Electronic – Why are there only four passive elements


I've read that there are four types of passive elements: resistances, capacitors, inductors and memristors.

The memristor was predicted 30 years before it was produced. But why couldn't you invent other type of passive element? Is there a proof?

The definition I'm using of passive elements is something with no gain, no control and linear.

Best Answer

There are four physical quantities of interest for electronics: voltage, flux, charge, and current. If you have four things and want to pick two, order not mattering, there are 4C2 = 6 ways to do that. Two of the physical quantities are defined in terms of the other two. (Current is change in charge over time. Voltage is change in flux over time.) That leaves four possible relationships: resistance, inductance, capacitance, and memristance. enter image description here

If you want another fundamental component, you need another physical quantity to relate to these four. And while there are many physical quantities one might measure, none seem so tightly coupled as these. I'd suppose this is because electricity and magnetism are two aspects of the same force. I'd further suppose that since electromagnetism is now understood to be part of the electroweak force, one might be able to posit some relationships between the weak nuclear interaction and our four elements of voltage, current, charge, and flux.

I haven't the first clue how this would be physically manifested, especially given the relative weakness of the weak nuclear force at anything short of intranuclear distances. Perhaps in the presence of strong magnetic or electrical fields affecting the rates of radioactive decay? Or in precipitating or preventing nuclear fusion? I'd yet further suppose (I'm on a roll) that the field strengths required would be phenomenal, which is why they're not practical for everyday engineering.

But that's a lot of supposition. I am a mere engineer, and unqualified to speculate on such things.