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

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

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'?

> People who deal with electronic design very soon develop excellent 
> intuition into the voltages, currents, and to a minor extent charges
> to be expected by varying arrangements of serial and parallel capacitors.

I should hope so.

> It has been surprising how willing the people here have been to divide the
> system inappropriately - by splitting a capacitor, plate from plate for
> instance, or visualizing a pathological cap design with one plate and one
> wire as electrodes.

Inappropriate?  Extreme cases can help aid understanding.  The original 
questioner intentionally asked about unconventional geometric arrangements to 
aid in understanding matters of principle.

> 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 engineer is immediately able to assign voltages to each point of the
> series arrangement; he can compute the charge in each; and when
> the series arrangement is connected to a battery, what the extra charge is
> and how it impacts the voltage at each point.

Again, that's to be expected.  But 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?  Maybe the engineer lumps such breakdowns into the catagory of
inappropriate pathological cases that should not be considered.

> I am less than confident that physicists can execute this task after
> reading their commentaries.

Huh?  I certainly did not get this impression.  Of course, I did not read
every response with the care and attantion to detail that I should have.

> Care to try?

OK

> Cap 1; leads A, B  Value 3 microfarad
> Cap 2; leads C, D  Value 6 microfarad
> Battery 3; pos lead E, neg lead F  10 volts
> Battery 4; pos lead G, neg lead H  30 volts 

> Procedure:
> Connect cap 1 and 2 to battery 3.  
> Leads B and C to pos terminal
> Leads A and D to neg terminal.

> Q's ???

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)

> Then
> Connect lead B to lead C
> Connect lead A to pos lead G of battery 4.
> Connect lead D to neg lead H of battery 4.

> Q's ???

Q_1 = 30 uC (Q_A = +30 uC, Q_B = -30 uC), Q_2 = 120 uC (Q_C = +120 uC,
Q_D = -120 uC)

> Voltage at leads B and C with respect to D ???

+20 V

> (The answers comprise five numbers...)

(Assuming that the cap charge polarities are unambiguous)

(BTW, do you also think that physicists don't know how a voltage doubler
power supply works?)

David Bowman
dbowman@gtc.georgetown.ky.us