What Are the Pros and Cons of Different Statements of Ohm's Law?

[Philip Wood]

(a) The current through a conductor is proportional to the pd across it.

(b) Provided the temperature is kept constant the current through a conductor is proportional to the pd across it.

(c) Provided the temperature is kept constant the current through a metal conductor is proportional to the pd across it.

Each has its pros and cons. For example, (a) is a law more honour’d in the breach than the observance.

I'd be interested in opinions.

EDIT: I know what the Physics is. I'd like to know what people think is included in the statement of the law.

 

[phinds]

(a) The current through a conductor is proportional to the pd across it.

(b) Provided the temperature is kept constant the current through a conductor is proportional to the pd across it.

(c) Provided the temperature is kept constant the current through a metal conductor is proportional to the pd across it.

Each has its pros and cons. For example, (a) is a law more honour’d in the breach than the observance.

I'd be interested in opinions.

Why do you think that varying the resistance would somehow invalidate Ohm's Law or make it need refinement? Whatever you do to an element, it has some resistance. You CAN vary that resistance by changing the temperature and how much it changes will depend on the temperature change and the specific material, but so what? At any given point in time it will have a particular value of resistance and the current through it will be correctly calculated by Ohms Law, knowing what that resistance is and what the voltage across it is.

 

[Philip Wood]

phinds. Thank you, but I'm at a loss to understand your post unless – and I find it hard to believe – you believe that Ohm's law is merely the equation $V=IR$ with no restriction on R. Please give your own statement of Ohm's law.

 

[rumborak]

Philip Wood, I think the question here is why you would think a change in temperature would invalidate Ohm's Law.

 

[Philip Wood]

Rumborak. No, but thank you for the reply. I simply want to know what you think Ohm's law is. I've given three popular versions, but I'm sure there are others.

 

[phinds]

I'm an engineer. I think Ohms Law is V=IR. And you have not answered my question. Why do you think that varying the resistance would somehow invalidate Ohm's Law or make it need refinement?

EDIT: In other words, in case I'm not PERFECTLY clear, I think your statements b) and c) above are a waste of words and add nothing at all to a perfectly understandable, simple, law. V=IR.

 

[Vanadium 50]

Ohm's Law is a statement about ideal resistors (one can argue that it defines an ideal resistor). You can talk about physical resistors and temperature dependances if you like, but that won't make any difference with respect to Ohm's Law.

 

[Philip Wood]

phinds. I'm a physicist. I distinguish between (a) $V=IR$ or $R=\frac{V}{I}$ used as an equation defining resistance and holding whether or not R is a constant, and so not telling us anything about the way anything behaves, and (b) Ohm's law, which says that [in some circumstances], R (defined by $R=\frac{V}{I}$) is a constant. (b) does make a testable claim about nature.

 

[CWatters]

Does it need amending to include constant pressure?

The Electrical Resistance of Metals under Pressure
P. W. Bridgman 1917
http://www.jstor.org/stable/20025699?seq=22#page_scan_tab_contents

 

[phinds]

phinds. I'm a physicist. I distinguish between (a) $V=IR$ or $R=\frac{V}{I}$ used as an equation defining resistance and holding whether or not R is a constant, and so not telling us anything about the way anything behaves, and (b) Ohm's law, which says that [in some circumstances], R (defined by $R=\frac{V}{I}$) is a constant. (b) does make a testable claim about nature.

The bottom line is VERY simple. Do you or do you not contend that at ANY point in time a passive circuit element will have a voltage, current, and resistance that do NOT conform to V=IR ? If so, then please explain. If not, then this is all a waste of time.

 

[CWatters]

I'm with you phinds. Keep it simple.

 

[Philip Wood]

phinds. I don't so contend. $V=IR$ is true by definition of R.

I just wanted the good citizens of Physics forum to give me their statements of Ohm's law. I take it that yours is $V=IR$ with no stuff involving constancy of R.

No one else has given their statement.

CWatters. Thanks for the Bridgman reference. And I'm all for keeping things simple. Who was it who said, "Everything should be kept as simple as possible, but no simpler."

 

[phinds]

I'm perfectly happy with "stuff involving the constancy of R". Any function of time that describes a changing R, R=f(t) can be put into V=If(t). This is still Ohm's Law because at every instant of time, it reduces to V=IR.

 

[rumborak]

I find it particularly confusing that you would point out things that truly have no influence on the validity of the law itself, but not mention the onbes that *do* break it. Neither temperature nor it being a metal/nonmetal breaks it.
I could imagine the modifier "for small V&I combinations" since with too high current it will likely become nonlinear, similar to how Hooke's law is only valid in the realm of plastic deformations.

 

[phinds]

I find it particularly confusing that you would point out things that truly have no influence on the validity of the law itself, but not mention the onbes that *do* break it. Neither temperature nor it being a metal/nonmetal breaks it.
I could imagine the modifier "for small V&I combinations" since with too high current it will likely become nonlinear, similar to how Hooke's law is only valid in the realm of plastic deformations.

Good point. I guess if you could get the current low enough it would become somewhat like counting electrons and Ohm's Law is a macro level law.

 

[Philip Wood]

All I asked for was your (that is any Forum member's) preferred statement of the law… You may not like any of the ones I offered initially (I've seen them all in books or online). That's fine, but could you please give YOUR statement. I simply want to know. I have no wish to stir up controversy.

 

[phinds]

All I asked for was your (that is any Forum member's) preferred statement of the law… You may not like any of the ones I offered initially (I've seen them all in books or online). That's fine, but could you please give YOUR statement. I simply want to know. I have no wish to stir up controversy.

Uh ... what do you think we have BEEN doing? As far as I can see, every responder sees Ohm's Law as V=IR. End of story.

 

[rumborak]

V=IR.

EDIT: Actually: U=IR. I'm from Germany. Voltage is "U" for us :D

 

[phinds]

V=IR.

EDIT: Actually: U=IR. I'm from Germany. Voltage is "U" for us :D

Wait, what? You call Alexander Volta "Uolta" I would have expected it to be "Wolta"

 

[rumborak]

Haha. I have absolutely no idea why they settled on U. One thing of course it's that we don't make reference to Volta at all, as "voltage" is "Spannung" in German ("tension"). Just like English also uses the more colloquial term "current" instead of "ampere-age" or something.

 

[berkeman]

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