Re: Ohm's Law

[Bernard Cleyet <anngeorg@PACBELL.NET>]

not exactly -- T^4 applies to black bodies (or gray with constant "grayness")

W's "grayness" deviates such that between 1k deg. K and 3.6 k  T^4.8709 is sl.
more accurate than T^4.00.  R= 0.9988, 0.9981;  the "goodness of fit" difference
is considerably greater visually than indicated by the R.  The total emissivity
increases, over the same range, 0.11 => 0.34.  Curiously, emissivity in the
visible (color emissivity) decreases sl., 0.395 => 0.317----

"....  More easily, one (bc hopes to do) may use a dual
beam (dual trace) o'scope directly.  Or more hi-tech, digitize and plot the
product."

This I threatened to do last Fri., and DB beat me to it:

"To test this prediction I connected a small incandescent lamp (rated
2.5 V & 0.3 A) to a sufficiently powerful adjustable
amplitude/frequency AC sine-wave signal source and monitered the
lamp's AC I-V characteristic using a 2-channel scope." [DB]

However, DB's lamp, [3/4 W, 8 ohm hot.  -- my Kr 2.5 V is  ~ 10 ohm, and  v.~ 0.8
ohm, cold)], I suspect, has a larger diameter filament than my 7 1/2 W, and,
therefore, a greater * "thermal inertia".  I did measure a 7 1/2 W lamp, but in
more detail a 4 W.  candelabra (cold ~ 380 ohms and 5.86 k @ 125 V)  note: the
res. ratios for the lamps are v.~ the same.

Using a Tek 2230, I found noticeable hysteresis (remember I claimed, tho the
resistance is ~ linear **, it would be quite noticeable).   I adjusted the I-V
curve ~ 45 deg. (retained calibration).  At the greatest separation (vertically,
i.e. at the same V) of the heating / cooling, the difference was ~> 5% ***.
Increasingly higher "wattage" (power) lamps (7 1/2, 25, 40, etc.) had smaller
differences, also over shorter times -- the 40 W being unresolvable.

Now "we" must decide what is meant by ohmic -- I'll suggest an operational one by
examples..  Would one want to use such a lamp to set the gain (fixed) of an op.
amp.?  Would one want to use it as a high "wattage" (dissipation) resistor to
limit the current in some circuit whose load varies only a few %.  See what I
mean?  note, I did mention that the NON-ohmic nature of a small (low?) "thermal
inertia" lamp was used to set the gain of a DC amp. in an audio oscillator.
Finally, I evidently missed the boat, because I thought  the question was
settled:  W was considered ohmic, but a lamp not, because its resistance varies by
more than a decade, cold / hot.  BTW one of the exercises in the low frewuenc
impedences experiment (intermediate (Juniors) Lab. is to examine the hesteresis of
a thermistor


"Do not confuse the amplitude of the AC excursions in the intensity
of the filament brightness in the visible part of the spectrum (i.e.
relative changes in the lumens) with the amplitude of the AC
excursions in the instantaneous resistance of the filament due to its
time dependent temperature.  We would expect that the relative
brightness excursions in the visible band to be about an order of
magnitude greater than the resistance excursions." [DB]

Judging from the small, but quite noticeable -- in my selected case, variation in
the resistance compared with the much greater variation in the flicker amplitude
**** one would expect the power exponent of the two (T^1.2) / T^?) to be very
different,  and so they are.  However, because of the two effects (emittance and
Wien) a simple power fit is inadequate over the range I have been using.  However,
I found a reasonably good fit (R=0.9996!) when using Luminance data limited to
approximately the W temp. corresponding to commercial lamps' color temperature
range (2400 => 3400; 40 W => photoflood).  The exponent is 8.458!




* intuition w/o much thought.  However, Levi gives formulae for the "flicker
amplitude as a function of filament diameter.

** A fit of plot of resistivity (T) (same range as above) gives T^1.1912
(R=0.99998), confirming DB.

*** increases when "over voltaged" using a Variac.   Note the most IMPORTANT
device used is an isolation xformer!

**** note the persistence of vision (~ 20 Hz sufficient for movies cf. 120 Hz)
requires a strobe to detect (visually). Note the CFF (critical flicker frequency),
no matter what the amplitude or peak brightness, is < 100 hz (Levi).

bc

p.s. graphs, etc. supplied to squeakers.
p.p.s to be continued.



Mark Sylvester wrote:

> Thanks for spelling this out so clearly. I had the T^4 law and the fact
> that the visible is only a small spectrum window both in mind rather
> vaguely when I remarked later that this seemed like an interesting project
> to tackle. I continue to be amazed at the amount of basic physics that can
> be extracted from the incandescent light bulb.
>
> Mark

cut (much!)