General definiton of Ohm's law
Despite all the translations and misinterpretations, there is only one definition of Ohm's theorum, the original penned by the great man himself.
In it is the answer to non-linear parts, which are clearly included, and covered in their own dedicated appendix.
See my augmented answer here.. which includes links to Ohm's paper.
The fact is Ohm simply stated, once it settles into a stable state the voltage across the circuit is the sum of the current times the resistances of the parts.



simulate this circuit &ndash; Schematic created using CircuitLab
\$E = I.R1 + I.R2 + I.R3\$
The formula above is true whether R3 is a diode or not.
It goes on to say if the resistance of any part is non linear and dependent on the stimulus, one must wait until the circuit balances for the above to continue to be true.
The issue is folks tend to read more into &quot;Ohm's Law&quot; than is actually there, or not understand it fully enough, or worse propagate the simplified version without passing on the qualification that it is a subset of Ohm's work. But, I guess that's what happens when you try to condense a 280 something page booklet into a single paragraph.
In particular the notion mentioned in the paper that changing I will change E linearly is often miss-quoted. The paper specifically states that particular extrapolation of the Law is only true for linear parts, any change in excitation requires the circuit to rebalance with different R values.
As such, the usefulness of Ohm's Law in a circuit with non-linear components is severely limited.