🚀 go-pugleaf

On 3/22/95 Arthur B. Western, (the author of "University Physics: Models
and Applications", published by Wm. C. Brown, Dubuque, 1994,) wrote:

    > As one of the offending authors I will have to step up and take my
    > scolding.  The point which Kowalski makes regarding the importance
    > of leakage resistance of capacitors in series is well taken.  I will
    > certainly see to it that at least a couple of problems are devoted to
    > the effect in the second edition of [our book].

I THINK THIS IS NOT POSSIBLE UNLESS YOU CONTRADICT THE "EQUAL CHARGES"
ASSUMPTION AND THE  1/C=1/C1+1/C2 FORMULA.

In the case of a cannon ball you can say "ignore air resistance" and you
are OK in avoiding the ambiguity. Nobody will say "not enough information
given" because you are asking about what happens in a vacuum. Likewise you
can say "assume the lens is thin and rays are paraxial" and your problem
becomes unambiguous. The same applies to all properly used idealizations
such as massless puleys, nonrelativistic velocities, wires with negligible
resistane and batteries whose voltages do not change with loads.

But what will you say to justify a textbook answer to a problem of voltage
distribution on two capacitors in series? Suppose that the textbook expects
students to show numerically (or in general) that V1=V2=V/2 when C1=C2.
Under what conditions is this true for an equilibrated system? Under what
conditions is the textbook idealization applicable? (Sure, you can say
"assume that leakage resistances are identical" but in that case the major
piece of information given, C1=C2, becomes totally irrelevant. You can also
say "assume that R1 and R2 are extremly large" but how does this help to
justify the answer?  Large with respect to what?)

In my opinion the theory of capacitors in series is incorrect in our physics
textbooks. I see no way of fixing it in the context of equilibrated voltages.
Do you agree or not? Why do we have to keep a wrong theory? Why hasn't it
been verified experimentally (by those who teach it) for more than a century?
I have no answer to the last question. Can you answer it?

>   The formula 1/C=1/C1+1/C2, derived from the electrostatic model, leads
>   to conclusions which are contradicted by experimental data and it should
>   not be used in dealing with equilibrated DC circuits. (It is a very
>   reliable formula, however, for dealing with the nonstatic circuits.)
>   The dynamic theory of capacitors in series was described in The Physics
>   Teacher (by A.P. French, March, 1993) and it should be used instead of
>   the incorrect static theory, when students are ready.

And a simplified "constant current" theory may be used to deal with capacitors
in series when (and if?) the subject is first introduced in the context of dc
circuits. Once V1=i*R1 and V2=i*R2 are calculated the charges can be found as
Q1=C1*V1 and Q2=C2*V2. It is so simple. Why do we have to lie to students by
saying that Q1 and Q2 are equal?  What is gained by keeping a wrong theory?

>        HOW DO YOU DISTINGUISH "I AM WRONG" FROM "I AM IDEALIZING"?

             Ludwik Kowalski      kowalski@apollo.montclair.edu