So you propose a superconducting resonator? Yeah, those resonate too.
Examples that come to mind are the cavities used in particle accelerators, with Q factors up to 10^8 (it's not quite infinite because there's always some loss at AC), and superconducting qubits which, being small enough and cold enough that quantum mechanics is quite relevant, have ground states that are effectively resonators in perpetual motion (and for which, bulk measures like Q aren't so meaningful).
The bulk metal forms of these resonators might not be called high inductance, but the fact that they resonate at 100s or 1000s of MHz makes that irrelevant.
Low inductance is not no inductance!
The permeability of free space has units of per-length. Anything that has nonzero physical size, must necessarily have inductance! Even free space itself, or else waves wouldn't propagate (that, or some wierd causality shit that would be even more bonkers if true..).
It seems your gap in knowledge comes down to magnetic aspects:
- Length corresponds to inductance (notice I hinted earlier that the waveform and capacitance were sufficient to solve for the wire length -- evidently around 71m. Hm, it's quite a bit less than that actually, I think; I was lazy and just coiled it up on a spool, magnifying the effect.)
- Energy is stored in the magnetic field, proportional to current flow.
- Energy conservation is true, AND charge conservation is true. Both must be true jointly. However, it happens to be a hell of a lot easier to lose energy to dissipation or radiation into the surroundings, than charge into the surroundings!
- We can assess the behavior of a series RLC circuit (which this is, necessarily: see points above) based on the ratio of Zo = sqrt(L/C) to R. When Zo > R, some oscillation will be evident; when Zo = R, critically damped; Zo < R, overdamped (RC dominant).
- This is a
continuum relationship and no distinction appears for R --> 0.
- As a special case, for R = 0,
any combination of L and C will resonate; the damping factor is 0 regardless!
So I maintain that my waveform was obtained from a superconducting apparatus until proven otherwise.
I mean, how would you know? Given the above information, can you solve for the resistance (if any) in my circuit?
And there's nothing wrong with the waveforms; half the time, the energy difference (the "missing" 0.5 Ei) is stored in the inductance as current flow. The other half it's in one or the other capacitor, hence the voltages alternate between 0 and Vi. Energy is always conserved! And charge is always conserved too, which is why this process averages 0.5 Vi during the wave, and as the AC transient decays (when R > 0), the energy difference is dissipated as heat. The fact that the capacitors end with 0.25 Ei each, 0.5 Ei total, is also no coincidence; perhaps less satisfying than having no dissipation, but the dissipation itself is a necessity (for such simple circuits; else, we must go to great lengths if we wish to avoid it -- such as DC-DC converters!) and so this is the result, no sqrt(2) to be found.
As for the sqrt(2), there is a separate chain of logic which should sound immediately. Such special ratios are EXTRAORDINARILY rare from simple systems. Impossible even, for suitable definition of "simple systems". Such ratios are more likely to be found in, say, properties of signals -- take the peak to RMS ratio of a sine for example, or its integral which picks up a factor of pi -- but not from such simple, finite, geometric relationships like two capacitors rubbed together. This is ultimately a deep truth about numbers themselves, you can't get an irrational (like sqrt(2)) from a rational (like 1/2) without going to some lengths first (sqrt(2) is an algebraic number).
Or, if we could easily construct such ratios -- it would certainly make transformer design easier. We could easily and accurately match 50 to 75 ohms, for example: a 1.5:1 impedance ratio. But we cannot: a 1.22474... turns ratio is needed. We can only get arbitrarily close. (The continued fraction representation of this ratio goes [1; 4, 2, 4, 2, ...]; large numbers in the continued fraction are desirable as they represent points of especially good (but still not perfect!) fit, but repeating sequences like this don't give any especially good stopping points.)
Tim