ##R## its total ohmic resistance.
You are missing the point. We have no information regarding the ohmic resistance of the transmission line. The ##6000\Omega## calculated appears to be the effective resistance of the transformer + downstream load.

haruspex said:
You are missing the point. We have no information regarding the ohmic resistance of the transmission line. The ##6000\Omega## calculated appears to be the effective resistance of the transformer + downstream load.
ok, fine if that's your point I agree.

alan123hk said:
part D does not explain how the value of 200 ohms is obtained
Perhaps we were meant to be given 200 Ohms as the transmission line resistance (still high, but at least feasible) and the part c solution should have used that value too.

I have contacted the site.

Delta2
OK, only slightly off-topic...

I am so G%$D%$@ tired of students being confused and asking questions that are solely the result of the apparent fact that their instructor is an idiot or too lazy to write comprehensible questions. This seems to be about 80% of the EE questions I see here. I think it's really unfair to confuse people that are new to a subject. They just don't have the background to question the quality of their course work; they think they don't understand, when, in fact, it's not understandable.

Sorry, I'm frustrated and needed to vent. Y'all can go back to this seemingly unending discussion about missing information.

Delta2
Delta2 said:
Ok but your solution attempt indicates that you are looking for the power loss in the secondary of the transformer.
That's what the answer key says the solution is, which I am trying to ask how they figured it out.

annamal said:
That's what the answer key says the solution is, which I am trying to ask how they figured it out.
I think we have consensus that the given solution is nonsense.

My best guess is that the problem statement was supposed to tell you that the resistance of the transmission line is 200 Ohms (as assumed in the solution to part d), and that that value should have been used in part c, not 6000 Ohms. 200 still seems a bit high to me, but 6000 for a transmission line is ridiculous.

This is the message I sent to OpenStax:
Message: I wish to draw your attention to some misinformation on your website at https://openstax.org/books/university-physics-volume-2/pages/15-6-transformers. Part c of the example 15.6, Step-Down Transformer, is nonsense.
The question is unanswerable with the given data because there is no way to determine the resistance of the transmission line. The 6000Ohms used in the solution appears to be the combined resistance of the transformer and the downstream load. (I believe typical transmission lines have resistances of a few tens of Ohms at most.)

annamal
haruspex said:
My best guess is that the problem statement was supposed to tell you that the resistance of the transmission line is 200 Ohms (as assumed in the solution to part d), and that that value should have been used in part c, not 6000 Ohms. 200 still seems a bit high to me, but 6000 for a transmission line is ridiculous.

The ohmic resistance of a transmission line is really hard to estimate and depends on many factors.
In this example, the input power of the transformer is ##12KV\cdot 2A=24KW ##. If the ohmic resistance of the transmission line is 6000 ohms, then its ##~2^2\cdot6000=24kW~##power loss is as high as the input power of the transformer. I don't think the power company will accept it.
Also, this question is really confusing. If you get a reply from OpenStax, please share the answer to this unsolved mystery.

OpenStax is riddled with errors like this.

vela and Delta2