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Ohm's law state that the ratio of V and I gives us a constant value of R provided that the temperature is kept constant throughout. However, in accordance with the joule's heating it would get heated by Isquare. R. So, even if the I and V remains in a linear slope of the graph, should it be rendered as ohms law since that requires temperature to be constant.

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Ohm's law doesn't say anything about temperature. Ohm's law is analogous to Hooke's law in the sense that it is an idealization. Hooke's law idealizes a spring (or "spring-like" system) by assuming that the restoring force always is proportional to the displacement from equilibrium. Ohm's law idealizes resistors by assuming that the current through the resistor is always proportional to the voltage across the resistor.

Of course in the real world the heating of resistors can change their resistance, so we would say in those scenarios Ohm's law is no longer valid. This is analogous to "springs" that do not exactly follow a quadratic potential energy function, or perhaps even for springs that undergo deformation; we would say Hooke's law is no longer valid.

The above laws aren't laws in the same sense as say Newton's laws. They are better understood as idealizations.

So, even if the I and V remains in a linear slope of the graph, should it be rendered as ohms law...

Yes, I would say so.

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  • $\begingroup$ As you said that ohm law only idealizes resistors by assuming that the current through is always proportional to voltage, then should the concept of ohmic metals exist? $\endgroup$
    – Abdullah
    Sep 11 '20 at 16:56
  • $\begingroup$ @Abdullah Yes, "Ohmic resistors", just like "Hookean springs". $\endgroup$ Sep 11 '20 at 17:01
  • $\begingroup$ Just to clarify, are you saying that if the resistance changes (considerably) with temperature, then Ohm’s law is not satisfied? $\endgroup$
    – alejnavab
    Nov 5 '21 at 15:36
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    $\begingroup$ @AlejandroNava Technically if the resistance changes at all for any reason then Ohm's law is not satisfied. $\endgroup$ Nov 5 '21 at 15:38
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The real "Ohms law" just defines what resistance is. $$R=\frac{U}{I}$$ and for real objects R can increase , decrease or stay constant when I,U or T changes, thats why you get a characteristic curve for resistors, or you buy one whose R is constant over a certain range you need. Usually in school, Ohms law is U=R*I, since you don't vary U or I over a wide range.

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    $\begingroup$ Ohm's law doesn't define resistance. Resistance exists outside of Ohm's law $\endgroup$ Sep 11 '20 at 16:21
  • $\begingroup$ Sure, resistance exists, but how exactly it is defined depends on definition , Resistance would exist also, if it was defined as 10U/I $\endgroup$
    – trula
    Sep 11 '20 at 20:52
  • $\begingroup$ Ok, but Ohm's law doesn't define resistance. Ohm's law assumes that resistance is constant. More generally is assumes that the current density is proportional to the applied electric field. You can give resistance values that change for non-Ohmic devices. $\endgroup$ Sep 11 '20 at 22:30
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    $\begingroup$ I looked it up in wikipedia, so you are right, but it still is true that R is defined as U/I. and if R = const, the resistor or its material is called a ohmic $\endgroup$
    – trula
    Sep 12 '20 at 15:36

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