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First, the ordinary light bulb runs at 60 Hz. This is so far
short of being fast enough to reach thermal steady state, as you
guessed, that I have seen its effects in high shutter speed
videotapes. The illumination brightens and dims slowly as the
field frequency beats with line frequency. (This was done with a
halogen lamp illuminant. The effect is greater for such a bulb
than it would be for a non halogen bulb.)
Hysteresis is important here because of heating. The temperature
of the filament's surface will vary with a phase lag with
respect to that of the current squared, the reason being that the
thermal conductivity of the filament requires that there be a
higher temperature at the filament's center than at its surface.
Since heat is produced at a not inconsiderable rate (power
density = j E = j^2 / sigma) and there is no phase change taking
place, thermal equilibrium would require the magical removal of
energy, since finite thermal conductivity limits the rate at
which it can be removed by other means. In the AC case the
specific heat of the metal also matters.
In consideration of this energy disposal problem, do you still
feel that a requirement of isothermality serves any physically
useful end in discussion of the ohmicity of a material?
Do you
feel that some materials would be found to be ohmic and some
not?
If your answer to that question is "Yes", please give me
some examples (I can only think of one). If your answer is "No"
(or if my example is the only one extant) then I would say the
concept is not useful.