Re: Ohm's Law

[Bernard Cleyet <anngeorg@PACBELL.NET>]

"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



David Bowman wrote:

> Regarding Mark's observation:
>
> > Interesting to see the evolution of consensus on this topic. In its
> > previous incarnation (inverbation?) on this list (when I brought it up) the
> > view was that the filament lamp is a non-ohmic *device* even if the
> > tungsten wire is an ohmic conductor.
> >
> > Mark
>
> I suspect that this phenomenon may be a function of the set of just
> which list members happened to respond in these two cases.  Maybe
> last time more of the non-ohmites answered the call, and this time
> the ohm-ites responded.
>
> The thing is that an incandescent lamp plugged in to the local
> electric utility will behave, to a pretty decent approximation,
> 'ohmically' because the filament doesn't change its absolute
> temperature by a very great fraction over the time between heating &
> cooling cycles (1/100 sec in Europe & 1/120 sec in North America) of
> the applied AC waveform.  To a semi-decent approximation, when the
> lamp is operating the instantaneous voltage and current wave forms
> obey V(t) = R*I(t) throughout all phases of the applied AC wave
> where R is almost time independent.  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.
>
> Of course if the lamp was operated with a much higher frequency AC
> power source, then even these tiny (so-called non-ohmic) hysteretic
> effects would vanish.  We just must not operate the lamp at *such* a
> high frequency that the filament's inductive reactance becomes a
> significant fraction of its resistance (otherwise it would be an
> inductive load rather than a resistive one).  But there is a wide
> range of frequencies where this is not a problem and still the
> lamp acts fully "ohmically".
>
> David Bowman