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Just wanted to confirm if the statement is always true or not

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I'm going to somewhat contradict the other answers. They are right in saying that $V=IR$ is only true for certain materials where $R$ is constant.

However, your wording is about asking if "this defines resistance", so you would then want to have the equation $$R=\frac VI$$

and in this case you can say this "always holds" if this is what you define resistance to be. Then you can have materials where the ratio between the applied voltage and resulting current is not constant, but you can still apply your definition of resistance by calculating $V/I$ and seeing that it does not remain constant.$^*$

It is for this reason that the undergraduate lab director at my university says that $R=V/I$ should be the definition of resistance, and that actually Ohm's law is given by $\mathbf J=\sigma\mathbf E$ for a constant $\sigma$ which then leads to $V=IR$ for a constant $R$.


$^*$ For example for a diode that only allows current flow in one direction, yet exhibits ohmic behavior when current flows in the other direction, you would say that $R=\infty$ (poor math talk) when $V<0$ (trying to push current in the wrong direction) and $R=V/I$ when $V>0$ (trying to push current the right way).

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    $\begingroup$ I agree. For a diode in the forward direction, there is also the differential resistance, which is about $r \approx 25/I \ \Omega$ where the current is in mA. physics.stackexchange.com/questions/387030/… $\endgroup$ – Pieter Mar 7 '19 at 7:29
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    $\begingroup$ With this definition $ P=VI = I^2R$ still holds so I agree. $\endgroup$ – my2cts Mar 7 '19 at 9:12
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    $\begingroup$ +1 for "poor math talk" ... and for a good answer. $\endgroup$ – Steeven Mar 7 '19 at 11:54
  • $\begingroup$ I am not sure it is always possible to define R as V/I. Take the example of a non-homogeneous doped semiconductor and consider the generalized Ohm's law $\vec J = -\sigma \nabla V - \sigma S \nabla T$. There will be (in addition to the Seebeck effect), a non-homogeneous Thomson heating across the resistor, as well as (possibly) a Peltier effect at the ends of the material. I think this can lead to two different values for R, if R is defined as V/I, according to the direction of the current. Am I missing something? $\endgroup$ – thermomagnetic condensed boson Mar 7 '19 at 12:03
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    $\begingroup$ Thank you! I wish they've phrased the question as "does R=V/I define the resistance for any conductor" so that students like me wouldn't fall into the bait of nonohmic resistors $\endgroup$ – Beyza Yıldırım Mar 16 '19 at 21:16
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This equation is obeyed by the ohmic devices. There are objects (diodes,LED) which doesn't follow Ohm's law ($V=IR$). Such devices are called Non Ohmic devices. Eventhough they don't follow Ohms law they do have effective resistance, not defined as $V=IR$. The difference between Ohmic and non Ohmic devices are shown in the link. https://electronics.stackexchange.com/questions/236990/what-is-the-difference-between-ohmic-and-non-ohmic-devices

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The equation/formula $V=IR$ is named the ohm's law. The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827. Any conductor that has current passing through has some degree of resistance, and as long as you can quantify how much resistance, you can apply ohm's law.

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For the purposes of a linear (ideal) approximation, V=IR is the standard rule and applies not only to electrical circuits but also to mechanisms and hydraulic systems.

As such, it is the default model for what are called ohmic systems- where effort losses are linearly proportional to flow variables.

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This law is also not true for when you're dealing with EMI. Potential difference will be zero across a circuit yet a current will flow. Rather use current density = conductivity * Electric field. (This is the original ohm's law from which V= IR is derived . Just substitute J = i/A and E = V/l , you'll see)

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  • $\begingroup$ What is / are EMI? And isn't simply R=0 in this case? $\endgroup$ – my2cts Mar 7 '19 at 9:05
  • $\begingroup$ EMI - Electromagnetic Induction ; R = resistivity*(length/area). Putting resistivity = 1/conductivity in the above formula, you'll derive Ohm's law. $\endgroup$ – Ishan Jawale Mar 8 '19 at 15:35

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