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Re: Ohm's Law



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

At 14:51 11/03/03 -0500, David Bowman wrote:
Regarding Mark's comment of 07 MAR 03:

>The variation is certainly noticeable when one uses the Pasco "light
>sensor" with a datalogging interface. We were using a halogen lamp on 12V
>ac as the source in a polarisation experiment some time back. The
>measurements drifted up and down in a regular way that turned out to be a
>slow beat between the 100 Hz of the mains and the sampling frequency, not
>quite 20 Hz. We learnt that we had to use well-smoothed DC. We also learnt,
>btw, that halogen lamps die very quickly when run at below their rated
voltage.

And BC's comment of the same day:

>At 14:28 07/03/03 -0800, Bernard Cleyet wrote:
>"There is some hysteresis caused by the time lag of the temperature
>response to
>the heating/cooling cycles, but the difference in resistance due to these
>temperature excursions isn't a great fraction of the overall average
>resistance
>as a function of time."
>
>A 71/2 W lamp works well as a strobe for setting the speed of a disk
>turntable. Knowing this prompted me to check in my favo. reference book,
>Levi's Applied Optics. Sure nuff, lotsa data.
>
>It gives heating ( brightness 0=>90% and cooling 100=>10%) times and total
>variation in brightness for various lamps powered by 50 and 60 Hz.
>
>They also have extensive tables on W props from which one may determine the
>temperature and resistance. 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.
>
>Here's some, 115V 60 Hz, extracted data:
>
>gas filled first:
>
>W M*% t(h) (msec) t(c) (M* % variation from
mean,
>total;
>40 27 65 26
>100 13 125 59
>500 4.5 380 190
>
>vacuum
>6W 74! 39 12
>40 14 128 58
>
>Another, rather interesting, but conforms to intuition, is a graph of
>brightness variation (M*) with wavelength for a 120 V lamp (wattage not
given
>-- is this like voltage?). The variation is 10% to 4%, 0.4 micron to 1.2
>(respectively)
>
>The large values of t(h) and t(c) paradoxically belie the large values
of M*.
>The paradox is resolved by examining the graphs of heating and cooling. The
>curves are approximately exponential, so, for example, a 40 W (gas filled)
>lamp's brightness (lumens) drops from 100% to less than 35% in only ten
>milliseconds. the eye's is a log detector, so not so obvious. Despite
W lamp
>resistance is ~ linear WRT the applied voltage (quasi DC), I suspect its
>variation should be quite noticeable.
>
>bc

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.

The reason for this is 2-fold. First, there is the T^4 dependence of
the luminosity on the temperature. The resistance dependence on the
temperature is closer to a T^1.2 behavior. This means that
relatively small flucuations in temperature will result in relative
fluctuations in luminosity that are 4/1.2 = 3.3 times greater than
the relative fluctuations in the resistance. Second, because an
incandescent lamp is operated at a temperature where the predominant
spectral peak occurs in the IR the visible part of the spectrum is
pretty far down the slope of the blue-ward side of that emission
peak. Asymptotically, the blueward tail has an intensity that falls
off exponentially with decreasing wavelength lambda and temperature
T like exp(-h*c/(k*T*lambda)). The visible part of the spectrum is
not fully down on the asymptotic part of this exponential tail, but
it is still far enough down on it so that a relatively small change
in temperature results in a proportionately much larger change in
the fraction of the luminosity that is in the visible band. In
essense, as the temperature drops the spectral peak shifts (Wien
law) farther into the IR and that pushes the visible band farther
down on the exponential tail--all the while the intensity *of* that
tail is dropping rapidly.

All this means that we expect the relative flicker in the luminous
output to be much greater than the corresponding relative
excursions in the filament resistance over the course of the AC
heating/cooling cycle.

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. When driving
the lamp at a full rated RMS voltage and at 60 Hz the I-V trace was
amazingly close to a straight line. There was no perceptible average
curvature of the trace, and the amplitude width of the (noticable
but small) hysteresis loop seemed to be only at most a few percent or
so. When the lamp was driven at 50 Hz the hysteresis loop opened up
a little more but it was still not very big overall. When the bulb
was driven at a frequency above about 200 Hz all the observable
hysteresis vanished within the thickness of the trace line, and the
I-V curve looked like that of a perfect resistor.

So I still stand behind my former claim that driving an incandescent
lamp with an AC waveform at line frequency makes it act close to
"ohmically" and its I-V trace is pretty similar to that of an
ordinary resistor (with only a relatively minor hysteresis) over the
time dependent excursions of the AC wave form. It seems that the
temperature fluctuations are not enough in 1/120 s (or even in
1/100 s) to strongly mess up the resistance by an annoyingly large
amount.

I suspect that if the experiment was to be redone using a halogen
bulb then the magnitude of the amplitude of the 'non-ohmic'
hysteresis loop in the I-V curve might be somewhat larger than for an
ordinary incandescent bulb. This is simply because the halogen bulb
operates at a significantly higher temperature and so the relative
temperature excursions would be greater.

David Bowman

Mark Sylvester
UWCAd
Duino Trieste Italy