# Non-ohmic conductors

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?

• 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. – Jon Custer Jan 16 '19 at 17:29

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: 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.

"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.

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