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Re: Light bulb ohmicity



But we often do an Ohmic heating lab in which a heating coil of nichrome
(or even a resistor) is immersed in water and the temperature rise is
limited to 5-10K.

On Thu, 12 Mar 1998, Leigh Palmer wrote:

David Bowman writes:

Light bulb filaments are made of tungsten. Tungsten is a metal. Metals are
ohmic substances. Ohmic substances obey Ohm's law. What it *means* to obey
Ohm's law is that for a uniform current through a uniform sample of the
substance, the current intensity in an asymptotic steady state is
proportional to the electric potential difference across the sample for a
wide range of current intensities and potential drops. The proportionality
constant *may* be (and almost always is to some degree) temperature-
dependent. The proportionality condition is to hold for a given *fixed*
temperature of the sample.

If the temperature of a light bulb filament is held constant by an
appropriate thermostat then for any temperature you pick for it to operate
at (assuming the it operates below the melting point of tungsten so it can
hold together) you will observe that the current through the filament is
directly proportional to the potential difference across it over a wide
range of currents and potential differences. Therefore at each temperature
the filament has a well-defined ohmic resistance. Just because this
resistance is temperature-dependent is not an excuse to claim that light
bulbs are not ohmic. After all, all realizable resistors have a
temperature-dependent resistance, and the defining property of a resistor is
that it be ohmic.

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. 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. Light bulbs operate in a range of
currents for which their behaviour would most certainly be
considered non-ohmic by any engineer, and by this physicist as
well.

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

where V is the voltage (not the potential difference, because
one might want to discuss AC) across the component and I is the
steady state current which flows through the component when V
is impressed across it. An ohmicity of unity for all values of
V is ideal. Light bulbs in the vicinity of their operating
points deviate greatly from the ideal, though without a
laboratory I can't estimate how greatly.

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.

Leigh