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Re: [Phys-l] Capacitance problem



On 03/26/2008 12:01 PM, mrmeyer@mtu.edu wrote:
If you want some more hints (including the solution), see:
http://www.av8n.com/physics/capacitive-divider.htm


I showed the author of the problem (who asserted its unsolvability) your
solution. This is his response:

The assumption that the voltage across C1 does not change when
the switch is opened is flawed.

The switch? Which switch? From context I'm guessing this
refers to S2 ... if not, please re-ask the question.

Remember, there are hundreds of people on this list. If
you can save each reader half a minute of guessing, it's
worth your time. It's worth hours of your time.

While it is true that
no current flows, the charge can redistribute and the
electric field due to that unbalanced charge across C1,
is no longer solely confined between the plates of the
capacitor.

Unbalanced charge? What unbalanced charge? Have Kirchhoff's
laws been repealed?

These circuit elements are drawn as capacitors. Until I hear
otherwise, I will continue to treat them as capacitors. Sometimes
Kirchhoff's laws are good approximations and sometimes not, but
I don't see even the slightest reason to question them in this
case.

Hence the voltage can change and the electric
field external to the capacitor can interact with the room
giving a very "environmentally sensitive" result.

Very? What does that mean? Note that the size of the capacitors
is not specified. I assumed that they were large compared to
the typical "environmental" stray capacitance, and that the
circuit was built inside a chassis so as to cut down the worst
of the stray fields, in accordance with the most basic of basic
electrical engineering principles. In other words, I made the
assumptions that one always starts with. These are sufficient
to make Kirchhoff's laws be useful approximations.

I know a thing or two about grounding and shielding, having done
that for a living at one point. If you want to treat this as a
grounding and shielding problem, that's fine ... but you ought
to say so. For starters, specify the size of the capacitors
and specify the nature of the stray fields. Also draw the
circuit diagram properly, showing the "environmental" sources,
showing the chassis, and showing where the principal stray
capacitances are injected into the circuit.

Also note that the /rate/ of switching has heretofore not
been mentioned or even hinted at, yet it plays a role in
competition with the various stray junk effects.

The problem is that the two capacitance values given
are insufficient to describe the electromagnetic
situation -- one relevant discussion I found is in Berkeley
Physics series, Volume II, "Electricity and Magnetism"
by Purcell (near page 100). There are three conducting
objects here: the infinite ground,

There's no such thing as "the infinite ground". There is
nothing in the Maxwell equations that requires or even permits
there to be an "infinite ground". There might be a chassis
ground, but if so it should be shown in the circuit diagram.

the upper plate of C2 connected
to the lower plate of C1, and the upper plate of C1 (and any
wire attached). There will be three coefficients relating
charge on those objects to their potentials. Only two
coefficients are given. I contend this problem cannot
be solved (correctly) because there is insufficient data given.

The circuit consisting of the circuit elements as shown and/or
mentioned is perfectly solvable.

If you change the problem ex post facto by adding new components,
then sure, you can change it into an unsolvable problem. This is
true of any problem the world has ever seen. What's next, are we
going to say that the simple harmonic oscillator is unsolvable,
because the standard solution fails to account for bats flying
in and leaving guano on the bob?


There may be cases where making an assumption about that
third value is a good approximation. Explicitly adding a
capacitor C3 from node V1 to ground (modeling the third value
needed) leads to a (correct) solution, but the value of C3
needs to be known to get an answer and/or a limit taken if
one wants to assume it is "small."

1) The convention in *every* electrical circuit diagram is that
if a capacitor is not shown, it must be negligibly small. If
you want to draw circuit diagrams, you have to play by the rules.

2) Adding a capacitor C3 from node V1 to ground does not change
the character of the circuit, not in any fundamental way. It
cannot possibly change the circuit from non-analyzable to
analyzable. There is *already* a capacitance from node V1 to
ground at all times, namely the capacitance of C1 in series with
C2 (if not more). This is a perfectly ordinary macroscopic
capacitance, and ensures that node V1 is *not* pathologically
sensitive to small stray fields.