Why are there only four passive elements?
Why are there only four passive elements?


  But why couldn't you invent other type of passive element? Is there a proof?


Well, there is a proof, but it's circular. If you take "the four fundamental electronic variables", there are only six ways to combine them linearly. Four of the ways are components, and the other two are definitions. Stephen's answer explains this well. There are only four passive components because whoever made that claim only allowed four variables.

I can "invent" more "missing components" by introducing more variables. Current is the derivative of charge with respect to time:

$$ i = \frac{\mathrm dq}{\mathrm dt} $$

I'm going to define a new term: surgingness. It's the derivative of current with respect to time:

$$ s = \frac{\mathrm di}{\mathrm dt} $$

Mind blown? Put it back together. We do this all the time in physics. These sequences are analogous:


position, velocity, acceleration
charge, current, surgingness


We can differentiate variables as many times as we want and give the results names, if we want. Physics even has a name for the derivative of acceleration: jerk.

Now we can stick surgingness in that graphic from Stephen's answer. It goes below and to the left of current.

Now we can ask, what's the component that connects surgingness with voltage? It would be a component that obeys:

$$ \mathrm dv = P \mathrm ds $$

I'm going to call \$P\$ Philistance. The component is called a Philator.

What's the utility of this component? I haven't a clue, but I predict it exists. In a few decades, when it's invented, I'll say "I told you so" and be famous.
    