The reason we get involved with reactance is to avoid dealing with differential equations. Reactance is easy, differential calculus is hard.If he could just learn to differentiate the voltage equation, then he would not have to get involved with reactance.
I'll go with what most folks believe, because we can honor Georg Simon Ohm for his contribution by naming anything we want as Ohm's Law; not necessarily what he proposed in the 1820's. Back then nobody knew what galvanic electricity even was, not even Ohm who used Fourier's heat diffusion equations to explain his experimental results (because everyone back then recognized Fourier as a smart guy.)By the way, Ohm's law is not R=V/I and all its variations, like most folks believe. That formula is the definition of resistance or impedance. Ohm's law is a property of a material, specifically its resistive linearity.
There is no reason to refer to some crackpot physicists when we can read any introductory textbook on Electric Circuits to learn everything anyone would ever need to know about Ohm's Law. Or possibly, it is not the author of the physics textbook who is the crackpot.I can show you quotes in a couple of good physics books that show that my statement to be true.
Current flows into one terminal, the same current flows out the other terminal. Current flows through whatever is between those terminals. And the capacitor obeys Kirchoff's current and voltage laws just like any resistor must. If there is a capacitor in a branch of a circuit network, will mesh current flow through the capacitor? How would it be a useful concept for circuit analysis if current did not flow through a capacitor? Or do you propose changing the notation for mesh currents when they reach the capacitor terminals to show that the mesh current does not flow through the capacitor? How would that be more useful?If a capacitor allowed current to pass, it would instead be a resistor.