🚀 go-pugleaf

 A TEXTBOOK ERROR?  WHAT DO YOU THINK?  PLEASE DO NOT REMAIN INDIFFERENT!

P.S.    Harold, we are nearly neighbors; feel free to come and borrow my
demonstration setup. It was used at four AAPT gatherings, (last 4 years)
and seen by authors of several textbooks. But I am still waiting for them
to write publicly about the old error. Why don't they practice what they
preach in the introductory chapters about scientific methodology?

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> Thanks for the suggestion on determining the charge on a capacitor
> as I am starting that topic at the moment.
>                                      Harold Lefcourt  HLefcourt@AOL.COM
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Here is something else you may consider. Take two capacitors and connect
them in series with a source of constant voltage. Make sure the dielectric
materials are different. C1 and C2 may be the same but that is not important.
Wait long enough for the eqiulibrium to be established. According to most
physics textbooks charges on capacitors Q1 and Q2 are identical. But measure
them to discover that Q1 and Q2 can differ very significantly, often by a
factor of 10 or more. I think the textbooks are wrong. The distribution
of equilibrated charges (in DC circuits) depends on the leakage resistances
of dielectrics (R1 and R2). The ratios Q1/Q2 are equal to unity only when
R1=R2. This may happen "by coincidence" but in general the ratio does not
approach unity when INDIVIDUAL LEAKAGE RESISTANCES BECOME EXTREMLY HIGH.
Idealizations are often very useful because they show what is approximately
correct. But this idealization may lead to highly unrealistic expectations.

Good students will be excited to discover that textbooks have been wrong
about capacitors in series for more than a century and that the 1/C=1/C1+1/C2
formula is a myth. It is a mathematically correct conclusion from the wrong
ASSUMTPION OF EQUALITY OF CHARGES. The formula is often "verified" in a
laboratory when students are given capacitors made from the same dielectric
material. Is it honest to deal with a special case which confirms expectations
and to ignore what happens in most other cases? There were two articles on
this subject in The Physics Teacher: May 1988, p 286 and March 1993, p 156.
The second article shows that the formula 1/C=1/C1+1/C2 is valid only at the
beginning of charging, very long before a steady state is established, but
not in equilibrium. (The formula is also valid in most AC circuits.)
The first article shows how an experiment can be performed. A student
electrometer from PASCO is highly suitable for that kind of investigations.

 All comments will be highly appreciated. See my favorite quotation below.

* Laboratories should be used for "asking or pursuing How do we know..? Why
* do we believe..? What is the evidence for ..? questions inherently
* associated with a given experiment". (A.B. Arons, TPT, May 1993, p279)

           Ludwik Kowalski   Kowalski@apollo.montclair.edu.