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series capacitors: more in sorrow than anger.



At 15:34 9/10/97 -0500, you wrote:
Dear PhysLers: I have a question about the usual formula for capacitors in
series...
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?

If the isolated circuit consisting of plates B and C and the wire between
them is initially uncharged, then the sum of the charges presumably has to
remain zero. But why couldn't I get -1.1Q and +1.1Q on these two plates,
say? Why *exactly* -/+Q? Is it always exact: what if plates A and B have
different shapes?....
Dr. Carl Mungan

I contributed a small piece to this thread and followed with interest
the contributions of the other folks.

I am left profoundly disturbed by how plainly unpractical and
inapplicable the models selected for explaining the sharing of charge
between capacitors have been.

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.

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.

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.

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.

I am less than confident that physicists can execute this task after
reading their commentaries.
Care to try?

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 ???

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 ???

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

(The answers comprise five numbers...)
Regards

brian whatcott <inet@intellisys.net>
Altus OK