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Re: Light bulb ohmicity



It seems that the issue of whether light bulb filaments can be said to
obey ohm's law or whether they have an intrinsically nonlinear I - V
function has stimulated a vigorous discussion.

For instance, Brian Whatcott wrote:
As far as I know, R (incandescent lamp) = E/Isub0 x G(E.I)

Isub0 current at ambient temp (low power)
G is a power function of temperature.

This is a non linearity not unlike the diodes!

Actually, it is a temperature dependent *linearity* quite *unlike* diodes.
For diodes the I vs V function at a given temperature is an (obviously
nonlinear) exponential function: I = I_0 * (exp(const*V) - 1). For a
fixed potential drop V the steady-state current is a complicated
exponential function of the absolute temperature
I = I_0 * (exp(const'/T) -1). A diode conducts better (in both
directions) at higher temperatures than at lower ones.

OTOH, for a metal (like tungsten) the steady state current at a fixed
temperature is directly proportional to the potential drop across it over
a very wide range of curents and potential drops. For a fixed potential
drop the the steady-state current is approximately (over nearly all
useful temperature ranges) inversely proportional to the absolute
temperature, so that conduction improves with *decreasing* temperature.

And Clarence Bennett wrote:
All very true.

But in the demo of different wattage bulbs in series and parallel,
and if you need to know the maximum transient current at startup,
Ohm's law doesn't seem to work very well, at least to an unsophisticated
student, which is why I threw in the comment.

I figured as much. Certainly the way light bulbs are normally used is
not under isothermal conditions for its filament which, as Leigh pointed
out, are difficult to achieve in practice. Since filaments are so narrow
and have a very small thermal inertia they tend to stabilize at an
elevated steady state temperature relatively quickly relative to student
experimental time scales such that the temperature is effectively
determined as a (positive) power law function of the applied potential
drop. (Presumably, we can infer from the info given at the www.picc.com
web site that Leigh referenced that this function is approximately
T = (const)*V^(0.45) ). This then causes the normal steady state I - V
function to obey the empirically useful function I = (const)*V^(0.55)
since the ohmic resistance is approximately directly proportional to the
absolute temperature. Since this empirical nonlinear I - V function is
not obtained under isothermal conditions it does not (contrary to its
naive appearance) represent an actual violation of Ohm's law. To claim
otherwise is analogous to claiming that an ideal gas does not obey Boyle's
Law just because P = (const)*V^[gamma] for such a gas under adiabatic (a
form of non isothermal) conditions. An ideal gas *does* obey Boyle's law
since inclusion of the condition of isothermality is part of the
definition of Boyle's law. A similar situation holds for light bulb
filaments and Ohm's law.

Leigh Palmer wrote:
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.

Karl Trappe wrote:
Provided, of course, that you operate your "ohmic material" in its ohmic
range of behavior, ie, where R=V/I is the *linear* fit of the plot of V vs
I. Light bulbs are ohmic as long as they are not operated as light bulbs!
Once you start getting near incandescent, the behavior is extremely
non-linear. Karl

I disagree. Although I haven't done the experiment I predict that even
tungsten at a nice hot 2850 K will be seen to be perfectly ohmic for the
normal operating voltages and currents of the bulb. Just be sure to
do the experiment measuring the I - V function under isothermal
conditions. Karl, this sounds just like an experiment you could do and
report back to the list what you find. (I don't think you would want a
theorist like me doing the experiment anyway.) Come to think of it
maybe using a triangle ramp wave would be better for taking the data
than a sine wave would be to prevent clustering of the data points near
the cycle peaks, but this would introduce high frequency harmonics which
may be troublesome if reactive effects are significant for them. I'm
sure you would be able to find the best frequency and wave shape to use
to optimize the experiment. Since the electron scattering relaxation
time in a metal like tungsten is many orders of magnitude shorter than
the time scale of any feasible experimental frequency we do not have to
worry that the current doesn't have time to adjust to the voltage to keep
up with its time dependence. We can assume that the instantaneous current
in the experiment is the asymoptotic steady state current for each
instantaneous voltage (again barring extraneous geometric non-material
based reactive effects).

David Bowman
dbowman@gtc.georgetown.ky.us