Well, actually, when the resistance approaches zero, the current approaches infinite, and the energy starts to get lost as electromagnetic radiation at that point.
Actually that can have better efficiency as stray inductance start to soft charge ("soft" comparing with resistance). The above analysis only assumes RC circuit without inductor.
1. There is ALWAYS loss. Even a superconducting resonator (a more subtle kind of inductor-capacitor circuit) has a finite Q (around 10^8 -- better than most quartz crystals, giving a time constant of ~seconds at a resonant frequency of 100s MHz, not bad eh?). Over a short time period, we can get reasonably lossless exchanges of energy, but over a long time scale,
thermodynamics ALWAYS wins.The equations for charge conservation, capacitor charging (RC or otherwise), and so on, are taken at \$ t \rightarrow \infty \$, so thermodynamics is the name of the game here.
![Smiley :)](https://www.eevblog.com/forum/Smileys/default/xsmiley.gif.pagespeed.ic.R8GFI-pF6f.png)
2. There is no circuit without inductance, or capacitance, either. Indeed, L and C are the electrical manifestations of physical
causality: anywhere the physical length of some system is nonzero, and where the speed of light* is finite, there must be components of L and C!
*Generally, the velocity of propagation. Equivalents can be derived in any wave system: e.g., in mechanics, the speed of sound causes finite and nonzero elastic modulus and mass.
So this teaches us a fallacy of our schematic notation: that all signals are instantaneous, or that the circuit has zero dimension, or the speed of light is infinite (all equivalent). We must think carefully to ensure we aren't deceiving ourselves with an overly greedy simplification, and draw circuits that are physically realistic.
![Smiley :)](https://www.eevblog.com/forum/Smileys/default/xsmiley.gif.pagespeed.ic.R8GFI-pF6f.png)
This is most applicable to SPICE modeling, where it is easy to create perfectly valid, but physically impossible, systems.
We're basically SPICEing this circuit by eye.
So there must, necessarily, be some L in the real circuit this represents. And that L (and the C as well) will couple into ambient fields, however slight (there is no perfect shielding, either). So that, even with a truly perfect resonator (better than any superconducting one we can actually make), the energy inside will inevitably leak into free space. At infinite time, the final state will be the steady state given exactly by thermodynamics.
![Smiley :)](https://www.eevblog.com/forum/Smileys/default/xsmiley.gif.pagespeed.ic.R8GFI-pF6f.png)
Tim