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Re: R = V/I with real lightbulbs



Try a vacuum bulb -- may still be available from CENCO -- it has a different non
linearity, but one perhaps may measure a sig. diff. between the vac. bulb and the std.
home gas filled W bulb WRT radiation, convection and conductive losses. Actually, I
strongly suspect so, as that's why they're vacuum "filled." So I think.

bc


Leigh Palmer wrote:

At 12:31 PM -0700 5/10/00, Doug Craigen wrote:
Leigh Palmer wrote:

I finally have time to put my foot into this mess.
William Lichten in his book "Data and Error Analysis" gives as an example
the current verses voltage relationship for a tungsten lamp from an applied
voltage of 30 mV to 5.3 volts. The log-log graph starts out with a slope of
about one (where Ohm's law is approximately correct) and then at higher
voltages it shifts over to about a 5/3 power law relationship where
radiation cooling becomes important. It is a nice example of how different
relationships are at work depending on the physical conditions of the
system.

In what way does radiation influence the I vs. V relationship? This
will surely confuse students, as it confuses me.

At the risk of repeating repeating myselfself [sic], this could be a great
experiment or it could be something which the students do what they're
told with little concept of what's going on. Furthermore, it might be
that it is producing the right answer for the wrong reasons. The above
power law tells me that either there is more going on than just T^4 of
the filament even at high temperatures (of course, we already know this
for low temperatures) or the correct relationship between resistivity
and the temperature is in fact linear:

P = IV = k1*T^4
& V/I = k2*T

so IV = k*V^4/I^4
I^5 = k*V^3
hence our 5/3 relationship

Equation 1 relies upon the validity of the premise that all other
forms of dissipation may be neglected. That is valid only at high
temperatures. So far, so good. For most metals I know of equation
2 is invalid in all temperature regions.

however the data you found in the rubber bible seems to exclude this
explanation.

Tungsten is merely one of those metals.

using V/I = k*T^0.5 - the 'expected' relationship for a metal, gives I^9
= k*V^7 for the high end of our I-V plot which doesn't match the claim
in the book. So, its up to whoever out there has some real data at hand
to provide some insight about what is happening.

I return to my earlier question: is convection important in this
process? If it is, then equation 1 is also invalid.

You have answered my latest question, however. I now understand
why the I vs. V relationship for a tungsten lamp depends on
radiative cooling. Thanks.

Once caution about log graphs with varying slope regions, it is often
possible to prove whatever slope you are expecting.

It also shows how it is possible to become uncritical when a
superficially plausible explanation is advanced for a phenomenon
which is presented in a graphically uncritical manner. This is
the process of seduction by a power law. When one plots data on
a log-log scale, one is easily misled into looking for straight
line regions. A good example is the mass-luminosity relation for
main sequence stars. One can get one-, two-, or even three-line
fits to this relation, and the theoreticians will say "Oh, yes.
Well, I can explain that, too."

Leigh