In a recent message in this thread, Leigh used the idea of a "black box." I
think the black box concept might be an interesting way to examine a couple
things about this thread.
Suppose we have some black boxes for which we can measure the current and
the voltage, and we are supposed to make guesses about what is inside. I'm
going to describe a few examples. Note that I am going to exclude the
possibility of something smart inside, like a microprocessor controlled
circuit designed to trick us. I will always seek the most simple answer.
Box 1. We vary the voltage and measure the current. We plot the current as
a function of the voltage and we get a straight line as far as we can tell.
I would conclude this box contains an ordinary resistor, and its physical
size is large enough that it did not have significant temperature change
over the course of data acquisition.
Box 2. Our plot of I-versus-V produces a slightly curved line. My first
guess would be an ordinary resistor that is getting hot. If the curve is
concave-up (resistance getting less) I would conclude it is a carbon
resistor. If the curve is concave-down (resistance getting more) I would
conclude it is a wire-wound resistor. There would be some other tests that
could help confirm this. Rather than take data points in a monotonic
manner, one could abruptly apply a significant voltage, then hold that
voltage steady to see what happens. If the current begins at one value then
slowly drifts to a new value and then holds steady, that would be evidence
in support of the device heating up and its material changing its
resistivity. Once thermal equilibrium is attained, the current remains
steady. This experiment could get tricky if the thermal mass is so small
that it does not take appreciable time for the device to establish thermal
equilibrium, but I think you get the idea.
Box 3. Our I-versus-V plot has one or more regions where the line has
abrupt changes in slope. Between those regions the line might be fairly
straight or slightly curved. I would conclude we have a solid-state device
such as a zener diode. From a practical viewpoint there would probably be a
resistor in series with the solid-state device so we don't destroy the
device. That would alter the behavior from what the device alone would do,
but the abrupt slope change is the important clue.
Box 4. Our I-versus-V plot is significantly curved concave-down. If this
device contains an ohmic material, it is having a significant change in
temperature. A tungsten light bulb would behave this way. Some
resistor-transistor circuits could do this, but the light bulb would be the
simplest answer.
Box 5. Our I-versus-V curve is significantly curved concave-up. A DC motor
under no load will do this.
Let me stop there, but we could obviously dream up quite a few interesting
black-box contents. I think it could be difficult to make definitive
conclusions about the contents based upon I-versus-V plots alone. But my
examples show how we can make some "educated guesses."
Of the black boxes I've listed, I would only assign a resistance to the
first box and maybe the second box. For the other boxes, what value of
resistance would we report? There isn't one value. With boxes 3,4,5 we
could make one measurement and calculate a V/I for that measurement. But
that number would not represent a general property of that box. On the
other hand, V/I for the first box is a general property of that box. V/I
for the second box is a general property of that box if we drop a
significant figure.
This brings me back to where I think I started. I don't like it if someone
calculates V/I from a single measurement on an arbitrary device and calls
that quantity the resistance of that device. Box 1 has a resistance, box 2
has an approximate resistance, but I don't think boxes 3,4,5 have a
resistance and I get bent out of shape when people calculate V/I for these
boxes and call this the resistance.
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