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The rebound phenomenon with a glass dielectric capacitor is quite
dramatic. You can demonstrate it with a Leiden jar as well. In
fact I do it with a disassemblable Leiden jar*. I can charge the
jar and remove the aluminum electrodes. After touching them
together, I replace them and a healthy arc can be drawn off the
jar. After a minute or so I can draw another spark.
It is clear that the energy is somehow stored in the glass. Is it
chemical energy? What does it matter what it is called?
The capacitance of a capacitor is merely an engineering parameter
that describes the linear approximation to the behaviour of the
component.
Resistance is a similar parameter. Ohm's law doesn't
hold rigorously for a real resistor. Even an ideal resistor with
a nonzero temperature coefficient of resistivity is evidently
nonlinear due to Joule heating. Inductances with iron cores are
(or used to be at any rate) sometimes designed as saturable
reactors (or "swinging chokes" as we used to call them) for which
the inductance is a strong function of the current. The
capacitance of an electrolytic is simply the parameter Ludwik
measured in his experiment. No electrolytic, supercap or otherwise,
behaves linearly.