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It is perilous to do so, but in the interest of removing what
I think may be a nascent misconception, I will have to disagree
with David Bowman here. Tungsten may be an "ohmic substance"
(though I am unable to define what that means). I'll say more
about it later later. Light bulbs, even though their filaments
are made of tungsten, are *not* ohmic devices.
Since you just admitted that you don't know what it means to be 'ohmic',
how can you be sure that tungsten filaments are not ohmic? BTW, what is
the "nascent misconception" that you had in mind?
Ohm's law is not
a law of nature any more than Hooke's law is. Both are simply
useful approximations of actual behaviour, and the degree to
which a particular resistor (or spring) is ohmic (or Hookeish)
has reasonable tolerances.
Very true.
Light bulbs operate in a range of
currents for which their behaviour would most certainly be
considered non-ohmic by any engineer,
I'm not all that surprised.
and by this physicist as
well.
OK, I'm surprised.
A measure of "ohmicity" might well be in order here. I'm at
home today nursing a cold, and I don't have access to the
references (and laboratory) I would like, but a good measure
might be the quantity
V dI
r' = --- ----
I dV
I like your definition as long as an isothermality condition is included.
I seems though that maybe r' - 1 is more properly a measure of
*non*ohmicity. Maybe 1/|r' - 1| would be a good candidate for the
ohmicity.
. . . . Light bulbs in the vicinity of their operating
points deviate greatly from the ideal, though without a
laboratory I can't estimate how greatly.
I disagree here. Since I want the isothermality condition enforced when
the ohmicity of the bulb is measured I suggest that the bulb be operated
with an AC power source whose frequency is high enough so that the
filament's temperature does not fluctuate appreciably between the peaks
and the zero-crossings of the AC signal. I suspect that a 120 Hz thermal
cycling rate (twice the 60 Hz North American line freq.) may be somewhat
too low for an accurate ohmicity measure. The frequency ought not be so
high, though, that reactive effects start showing up due to the nonzero
inductance and capacitance possessed by the coiled geometry of most bulb
filaments. My guess is that a frequency of the order of 1 kHz would be
sufficient. To measure the ohmicity one could simply sample the current
through the filament simultaneously with the instantaneous voltage across
it at all phases of the AC signal. The slope of a log-log plot of |I(t)|
vs |V(t)| would then display ohmicity r'. Note, I predict that if the
current signal and the voltage signal are each fed to a separate channel of
a two channel oscope and the resulting traces are observed on the screen,
a judicious scaling and shifting of the two traces could superimpose both
of them making the screen look like a single trace. This would be an
explicit demonstration of ohmicity. If the tungsten is truly nonohmic (or
if the scope has some systematic nonlinearities) then the nonlinearity in
the I- V function would make both signals have a different shape and thus
they could not be adequately superimposed. If the frequency is wrong for
the job there would be a phase shift between the traces of each channel due
to reactive effects if the frequency is too high, or possibly due to a time
delay between the peak surface temperature and the peak Joule heating power
due to some thermal "inertia" if the frequency is too low and the
temperature is not held very constant throughout the heating cycle. For
this experiment a sine wave voltage would not result in a sine wave current
if either the tungsten or the scope were truly nonlinear.
David's idea of immersing a tungsten filament in a constant
temperature environment is invincibly problematic. It would be
possible to do such a thing if Joule heating could be ignored,
but it can't. I appreciate the theoretical approach to many
problems, but a dissipationless flow of current in an ohmic
substance is, I'm afraid, out there with the spherical cow.
I don't care so much about whether or not the environment is the same
constant temperature at the filament. I really only care that the
filament be held at a constant temperature. My suggestion for
accomplishing this is to take the data for the experiment fast enough
so that the temperature doesn't have time to change. Hence the AC
measurement method describe above.