[...]. This represents the physical fact that there
are no absolute
voltages, only differneces.
That's actually not quite true. There is an absolute voltage reference
in the form of electrical neutrality, with objects with an electron
deficit being positive to it and objects with an electron excess being
negative to it.
However, for voltage magnitudes likely to be encountered outside an
electrostatics setup, absolute neutrality is hard enough to identify,
and deviations from it so small, that your statement is an excellent
approximation, certainly good enough for practical purposes. :-)
No matter, simply take a note (say node 0) to be
ground, and delete
the appropriate row an column from the matrix, the element from the
currnet and voltage vectors. The resulting matrix is non-singular,
invert, etc...
The resulting matrix _may be_ non-singular. There are two ways it can
be singular: if there is a dead short between any two voltage nodes, in
which case any attempt to solve the matrix will result in division by
zero at some point, or if there is a part of the circuit with no
connection to any voltage nodes, in which case all voltages in that
portion are indeterminate.
I ran into those conditions when building my resistor-blob solving
program - that's why I'm aware of them. :)
I once was at
work when someone walked in wearing a T-shirt which
said "SPEED LIMIT" with a formula, 4 pi h-bar / 137 mu_0 e^2
I asusme
that evaluates to c.
As I mentioned later, it evaluates to the _local_ speed of light
(always <= c, with equality only in a vacuum). Talking with the guy,
it turned out the shirt came from some undergrad physics club or some
such, and they wanted to come up with something at least a little bit
more interesting than just another way to write c. :-)
I said
"h-bar is Planck's constant,
Hmm.. I thought h-bar was conventionally
plancks constant _divided by
2pi_
Yes. I was being somewhat inaccurate in the interests of brevity (at
the time, I mean, not when reporting the event now).
[...]. But why mu_0, and not mu, then?
I'm not sure. I am and was not physicist enough to really understand,
nor explain, the formula. I discussed it briefly with him, but not in
enough detail to cover things like that.
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