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An ohmic experiment



I don't think anyone has specifically addressed Paul Johnson's question
about ordinary resistors. That is, assuming constant temperature, are
they ohmic?

I believe they are ohmic within the bounds of common use. I say it
this way because I just don't know what happens in carbon or nichrome
at extremely high potential difference or very high current density.
However, when ordinary carbon composition, carbon film, and wire-wound
(nichrome) resistors are used at power levels low enough that the
resistors can be kept cool (or better said, kept at constant
temperature) they are very ohmic in behavior.

I mentioned, in a previous message, that I have students plot I versus
delta-V for resistors over a range of power sufficiently high that they
nearly "smoke" the resistors. Then I have them repeat the experiment
over the same power range, but with a heatsink. I have them do this
with both a nichrome resistor and with a carbon-film resistor. There
are some neat things that result from this.

(1) The I versus delta-V plots for both types of resistors show slight
non-linear behavior when the resistors are allowed to heat-up. They
both display very linear behavior when fitted with a heatsink and
plotted over the same range as without the heatsink. This demonstrates
the non-linear behavior was temperature induced and not voltage
induced. That means these are actually behaving as ohmic materials.

(2) The carbon-film deviation from linearity is in the opposite
direction from the nichrome deviation. The resistivity of carbon goes
down with increasing temperature whereas the resistivity of nichrome
goes up with increasing temperature. The negative temperature
coefficient for carbon is typical for semiconductor materials. The
increased temperature results in higher population of the conduction
band, and this overshadows the normal thermal effect of increased
resistivity.

This means the students can identify which resistor is made of carbon
and which is made of nichrome. I do not identify the resistors ahead
of time, so this identification is "part of the lab." Of course, any
student familiar with electronics will already be able to identify (by
sight) a carbon-film resistor versus a wire-wound resistor. But the
typical student I see has no clue what resistors look like before they
take my class.

Note: Even when the resistors are hot enough to burn your fingers, the
deviation from linearity is slight. Students are not used to viewing a
graph by holding the paper so they can sight down the data points to
see if they're straight or not. I have to teach them to do this.
Also, if they just blindly fit a linear regression line to all the
data, the deviation from linearity at higher temperatures is not as
obvious as one might desire. That's because the linear-regression line
for the slightly curved line has data points on both sides, and
students might not notice they start on one side, migrate to the other,
then back again. The best way to observe what I want them to observe
is to use a graphing program (or, heaven forbid, graph by hand) in a
manner that all data points are plotted, but only the cool data points
are used to determine the linear regression line. Some graphing
programs allow this, and some don't (without doing various "tricks").
Anyway, if the linear regression line uses only cool data points, and
that line is extrapolation into the region where the resistor was
definitely hot, the high temperature deviation from linearity is easily
noticed, and it is also easy to see which way it deviates.

If you have time to incorporate this experiment into your curriculum, I
recommend it.

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