Dave,

Quote:
Originally Posted by Ratch
Indeed that is true, and it should be straightforward. I never said otherwise. That does not differ from Ohm's law as I quoted from the two textbooks cited previously: The resistance of metallic conductor is the same no matter what applied voltage is used to measure it.

The two statements are different, even if the differences are subtle. Ohms Law is stated in Georg Ohm's own words, not an interpretation of Ohm's words like the textbooks you cite. If you read the above, Ohm's Law is merely a statement of proportionality derived through empirical studies.

It appears to me to be a distinction without a difference. I agreed before that Ohm's law is a statement about proportionality, specifically linear proportionality. That does not make it a definition of resistance.

Quote:
Originally Posted by Ratch
The textbook goes on to say that if the resistance is not linear, then it does not follow Ohm's law. Yet most people want to tie the definition of resistance to a material property. That is wrong, not because of any semantic differences, but because it is a misnomer. Will you come out and say that the professors who wrote those textbooks are wrong? Can you find a good college level physics textbook that says uneqivocally that Ohm's law is V=IE?

I will say it again, in Georg Ohm's own words, Ohm's Law is a statement of proportionality. With that in mind, take a diode which has a non-linear I-V characteristic across a wide voltage range and hence in your world never meets the conditions of Ohms Law (whatever definition you wish to apply); however the diode is locally ohmic, that is over a very small change in applied voltage the current is (effectively) directly proportional to this voltage - and at a fixed applied voltage, in the absence of other extenuating factors as outlined by Ohm, the steady current definition applies and the diode has a resistance that is defined by R = V/I. It is said to be locally ohmic because the I-V characteristic satisfies Ohms' statement of proportionality.

R=V/I will always be correct anywhere on the diode V-I curve, because that is the definition of resistance. Three or more points are needed to determine linearity, and compliance with Ohm's law.

Ratch

 

It appears to me to be a distinction without a difference. I agreed before that Ohm's law is a statement about proportionality, specifically linear proportionality. That does not make it a definition of resistance.

No re-read the two definitions:

Georg Ohm's Definition: The amount of steady current through a material is directly proportional to the potential difference, or voltage, across the material, for some fixed temperature.

Ratch's Definition: The resistance of metallic conductor is the same no matter what applied voltage is used to measure it.

Ohm's definition is that of proportionality resulting in steady current and therefore can be applied, both locally and where applicable globally, to any conducting materials. Your definition is merely a sub-set where there are the conditions of any voltage resulting the same resistance, i.e. the material must be linear both locally and globally.

Not the same thing. Now who do I believe? Georg Ohm who formulated Ohms Law, or Ratch who trolls AAC looking for an argument?

R=V/I will always be correct anywhere on the diode V-I curve, because that is the definition of resistance. Three or more points are needed to determine linearity, and compliance with Ohm's law.

Ratch

No. Ohms Law says nothing more than for a given material at a given temperature that the steady current is proportional to the applied voltage. The resistance is a function of several parameters, material properties (resistivity), length, cross-sectional area, junction temperature; in other words the definition of resistance:

\(R = \frac{\rho L}{A}.\alpha\left(T - T_{0} + 1\right)\)

However that is not what Ohms Law is. I have said this to you previously, and I note that you took no notice whatsoever, that there is no mention in Ohms Law of the requirement for the resistance to remain constant across an I-V characteristic, just that there is proportionality between I and V for steady I; electrically that can be defined as the reciprocal of a "variable", where this "variable" - the material variable - is defined by other constructs. And it is only by investigating various material properties did he come to a law for steady current; a law that is Ohms Law.

I suggest you get his paper and read exactly what Ohm said. Until you are prepared to do this, then this discussion is going nowhere. This thread is closed, and if you are not happy with this then I suggest you ply your trade elsewhere - we are not here to micro-moderate you.

Dave