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Re: brightness vrs. power



* * * * * Preface: * * * * *

I had to drop out of this discussion for a day because of the e-mail virus.
Our campus e-mail system had to be shut down from 10 AM EDT to 5 PM EDT
Thursday while we uninfected all our computers. I got the virus, but
figured it was a virus before too much havoc was done to me. I am not aware
that I sent it to any of you, but if I did, I apologize. This thing really
went like wildfire, lodging itself on every computer on our campus network
within about a 5 minute period.


* * * * * Ohm's Law, etc.: * * * * *


I wasn't aware, until one of Leigh's later postings, that Leigh was
describing an experiment in which the brightness of the bulb was being used
to say something about Ohm's Law. If people are trying to do experiments
with light bulbs in parallel, series, etc., and using the brightness to
somehow indicate Ohm's Law, I agree this is crazy. I admit that the
original posting indeed discussed brightness and power, but the discussion
quickly turned into a discussion of what Ohm' Law means. Once that
occurred, my mind divorced itself from brightness measurements. I assumed
we were discussing the results we get with light bulbs and other devices
when we use ammeters and voltmeters. I apologize that this made me talk
past or around some of you.


* * * * * Good Experiment * * * * *


If you will indulge me for a moment, let me continue to describe what I
thought we were discussing, because my students do the following experiment,
and it is a good one.

Let's hook a light bulb to a variable power supply with a voltmeter across
the bulb terminals and an ammeter in series with the supply and bulb. Let's
record I and V data from V = zero up to some appropriate value (where
appropriate means we refrain from "burning up" the device).

Then change the light bulb to a carbon-film resistor and do the same thing.
Then switch to a ceramic-encased nichrome resistor and do the same thing.

My students have been doing this for 22 years. All three data sets give
nonlinear I-versus-V plots if the resistors are run-up to high-enough power
to make them hot. We don't smoke them, but they get too hot to touch
(perhaps 70 Celsius). To get the carbon resistors this hot we indeed exceed
the power rating; we run a quarter-watt resistor up to about 1.3 watts. To
get the ceramic-encased nichrome resistor this hot we do not exceed the
power rating; they are designed to run hot.

As mentioned, all three I-versus-V plots are curved. On that basis we say
none of these appears to obey Ohm's Law. Of course the light bulb plot is
highly curved, and the carbon and nichrome plots are only slightly curved.
In fact, if you try this, many students will not initially notice the
curvature for the resistors. If you blindly run a linear-regression line
through all the data points, you might not notice what's going on. What you
need to do is fit a linear-regression line using the first one-third or
one-half of the data (while the resistors are cool) then extend that line
through the whole plot. It will then be obvious that the higher-power data
points curve away from the "Ohm's Law" line. The carbon and nichrome
resistors curve in opposite directions, which is why we use both. [Note:
take data in a monotonically increasing manner. We start with a cold
resistor at V = 0 and run up to the higher voltage. Have the students take
their time writing down each data point so the resistor has a bit of a
chance to get in the ball park of thermal equilibrium for each data point.]

Then, we put heatsinks on the resistors (of course not the light bulb) and
repeat the experiment. With heatsinks the resistors only rise from 20 to
about 25 Celsius. This time the data plots come out linear as far as we can
determine using 0.25% meters reading to 3 significant figures. This makes
it quite clear that the reason the resistors originally appeared to fail
"Ohm's Law" was because the temperature did not stay constant. It is then
easy to infer that temperature is also the problem with the light bulb, but
on a bigger scale because of the incredible temperature difference that
occurs over the range of data collection.

Of course this is not necessarily an experiment for "general-education
physics." I do it in the calculus-based physics course. But it could be
done in a high-school physics course.

Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817