limitatons of ohm,s law
Ohm's Law was derived from observation of physical electrical circuits. Although Georg Simon Ohm was educated as a mathematician, Ohm's Law was NOT a mathematically derived theory.
Ohm spent a lot of time in a laboratory gathering experimental data. The relationship between current and voltage across a resistor was something he documented in extensive tables of data he collected. He never answered the question about WHY it was true, only that it was observed fact.
If you apply Ohm's Law outside of his field of observation, you do so at your own risk. Although there are analogies in hydraulics and other physical dynamics, the basic 'Law' is only a statement of observed electrical behavior. The analogy in fluid systems begins to break down when you take such things as flow turbulence and fluid viscosity into account. The closest analogy that works is heat conduction. You can interchange the terms in Fourier's heat conduction equation almost directly with Ohm's Law.
Why Ohm's Law is true involves understanding voltage (potential), current, and resistance at the atomic level. That's more than can be written in a brief forum post.