Characteristic functions of a non-ohmic material We know that Ohm's laws are experimental laws. Ohm's first law for ohmic materials follows a linear approximate progression of the kind:
$$\frac{\Delta V}{I}=R$$

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*What are the functions of type $$\Delta V(I)=f(I)$$ that are characteristics of non-ohmic materials?

*Are there any known functions for non-ohmic materials and how are they written?

In other words, for tungsten is there an analytical expression that you can study or you need to make an experiment in the laboratory and to plot the characteristic curve that best approximates the experimental points: polynomial, exponential, logarithmic $\ldots$?
For example I add this image:

where the word "pendenza=slope". It is easy that I have a function $\Delta V(I)=RI$, or straight lines that across the origin of the axes. In good approximation, ohmic materials are straight lines across the origin of the axes.
If I have this picture

semiconductor device where the curve is not linear, how do I find the equation associated with it?
 A: Typically, in a non-ohmic system, the current-voltage relationship doesn't just depend on the material, but also on the geometry.
For example, an incandescent light filament is non-ohmic because as it heats itself up, its resistance increases, limiting the current. But the change in temperature as a function of current depends not only on the material of the filament, but also its diameter, its length, the thermal masses of the objects it's mounted to on each end, the density of the gas around it, etc.
As another example, the PN-junction semiconductor diode is non-ohmic because it has (to simplify things greatly) very high conductance in one direction but almost no conductance in the other direction. But the details of the I-V curve (for example, how much leakage current is seen in the reverse direction, or exactly how much forward voltage is required to reach the region of high conductance) depend on the doping concentrations of the two sides (and how those concentrations vary with position near the junction), the cross-sectional area of the junction, the operating temperature, etc.
