# MWBC= more heat or Less heat?

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#### mivey

##### Senior Member
...Please, PLEASE show me one example in all of these posts where I have made such an argument...
fair question
You, sir, are a cur.
Stop that. Criticize what was said, not the one who said it.

#### david luchini

##### Moderator
Staff member
Originally Posted by mivey
But my point was that Ohm's Law could not be used to say that there will be zero current on the closed superconductor loop.

??????????
Mivey, I enjoy the zeal that you put into your posts, as evidenced your use of smilies. I think "confused" is good here, because it would appear that we are confusing each other. Let me try explain from top to bottom, as I must not be making myself clear. Crossman gary described (in post 167) a circuit made from a closed loop of zero resistance wire, with no potential source applied. He then made the argument that Ohm's law fails to predict that there is zero current flowing in the loop because I=V/R ---> I=0/0 which is indeterminable. Thus, your statement and his statement followed that ohm's law could not be used to say that there will be zero current...

But by saying "Ohm's law fails here," Gary was TRYING to apply Ohm's law for the circuit he described. He went through the "logical" exercise of figuring Ohm's Law says I=V/R, V=R=0, so Ohm's law can't tell us what the current flow in the circuit is because 0/0 is indeterminable.

In post 270, you said "I don't recall CG having stated there was no current." He may not have said those words, but he said that in his circuit description. A closed loop of wire - no resistance - no voltage source included. How could there be current flowing in the loop? So known conditions for Gary's circuit are Zero Volts, Zero Ohms and Zero Amps. Why would I want to try to figure I=V/R when I already know 0=0/0?

If he had applied a source to get start the current flowing, shorted the source out and then removed the source such that current continued flowing through the loop, then it would be a fair point to say that Ohm's law could not be used to determine the current in the loop. But clearly, this was not the case as he laid out his circuit example in post 167.

I think part of the problem is the way these posts continue on, some "quoting" earlier posts. It is very easy to lose sight of the paramaters of the complete circuit as originally defined, which is why I think we have been confusing each other on this matter. Anyway, I hope this has cleared up my view on this thread. For known values of V=0, R=0 and I=0, it is pointless to apply Ohm's Law.

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#### mivey

##### Senior Member
For known values of V=0, R=0 and I=0, it is pointless to apply Ohm's Law.
Agreed. There would be zero value in that.:grin:

#### crossman gary

##### Senior Member
Didn't have time today to post anything, and don't have time now, but let me jump in real quick concerning the last couple of paragraphs of David's last post.

Scenario 1:

You enter a laboratory and see a 2 ohm resistor. There is a 12 volt ideal voltage source connected directly to the resistor. We wish to determine the current flowing in the loop at some precise time. We have no knowledge of the past history of the resistor.

Logically, one of the following conditions must exist:

1. No current flows in the loop
2. A finite amount of current flows in the loop
3. An infinite amount of current flows in the loop.

We use the Ohm's Law formula E = I x R and algebra to determine that the current flow is 6 amps. We take an ammeter and confirm the prediction of the formula, 6 amps. Condition #2 is true, #1 and #3 are false.

Ohm's Law was used to narrow down the three possibilities, even to the point of quantifying the current flow. Ohm's Law was a valid tool to answer our question of current flow.

Scenario 2

You enter a laboratory and see a loop of zero impedance superconductor. There is no voltage source connected. We wish to determine the current flowing in the loop at some precise moment. You have no knowledge of the past history of the loop. (note: Winnie has already described the superconductor magnets in particle accelerators where current flows even after the voltage source is removed. Therefore, do not assume 0 current flow.)

Logically, one of the three possibilities must exist:

1. No current flows in the loop
2. A finite amount of current flows in the loop
3. An infinite amount of current flows in the loop.

We use Ohm's Law formula E = I x R. 0 = I x 0. Ohm's Law says the current flow is undefined because any number inserted at I satisfies the equation. Ohm's Law says the current can be anything from zero to infinity.

While this is true, logic dictates that one and only one of the three possibilities can be happening for that particular loop of conductor at the mentioned moment. Ohm's Law could not narrow down which of the three is occurring.

Therefore, Ohm's Law is not a valid tool to determine which of the three possibilities is occurring in the conductor at the precise moment. With a suitable and ideal ammeter, we could certainly and simply take the current measurement and say without doubt that "X" amount of current is flowing at the precise moment. Ohm's Law cannot do that.

Scoreboard:

Ammeter = 1
Ohm's Law = 0

------> Okay, some will say that "oh, this is not a failure of ohm's law, this is a failure of the components."

That is just wrong. If we assume that a zero impedance superconductor exists, which we did in the scenario, then how can the failure be in the component? And "the component failed to perform to the standards of ohm's law" is equivalent to saying "ohm's law failed to predict the circumstance of the component."

-----> And, some of you will say "Ohm's Law did exactly what it is supposed to do. The current can be anywhere between 0 and infinity."

Well... I walked up to the loop with the ammeter and directly measured the current. With the meter, I can narrow down to one of the three possibilities and even go as far as telling you what the exact current is. Ohm's Law couldn't. So you still are saying Ohm's Law is a valid tool for determining the current in Scenario 2??? Well, in any engineering calculations, I am pretty darned sure that an answer of "it can be anywhere between 0 and infinity" ain't going to cut it.

Junior engineer: "Well, the formula said anything between zero and infinity."

Lead engineer: "Woah, we are going to need a pretty darned big beam to meet the safety factor."

Edit twice: added winnie's info about superconducting magnets and current flow under zero applied voltage.

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#### crossman gary

##### Senior Member
Mivey said: "But my point was that Ohm's Law could not be used to say that there will be zero current on the closed superconductor loop."

Crossman said: "errrr.... that was MY point!!"

David said: "Let me jump in, because I think you are missing the bus here. You are trying to use Ohm's Law to demonstrate the value of current that will be flowing in a passive circuit..."

Mivey said: "But my point was that Ohm's Law could not be used to say that there will be zero current on the closed superconductor loop."

Hmmmm.... in other words, David is saying that Ohm's Law fails when applied to a passive loop?

:wink:

#### SAC

##### Senior Member
I think this is getting "just a bit" out of hand. Please consider two things:

1. Circuit theory is not a math field (if your looking for a good one, try Fourier transforms) - its purpose is to predict real world circuit behavior. If it doesn't, it isn't being used appropriately.

2. The corresponding circuit theory element for a superconductor is NOT a zero ohm resistor! (the "real world" just isn't that simple)

I'd either suggest giving up on the "zero-ohm" circuit theory discussions, as in the present forms they are simply not appropriate, or go and re-read your E&M field theory and then actually learn how a superconductor behaves, and then resume discussions. For starters, look at this abstract that gives a high level description of a circuit model of a superconductor to prepare you for what to expect:

http://ieeexplore.ieee.org/Xplore/l...211979.pdf?arnumber=1211979&authDecision=-203

"The model is based on Maxwell's equations, measurement results as well as on the physical structure of a superconducting tape. The incorporated circuit elements have been described in mathematical expressions: a nonlinear resistance and a nonlinear inductance (superconducting core) in parallel with a linear resistance and a linear inductance (silver sheath or by-pass material)."

Unfortunately, I must say that I'm just a little bit disturbed this discussion has gone on here like this for so long...

#### crossman gary

##### Senior Member
I'd either suggest giving up on the "zero-ohm" circuit theory discussions, as in the present forms they are simply not appropriate,
Thanks for the input. I'm just wondering whether ohm's law is valid for theoretical zero resistance conductors and superconductors. These are certainly valid questions, and non-disturbing questions at that.

There are many cases in Physics where a classical law fails under extreme conditions. To question when and where a "law" is appropriate seems, well, appropriate.

Question 1: Does ohm's law accurately predict current flow in a theoretical zero ohm conductor? (a "yes" or "no" answer would be fine, but if you need to elaborate, please feel free)

Question 2: Does ohm's law accurately predict current flow in a superconductor? (same as above on the "yes" or "no")

Unfortunately, I must say that I'm just a little bit disturbed this discussion has gone on here like this for so long...
It can be said that a wise man has a moral obligation to enlighten those of his brethren who are less enlightened, yet are thirsty for knowledge. This thread could have been cleared up a long time ago if said wise man had stepped in with clear explanations.

#### SAC

##### Senior Member
Thanks for the input. I'm just wondering whether ohm's law is valid for theoretical zero resistance conductors and superconductors. These are certainly valid questions, and non-disturbing questions at that.
Absolutely - it's that this has gone 300+ posts that is disturbing (the "for this long" part).

Question 1: Does ohm's law accurately predict current flow in a theoretical zero ohm conductor? (a "yes" or "no" answer would be fine, but if you need to elaborate, please feel free)
No. Circuit theory isn't a theoretical math system - rather it is a method of applying well known mathematical methods to circuit models to predict the behavior of electrical systems. It is a high level approximation of electromagnetic field theory used to make the analysis of electrical circuits a tractable problem. There is no such thing as a "zero ohm conductor" in the sense that it being used here. The closest thing - superconductors - are not able to be accurately modeled as a "zero ohm" resistor, as their models are much more complex.

I find that using the phrases "accurately predict" and "theoretical zero ohm conductor" make a strange question. Are you questioning the accuracy of the mathematical methods (which are theoretically infinitely accurate)? Math is definitely "accurate" when describing something that only exists within the theoretical realm - it is when using mathematical methods to describe "real" systems that there is inaccuracy. Hence part of the issue I have with the ongoing discussion of "zero ohm" resistances - they don't exist in the "real world" and fall outside of what circuit theory is applicable to.

I agree that there are many places where resistances are small in a relative sense such that they can be considered to be "zero" and not adversely affect the calculations of interest. However, when the dominating circuit elements of the model being analyzed have a "zero" resistance, circuit theory breaks down as there isn't any such "real world" system that can be described such a model.

Question 2: Does ohm's law accurately predict current flow in a superconductor? (same as above on the "yes" or "no")
I'll take your reference to "Ohm's law" to mean "circuit theory" in general (otherwise I'd say, no - as "Ohm's law" doesn't contemplate non-linear effects"), and say "maybe". I'm not a superconductor expert so I can't really make any statement on the accuracy of available circuit models with respect to superconductors. My guess based on what I have seen is that, like other non-linear devices, there are circuit models for superconductors that are accurate enough to be useful given restricted ranges of operating conditions.

#### mivey

##### Senior Member
I think this is getting "just a bit" out of hand. Please consider two things:

1. Circuit theory is not a math field (if your looking for a good one, try Fourier transforms) - its purpose is to predict real world circuit behavior. If it doesn't, it isn't being used appropriately.
Like I said, if the model fails, make one that works.
2. The corresponding circuit theory element for a superconductor is NOT a zero ohm resistor! (the "real world" just isn't that simple)...I'd either suggest giving up on the "zero-ohm" circuit theory discussions, as in the present forms they are simply not appropriate, or go and re-read your E&M field theory and then actually learn how a superconductor behaves, and then resume discussions...
What value will that bring to the current discussion? IMO, a zero ohm resistor works fine for what we are discussing. I fail to see why you think it is an inappropriate model given the current scope.
Unfortunately, I must say that I'm just a little bit disturbed this discussion has gone on here like this for so long...
Are you disturbed by the posters taking so long to finish their discussion or are you disturbed because we are not using some non-relevant (IMO for the moment) superconductor model? I don't see how the complex superconductor model will simplify our discussion.

Perhaps you can elaborate some more on your points as I did not quite follow where you were going and why you were so disturbed.

#### mivey

##### Senior Member
Absolutely - it's that this has gone 300+ posts that is disturbing (the "for this long" part).
It is a long thread but imagine if you were sitting around with your colleagues just talking over some things, it would not really be that long. Most topics are straight to the point "how many X's are needed to do y". Some are more thought provoking and lead to longer discussions. Probably equivalent to sitting around the grill talking about non-billable stuff while the burgers are cooking.
...The closest thing - superconductors - are not able to be accurately modeled as a "zero ohm" resistor, as their models are much more complex.
A simple representation of a superconductor consists of a normal resistor with normal electrons in parallel with a zero ohm resistor with superconducting electrons which appear when you reach the critical temperature. It does not address the finer points of superconductors like current limits, reactions to magnetic fields, etc., but certainly covers our simple discussion.
I'll take your reference to "Ohm's law" to mean "circuit theory" in general (otherwise I'd say, no - as "Ohm's law" doesn't contemplate non-linear effects"), and say "maybe".
I would say no.

#### crossman gary

##### Senior Member
it's that this has gone 300+ posts that is disturbing (the "for this long" part).
Perhaps we are in dire need of a wise man?

RE: Question 1

Thank you for the direct answer. This has been my claim all along.

Hence part of the issue I have with the ongoing discussion of "zero ohm" resistances - they don't exist in the "real world" and fall outside of what circuit theory is applicable to.
"and fall outside of what circuit theory is applicable to"

This merits further examination. Is it prima facie that circuit theory applies only to real world examples? Does circuit theory, by definition, automatically not apply to theoretical examples? These are valid questions. Did those who discovered the theories purposely tailor the theories so they did not apply to theoretical examples? It is my opinion that whether or not the theory applies is something that needs to examined and discovered through example and examination.

However, when the dominating circuit elements of the model being analyzed have a "zero" resistance, circuit theory breaks down as there isn't any such "real world" system that can be described such a model.
I agree completely. However, is it so obvious to render discussion of the topic moot? Again, how would one know that the theory breaks down unless one were to examine the theories being applied to the examples? Is it totally obvious where the theories work and where they don't? I don't think so. Further examination is warranted by anyone striving to know the answer to the question.

I'll take your reference to "Ohm's law" to mean "circuit theory" in general
I was specifically referring to Ohm's Law.

(otherwise I'd say, no - as "Ohm's law" doesn't contemplate non-linear effects")[/QUOTE]

There ya go! As you mentioned previously, there are quantum effects and other unfamiliarities that are not accounted for by Ohm's Law as applied to superconductors.

#### mivey

##### Senior Member
090715-0921 EST

An interesting article:
"The IRE Student Quarterly", Sept 1954
"125 Years of Ohm's Law", by Henry Berring.

The Google result from --- 125 years of ohm's law berring --- is:
http://ieeexplore.ieee.org/Xplore/d...on=-134&arnumber=4321401&productsMatched=null
I do not have access to this and thus I do not know its content.

.
From the document: Ohm's Law= The current through a conductor is proportional to the voltage applied across it : I = V/R

R was initially "reduced length" but he soon changed it to resistance.

Ohm identified V with a potential difference and recognized a potential gradient in the conductor. His first work on conduction was published in 1825 (he was 36) and he had formulated Ohm's Law by 1826.

The paper discusses some of the early experiments where he measured the magnetic force variances in different wires across a wet cell using a magnetic needle. He noted the change in the "loss of force" as the wire length changed. That is, Delta I = (Is-Iw)/Is where Is is a standard wire and Iw is an experimental wire. For a voltage with an internal resistance, (Is-Iw)/Is = (Rw- Rs)/ (Ri + Rw) where Ri is the internal resistance.

The "loss of force" has been interpreted by others as potential drop, current, and change in current. This normalization method removed the effect of the voltage.

In further experiments, he let the torsion become the dependent variable and found that current was dependent on the voltage and the resistance. These experiments led to the formula Iw = E / (Ri + Rw) where Iw is the current in the wire and Ri is the internal resistance and Rw is the wire resistance.

In his book, he stated that the amount of electricity transferred from one point to the next is dependent on the difference in potential between them. He calculated the currents based on the piecewise linear potential distribution through the circuit. He found the magnitude of the current varied directly as the sum of the tensions (potentials) and inversely as the length of the whole circuit.

The text discusses some prior works by others, early contributions that were a foundation for Ohm, the initial rejection of his work, modifications & extensions to the law for wider applications, etc.

It was noted that Ohm used the idea of excitation force as what made charges available at the terminals of an open battery. Once a conductor was connected, the battery "tension" was said to have vanished.