Re: series capacitors: more in sorrow than in anger.

[brian whatcott <inet@intellisys.net>]

Carl Mungan asked this:

Suppose I connect two capacitors in series across a battery. Label the four
capacitor plates from left to right as A, B, C, and D. Okay, suppose A is
connected to the positive terminal of the battery, so out goes charge +Q to
it, and compensating charge off D, leaving -Q on it. My question is: why
does the charge on B and C have to be -Q and +Q, respectively?
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At 20:06 9/11/97 EDT, David Bowman wrote:
> Brian Whatcott wrote:
> > I am left profoundly disturbed by how plainly unpractical and
> > inapplicable the models selected for explaining the sharing of charge
> > between capacitors have been.
>
> The original questioner was not interested in matters of practicality but in 
> matters of principle and of underlying understanding.  What do you mean by
> 'inapplicable'?

The original questioner was interested to know why the charge at point
B and C have to be numerically equal, as quoted above.

 The only person who explicitly contradicted this equality 
( as far as I recall ) was John Mallinckrod.
 You for example merely modelled the oscillation which could precede 
the new steady-state, did you not?

....
> > Even worse, the dominant models seem to have overwhelming difficulty
> > in explaining the reasonable case of two caps of different C value,
> > precharged to the same voltage ( i.e. with a different Q in each
> > cap) and then connected in series.
>
> What difficulty?

The difficulty of erroneously assigning equal charge on connected plates of
series caps.
> ... do most engineers know when and *why* the
> formulae, algorithms and rules of thumb that they as so adept at using
> actually properly describe the situation at hand, and when and why they may
> break down? 

I may have mentioned recently that I do NOT subscribe to the
orthodox ( I deliberately do not say "old-fashioned") view
that there are "natural laws" that scientists discover;
 I find it much more productive to suppose that there are man-made models -
any of which may be more or less suitable to any particular case.
 This has the particular virtue that when physicists comfortably think they
are dealing on a 'more-fundamental' level, I can as easily see the flaws in
their models as in any other man made elaboration.

....
> Let u = [mu] = 10^(-6)
> Q_1 = 30 uC (Q_A = -30 uC, Q_B = +30 uC), Q_2 = 60 uC (Q_C = +60 uC,
> Q_D = -60 uC)

So you can now easily admit a case where Qb is not numerically equal to Qc
 This was the crux of Carl's question, was it not?

> (BTW, do you also think that physicists don't know how a voltage doubler
> power supply works?)
>
> David Bowman
> dbowman@gtc.georgetown.ky.us

I am afraid that this was at the heart of my sadness.
 It was Cockroft and Walton who defined this arrangement for a 
voltage multiplier in the earliest accelerator experiments.
  They were physicists as I recall.
    But  I don't suppose their names are known to teachers hereabouts.

(On careful deliberation, I have deleted the putative reason I offered 
for this. I hope you will accept this as a tribute to your private coaching
in how to prevent public shows of sniping)

Regards
brian whatcott <inet@intellisys.net>
Altus OK