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Re: Explaining




I'm a little puzzled where this thread is wandering (see below). The
observable fact (at a freshman level) is that the current on one side of a
resistor is the same as the current on the other side. This is consistent
with Kirchoff's laws of current and potential, which are presented in such
a course, and used as the basis for understanding linear circuits. So,
understanding that by current we mean the macroscopic current, as measured
by a physical ammeter, we conclude that the average velocity of electrons
is the same going into the resistor as coming out. Consider identical
wires on either side of the resistor if this bothers you. We also
understand that no electrons were destroyed or created in the process.
Therefore we must conclude that the average kinetic energy associated with
the charge carriers is the same coming out of the resistor as going in. So
the student should conclude that it wasn't loss of *kinetic* energy which
heats the resistor.

Now what actually goes on within the body of the resistor is quite another
matter, but we can remark that the energy given up by the charge carriers
in going through the resistor is *potential* energy, as evidenced by the
fact that there's a potential drop measured by a voltmeter connected
across the resistor. All of this is, I think, the expected understanding
the student should grasp in a freshman course in physics. So the student
is not justified in saying that the electrons "come out of the resistor
slower than they went in". When students are asked to defend such an
answer, one often hears: "But doesn't resistance "impede" motion, and
therefore slow things up?"

Does anyone else see a semantic parallel here in the student's use of the
word "resistance "with our discussion of the meaning of the word
"charging"? And many textbooks speak of "current flow" when no one would
ever think of speaking of "flow of speed". Books speak of weightless
astronauts, and "loss of weight of a body suspended in a liquid" when they
have previously "defined" weight as mg. Can we blame students if they use
words as carelessly as we ourselves use them, even in books purporting to
"explain" physics?

We use words in physics with multiple interpretations. We scientists like
to present an image of ourselves as persons concerned about precision in
measurement and in description. Yet we tolerate (without even noticing it)
such ambiguities and inconsistencies in our own scientific language. Is it
any wonder that students are often baffled by our so-called
"explanations"? One psychologist who studied how physicists communicate
concluded that physicists tolerate the most sloppy language, and even
errors, especially in verbal communications with each other. They often
leave huge logical gaps in explanations. She concluded that what was going
on was that their brains were going faster than their mouths, they were
anxious to "get on with" the argument and impatient with the dirty
details. In talking to each other they were confident that their listeners
shared a pool of common knowledge so the listeners could continually
mentally correct these errors, fill in the logical gaps and would
understand what was intended, not what was *said*. However, outsiders (and
students) have not yet acquired that rapid translation ability, for they
haven't yet formed the same mental constructs as the experienced
physicists. Some even speculate that this is why physics is "the
worst-taught" subject. I don't quite buy this. It may seem to be the case
simply because mathematics and physics are inherently more difficult
subjects than others. The same study concluded that mathematicians
generally have a different personality than physicists. Physicists are
impatient with details. Once they realize that a problem *has* an answer,
and they know what that answer is, physicists lose interest in the
problem, or turn it over to a grad student, so they can get on to
something else. Mathematicians, on the other hand, are obsessive about
details, and are not satisfied with something till every logical nuance
has been satisfactorily dealt with. Then they try to figure out a
different or better way to do it.

Of course, some physicists are really mathematicians in sheep's clothing.

Before someone asks, I think this was in one of Anne Roe's books, back in
the 50s or 60s, but I don't have the exact reference. It might have been
in one of her papers in "The American Scholar".

-- Donald

On Thu, 19 Feb 1998, Leigh Palmer wrote:

In a message dated 98-02-19 18:21:31 EST, Leigh writes:

<<Unless you imagine that the electrons can acquire
their kinetic energy during their transit of the resistor,
however, you have to acknowledge that they pack the energy in
with them as electric potential energy when they enetr the
resistor, and they fritter it away in a series of short falls
and inelastic bounces, a frantic glissade.>>

Why can't the electrons acquire kinetic energy during their transit of the
resistor? Isn't the electric field continuous through the resistor? Would
this not affect the electrons' kinetic energies in a discontinuous way as they
drift through the resistor and interact with the lattice? Why couldn't the
electrons acquire, then transfer kinetic energy to the lattice as they drift
through it?

That is my point. That is just another way to "explain" the
phenomenon. The fact that I have suggested three ways, all of
which seem to get their energy from different places (or at
different times, is a strong example of the fact that our
"explanations" are nothing more than descriptions in a
consistent theoretical structure of Nature.

<< Such descriptions as these I find do stimulate students'
thinking, but they are too vivid for some. The latter group is
really turned on by the revelation that it can all be put down
to Pynting flux, by the way. >>

So, are you saying that some sudents would prefer the purely mathematical
approach and not consider the physical meaning?

Oh, no! The Poynting flux explanation may look mathematical
to some who are unused to it, but it is *very* physical. I
love it! I know of no case where it doesn't work.

Leigh