Re: Explaining things (was battery)

[John Denker <jsd@AV8N.COM>]

Ludwik Kowalski wrote:

> 4) What to do in a situation in which something
>       can not be explained in terms of what is
>       already known to students? Yes, I know that
>       this is not an easy to answer question. But it
>       worth addressing, I think.

First of all, the details of what I wrote previously don't
matter.  The central point is we all agree that the innards
of batteries are fiendishly complicated.  The details served
to illustrate that point, perhaps more luridly than
necessary, but the point remains.

Talking about the Thevenin equivalent circuit for a battery,
i.e. open-circuit voltage plus series resistance, is
manifestly a black-box model.
  a) It doesn't even try to tell us anything about the
innards of the battery.
  b) It doesn't even do a particularly good job of capturing
the two-terminal black-box properties anyway.

To answer Ludwik's new question:  Students have to accept
a lot of stuff as empirical facts, without explanations.
Hypotheses non fingo and all that.  Big-shot professional
physicists like us have the luxury of being able to understand
thing A in terms of thing B ... but intro students have never
heard of A or B so they will have to take one or the other as
an empirical fact, at least for now.

Is the Thevenin model of a battery really any worse than
Hooke's law?  Nobody feels obliged to "explain" Hooke's
law to high-schoolers in terms of chemical bonds and
solid-state physics.  It is simply asserted as an empirical
law.

Actually, I partially disagree with the premise of the
question.  These things are not completely unexplainable.
Once you accept that there exist empirical laws, then
Hooke's law is the obvious lowest-order expansion.  As
the saying goes, to first order everything is linear.
So a spring ought to be linear to first order.  I see
the empirical battery description in the same way: the
zeroth-order term is the open-circuit voltage, and the
first-order term is the Thevenin impedance.  What else
could it be?