Ohms Law and Its Practical Limits: Investigating a 10um Steel Wire

[Kholdstare]

Can anyone quote the exact statement given by Ohm with web reference. Just being curious.

Given a constant temperature current will be equal to voltage multiplied by resistance. - correct
Given a constant temperature current will be proportional to voltage. - wrong

 

[vk6kro]

Can anyone quote the exact statement given by Ohm with web reference. Just being curious.

Given a constant temperature current will be equal to voltage multiplied by resistance. - wrong
Given a constant temperature current will be proportional to voltage. - correct

The history of Ohm's Law is covered in the Wikipedia article:
http://en.wikipedia.org/wiki/Ohms_law

 

[sophiecentaur]

Can anyone quote the exact statement given by Ohm with web reference. Just being curious.

Given a constant temperature current will be equal to voltage multiplied by resistance. - correct
Given a constant temperature current will be proportional to voltage. - wrong

?
If you get your history right, you will realize that Ohm only introduced Resistance as the constant of proportionality for a linear relationshipbetween two quantities that he could actually MEASURE. They didn't sell Ohmmeters at the time!

 

[Nevertamed]

Can anyone quote the exact statement given by Ohm with web reference. Just being curious.

Given a constant temperature current will be equal to voltage multiplied by resistance. - correct
Given a constant temperature current will be proportional to voltage. - wrong

dude could u explain wtf are u talking about? under that condition voltage follows current proportionally: CORRECT

I= V R: WRONG

 

[Kholdstare]

?
If you get your history right, you will realize that Ohm only introduced Resistance as the constant of proportionality for a linear relationshipbetween two quantities that he could actually MEASURE. They didn't sell Ohmmeters at the time!

So Ohm did introduce resistance as a constant of proportionality. I think the statement of Ohm's law will be something very similar to this:
"Given a constant temperature current through a material will be proportional to the voltage drop across it (in steady state)."

Now, Ohm's law is indeed true if we do not take into consideration the quantum effects.
In fact if you are able to measure I-V curve for a long conductor with very high accuracy or say you measured it exactly, you will discover that the I-V curve is never linear. The variation in resistance is laughably tiny, but it exists and due to QM effects. In nano-scale structures the variation is tremendous. In those cases the resistance depends on the applied bias.

Now, as Ohm's law is only a model to predict the behavior of real materials (just like QM is a model to predict the behavior of electrons - we don't even understand what electrons actually are, only know their mass, charge, observables etc.), the idea that Ohm's law only predicts the behavior of ideal conductors is bogus. If it did that we won't be needing it cause there is no ideal conductor.

My conclusion is that when it comes to accuracy, the I-V relationship derived from QM beats Ohm's law (both in large and small materials) proving Ohm's law does have its limits.

 

[Kholdstare]

dude could u explain wtf are u talking about? under that condition voltage follows current proportionally: CORRECT

I= V R: WRONG

You got me wrong there. I said,

I = \frac{V}{R(V)}

But,

\frac{I_{2}}{I_{1}} \neq \frac{V_{2}}{V_{1}}

 

[vk6kro]

You actually said that

Given a constant temperature current will be equal to voltage multiplied by resistance. - correct

and this is totally wrong.

And this one is correct although you feel it is wrong:

Given a constant temperature current will be proportional to voltage. - wrong

This is a practical subject and nobody cares if a wire has a resistance of 100 ohms or 100.001 ohms.

 

[jim hardy]

i'm real simple. sometimes to the point it bothers folks, but here's my two cents:

an ohm is what a volt will push an amp through.
that's proportionality
and there's no temperature in that.

if some piece of real world conductor is one ohm at , say the ice point,
and you change its temperature
it won't be one ohm anymore
and a different voltage will be necessary to push one amp through it.
that's still proportionality.

don't complicate what is simple.

maybe you are confused by ohm's thermocouple source which is a strong function of temperature. that's part of the applied voltage, not the resistance.

keep the change --

old jim

 

[Kholdstare]

You actually said that

Given a constant temperature current will be equal to voltage multiplied by resistance. - correct

and this is totally wrong.

And this one is correct although you feel it is wrong:

Given a constant temperature current will be proportional to voltage. - wrong

This is a practical subject and nobody cares if a wire has a resistance of 100 ohms or 100.001 ohms.

@nevertamed - I'm very sorry that my first post had the mistake I = VR. What I actually meant is clarified in my third post.

@vk6kro - I was just saying that even in constant temperature QM effects will very the resistance depending on bias. Of course it is convenient to tolerate this variation and use Ohm's law in large conductors in practice. But that does not alter the fact that QM effect gives a more accurate description of I-V than Ohm's law does.

 

[Kholdstare]

i'm real simple. sometimes to the point it bothers folks, but here's my two cents:

an ohm is what a volt will push an amp through.
that's proportionality
and there's no temperature in that.

if some piece of real world conductor is one ohm at , say the ice point,
and you change its temperature
it won't be one ohm anymore
and a different voltage will be necessary to push one amp through it.
that's still proportionality.

don't complicate what is simple.

maybe you are confused by ohm's thermocouple source which is a strong function of temperature. that's part of the applied voltage, not the resistance.

keep the change --

old jim

Please refer to my earlier posts... I've always considered the temperature to be fixed.

 

[Kholdstare]

Finally I had found a Finnish teacher's lecture ppt
http://users.jyu.fi/~mmannine/BasicNanoSci/QTnanoIM1.pdf

Search "Ohm" in this pdf and you will learn about it.
The book mentioned in the third page even describes how you calculate I-V curve in nanomaterials.

You can read this book also. Its a very interesting book about nanotechnology.
http://books.google.co.in/books/about/Nanotechnology.html?id=m9Tn_V4an28C&redir_esc=y

 

[Kholdstare]

Finally I had found a Finnish teacher's lecture ppt
http://users.jyu.fi/~mmannine/BasicNanoSci/QTnanoIM1.pdf

Search "Ohm" in this pdf and you will learn about it.
The book mentioned in the third page even describes how you calculate I-V curve in nanomaterials.

You can read this book also. Its a very interesting book about nanotechnology.
http://books.google.co.in/books/about/Nanotechnology.html?id=m9Tn_V4an28C&redir_esc=y

 

[Nevertamed]

@nevertamed - I'm very sorry that my first post had the mistake I = VR. What I actually meant is clarified in my third post.

@vk6kro - I was just saying that even in constant temperature QM effects will very the resistance depending on bias. Of course it is convenient to tolerate this variation and use Ohm's law in large conductors in practice. But that does not alter the fact that QM effect gives a more accurate description of I-V than Ohm's law does.

its ok! =)

 

[sophiecentaur]

@nevertamed - I'm very sorry that my first post had the mistake I = VR. What I actually meant is clarified in my third post.

@vk6kro - I was just saying that even in constant temperature QM effects will very the resistance depending on bias. Of course it is convenient to tolerate this variation and use Ohm's law in large conductors in practice. But that does not alter the fact that QM effect gives a more accurate description of I-V than Ohm's law does.

Macroscopic or QM - it's all a matter of 'horses for courses'.
Whilst one might well use QM to design a circuit component, one would never design a whole circuit using more than Ohm's law.
I don't understand what people are wanting out of this thread. Do they want to prove it 'wrong' or something? It's no more than an equation that operates over the linear regime. The fab thing about metals is just how wide that regime happens to be. I think George did very well, all those years ago, to get it down on paper. Just think of the muddled thinking that used to be applied to Science in those days. (And, even today, on some of these threads!)

 

[Antiphon]

In its most general form, the Ohm has nothing to do with materials and everything to do with the scalar ratio of Electric to Magnetic fields over suitable line integrals.

The propagation of energy in free space takes place at 376.7 Ohms.

All material characterizations are specific cases of this general definition.

 

[Studiot]

In its most general form, the Ohm has nothing to do with materials and everything to do with the scalar ratio of Electric to Magnetic fields over suitable line integrals.

The propagation of energy in free space takes place at 376.7 Ohms.

All material characterizations are specific cases of this general definition.

My vote for the best answer so far.

 

[Averagesupernova]

I don't understand what people are wanting out of this thread. Do they want to prove it 'wrong' or something?

I have refrained from posting in this thread because I don't understand what people want out of it either.

 

[Kholdstare]

Macroscopic or QM - it's all a matter of 'horses for courses'.
Whilst one might well use QM to design a circuit component, one would never design a whole circuit using more than Ohm's law.

You're right!

I don't understand what people are wanting out of this thread. Do they want to prove it 'wrong' or something?

That's exactly what I'm trying to do.

It's no more than an equation that operates over the linear regime. The fab thing about metals is just how wide that regime happens to be.

Even in case of large materials QM description gives much better accuracy than Ohm's law.

I think George did very well, all those years ago, to get it down on paper. Just think of the muddled thinking that used to be applied to Science in those days. (And, even today, on some of these threads!)

I appreciate that he really did very well to propose the law at that time. But when a more accurate law comes out it replaces the old one. Just like general relativity replaced Newton's law of gravity.

Remember Ohm's law can be applied in some cases with approximate result. But when one asks about a limit of a law, one usually looks for a more accurate one and compares the previous one with the new one.

PS: I think you might be interest to know that Ohm actually did not published it. Maxwell did.

 

[jim hardy]

rigo.altervista.org/papers/engineering_procedure.pdf

 

[Kholdstare]

rigo.altervista.org/papers/engineering_procedure.pdf

Thank you very much sir for the sheer cheeks. I wonder why Monty Python did not do anything on that.

Well in reply I'll quote Richard Feynman.

Saying that you don't understand it. Meaning "I don't believe it, it's too crazy, it's the kind of thing I just ... I'm not going to accept."

Eh. The other part well... this kind, I hope you'll come along with me. "I don't have to accept it". Because it's the way nature works. If you want to know the way nature works, we looked at it, carefully, ... that's the way it works.

You don't like it..., go somewhere else!

To another universe! Where the rules are simpler, philosophically more pleasing, more psychologically easy. I can't help it! OK! If I'm going to tell you honestly what the world looks like to the... human beings who have struggled as hard as they can to understand it, I can only tell you what it looks like.

And I cannot make it any simpler, I'm not going to do this, I'm not going to simplify it, and I'm not going to fake it. I'm not going to tell you it's something like a ball bearing inside a spring, it isn't.

So I'm going to tell you what it really is like, and if you don't like it, that's too bad.

http://www.youtube.com/watch?v=iMDTcMD6pOw

 

[jim hardy]

and Francis Bacon :

Read not to contradict and confute, nor to believe and take for granted... but to weigh and consider.

 

[sophiecentaur]

Like the Curate's Egg, this thread has some very good parts in it. However, they are mixed with some naive and badly informed bits. As with many of the questions that get asked on these fora, there are several possible levels of treatment and this has surely led to some confusion here.
There is no essential contradiction in the Macroscopic and QM approaches but I think some of the contributors are glorying in the prospect of there being some conflict. A very counter - productive attitude.

 

[jim hardy]

there are several possible levels of treatment and this has surely led to some confusion here.

amen

when i re-read thread and realized "QM" effects was relating to nanostructures , well,
okay;
i don't deal with anything smaller than surface mount resistors.
QM is outside my experience.

consider another proportionality

Rate = Distance/Time

As a member of 'unwashed masses' i won't embrace QM unless it'll get me out of a speeding ticket.


-----------------

if i offended anyone please accept this apology.

 

[sophiecentaur]

i don't deal with anything smaller than surface mount resistors.
QM is outside my experience.

consider another proportionality

Rate = Distance/Time

As a member of 'unwashed masses' i won't embrace QM unless it'll get me out of a speeding ticket.
-----------------

if i offended anyone please accept this apology.

Amen to that. You are obviously a practical person and Ohm's Law is one of the best practical descriptions of a physical process in the book. It beats the 'SUVAT' equations of motion into a cocked hat for getting things right.

"Unwashed" is the way forward.

 

[Kholdstare]

there are several possible levels of treatment and this has surely led to some confusion here.

I'm sorry. But when someone asks me limit of something I usually look for the validity of that thing in more difficult levels where it might fail. If we only considered the easier levels we would not be looking for its 'limits'. Would we?

There is no essential contradiction in the Macroscopic and QM approaches but I think some of the contributors are glorying in the prospect of there being some conflict. A very counter - productive attitude.

There is contradiction. The application of macroscopic and QM approach on same structure gives different results.

PS: Rate = 1/Time and Velocity = Distance/Time

----------------

If I had been rude to anyone or offended anyone please accept my apology.

 

[sophiecentaur]

I guess you haven't read what's been written in the same way as I have read it.
I take your point about 'limits' but many of these posts are referring to a strictly practical case yet ignoring the fact that Ohm's Law specifies constant temperature. A hot wire does not 'disobey' Ohm's Law because its conditions are not those which are specified in the terms of Ohm's Law. Treating the Original Question in macroscopic terms is quite valid and some of the misconceptions, at that level, need to be sorted out first - before bringing in QM. (You clearly never had a problem at that level so you may not appreciate that some mere mortals actually struggle, even there.)
There is no question that QM and macroscopic treatments will give different answers for small numbers and the 'limits' are, of course, worth discussing. It is as well, however, to avoid confusion which can (and does) frequently occur when a thread continues on two levels with the two sets of contributors continually mis-interpreting the contributions of the other set.
I would challenge you to find a Classical Law that does anything like as well, in practical applications, over such a vast range as Ohm's Law manages to.

Incidentally, "rate" is frequently used in other contexts than 1/time. Take the financial interest 'rate' and the atmospheric temperature lapse 'rate', for instance.

 

[jim hardy]

might this QM effect be at all related to the observable physical phenomenon of "noise" generated by resistors? Carbon I'm told is worst and wirewound the best..

 

[sophiecentaur]

might this QM effect be at all related to the observable physical phenomenon of "noise" generated by resistors? Carbon I'm told is worst and wirewound the best..

Well. Carbon is not a metal so it can't be expected to follow Ohm's Law!
In a metal resistor, the noise is largely due to the distribution of KE amongst the electrons, I think, giving a varying value of thermally generated volts. The thermal noise power is kT.