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Non ohmic conductors are said to be the conductors that do not obey Ohm's Law. The V-I graph for them is not a straight line unlike ideal ohmic conductors.

According to me Ohm's Law states: The voltage across a conductor is directly proportional to the current in it given that other factors such as temperature remain constant. ie.

$$R=V/I$$

I have also read that change in temperature due to heat dissipated is also a reason for varying V/I values for non ohmic conductors. My question is that,given this, how can we say that a conductor doesn't obey Ohm's law. Shouldn't everything be having a constant voltage to current ratio at a given point in time (or an infinitesimal time interval). Similarly shouldn't the resistance be then defined to be the derivative of voltage with respect to current?

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  • $\begingroup$ There are devices that have two different operating regions such that a given voltage applied may lead to several different possible currents - I(V) is not a single valued function. $\endgroup$ – Jon Custer Jan 16 at 17:29
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My question is that,given this, how can we say that a conductor doesn't obey Ohm's law.

For an example of how, consider a conductor with a voltage dependent resistance, e.g., a varistor

Similarly shouldn't the resistance be then defined to be the derivative of voltage with respect to current?

The derivative $\frac{dV}{dI}$ is called the differential or dynamic or small signal resistance as opposed to the static resistance $\frac{V}{I}$. For an ohmic device, these two resistance measures are equal.

See, for example, this section of the Wikipedia article Electrical resistance and conductance:

enter image description here

The IV curve of a non-ohmic device (purple). The static resistance at point A is the inverse slope of line B through the origin. The differential resistance at A is the inverse slope of tangent line C.

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"Shouldn't everything be having a constant voltage to current ratio at a given point in time [... ?]"

That's not what we mean by $\frac{V}{I}$ = constant. What we do mean is that even when we change $V,$ we find that $I$ changes in such a way that the ratio $\frac{V}{I}$ stays the same. And if we find that the ratio really does stay the same, we say that the conductor is Ohmic.

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If voltage and current are proportional at constant temperature then the conductor is ohmic, else it is non ohmic.

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