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Sender:       Forum for Physics Teachers <PHYS-L%UWF.BITNET@uga.cc.uga.edu>
From:         ART <WESTERN@PHAO.ROSE-HULMAN.EDU>
Subject:      Re: a myth about capacitors in series
Comments: To: PHYS-L%UWF.BITNET@uga.cc.uga.edu
Comments: cc: uphwc@msu.oscs.montana.edu, tomri@wcbc.com
To:   Multiple recipients of list PHYS-L <PHYS-L%UWF.BITNET@uga.cc.uga.edu>

Colleagues;

I'm a newcomer to the list.  And I'll probably hate myself in the
morning for rising to the bait, but ...

Ludwik Kowalski raises an objection to the treatment of potentials on
capacitors in series as found in many introductory physics texts.
Kowalski objects to textbooks that teach "that the [potential]
distribution depends on the values of C1 and C2 while in reality it
depends only on leakage resistances."  Kowalski illustrates the
potential danger with a "myth" wherein inquisitive students
are penalized by a pedantic teacher/author who denies reality in favor
of a textbook idealization.

Kowalski then concludes,"Yes, the story is imaginary but the problem
is real. Physical reality does not have to agree with our ideas but IN
PHYSICS our ideas must agree with reality. Otherwise we are not
doing physics. Why is common knowledge of practitioners ignored by
the writers of physics textbooks? Can you find an author and ask for
an answer which can be shared with all of us?"

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 <warning: crass commercial message
follows> University Physics: Models and Applications, William P.
Crummett and Arthur B. Western, (Wm. C. Brown, Dubuque, 1994)
<end: crass commercial message>.

Having thus agreed with the validity of Kowalski's admonition, I must
say I am far less exercised about the matter than he.  Yes, capacitors
do have leakage resistance.  Yes, a complete description of series
capacitors should include the fact that the equal-charge assumption
holds only for times short compared to the RC time constant of the
capacitor and leakage resistance. This time constraint imposes a
similar restriction on the output resistance of the charging source.
BUT, people do use capacitive voltage dividers, usually of the air-gap
type or polystyrene.  (An 8 microfarad polystyrene capacitor has an
RC time constant due to leakage on the order of 8x10^6 s [A. B.
Western, et al., Phys. Rev. B, 17(11),1978 pf. 4461-4473].  This
interval leaves plenty of time for student measurements!)

Should introductory students be burdened with all of this on their first
encounter with capacitance?  My answer is, "No."  The point of the
capacitors in series and parallel to allow students to practice with the
concepts of conservation of charge and summation of potentials. The
ideal capacitor, like the frictionless incline, provides a convenient and
relatively uncomplicated context in which to explore these concepts.

Should students be warned about the limitations of the ideal-capacitor
model?  My answer is, "Yes, certainly."  It seems to me that the topic
would be nicely raised in a couple of problems in the section on RC
circuits where the capacitor leakage resistance could be modeled as
a parallel resistor.  (Alas, even this model is an approximation: the
leakage resistance of many capacitor types is nonohmic, that is,
voltage dependent.  If one is determined to tell the *whole* truth, one
must have lots of disk space.)

Let me again emphasize that I am very much in agreement with the
spirit of Kowalski's fundamental premise:  we instructors (OK, and
textbook authors) must set a good example in choosing realistic
models for physical phenomena.  (My own pet peeve is projectile
motion problems in which the constant-acceleration model is
employed even when velocities are so large that air resistance is
THE dominant effect.)  So, if Professor Kowalski is open to plea
bargaining, I will plead *nolo contendere* to the charge of missing an
opportunity to point out a limitation of the ideal capacitor model when
leakage resistance is important.  But as for the charge of ignoring
the real world, I want a jury trial.  (Please vote.  We're writing the
second edition right now!)

Art
----------------------------------------------------------------------
arthur.western@rose-hulman.edu
FAX   (812) 877-3198
voice (812) 877-8337

Department of Physics and Applied Optics
Rose-Hulman Institute of Technology
5500 Wabash Avenue
Terre Haute, IN 47803