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Re: Definition of Capacitance

• From: John Denker <jsd@AV8N.COM>
• Date: Sat, 14 Feb 2004 09:19:39 -0800

Quoting Richard Tarara <rbtarara@SPRYNET.COM>:

I'm for keeping thing the way they are because of the conceptual nature of
the labels. Capacitance is the capacity to store charge--bigger
capacitance, bigger capacity.

I agree ... that's the core of why capacitance and inductance
are defined the way they are. They are the fundamental extensive
quantities. To say it more quantitatively:
-- If you take a capacitor and double all the dimensions (X, Y, and Z)
you get twice the capacitance.
-- If you take an inductor and double all the dimensions (X, Y, and Z)
you get twice the inductance.

This is the *physics* argument, and it wins over all the electronics
arguments that might tempt you to use (C, G, 1/L) or (1/C, R, L).
This is a clearer version of the point I tried to make yesterday
with the coax example.

Again: If you just look at things with units of resistance or
conductance, you might think that C goes with 1/L and vice versa.
But there is more to life than impedance. Look at the symmetry
in the following energy expressions:
E = .5 Phi^2 / L
E = .5 Q^2 / C

Those are the most relevant physics expressions, far more fundamental
than anything involving voltage and/or current, because the flux (Phi)
is dynamically conjugate to the charge (Q). The importance of this
will be thrust upon you if you ever try to do the classical mechanics
(or the quantum mechanics) of an electric circuit. (Hint: start with
the LC harmonic oscillator.)

======================================
Quoting "Folkerts, Timothy" <FolkertsT@BARTONCCC.EDU>:

Secondly ... coax has a certain inductance per unit length
and a certain capacitance per unit length.

But this could also be a source of confusion. As a coax wire gets longer,
the inductive reactance increases, but the capacitive reactance decrease.

Really? That's news to me. All the coax cables I've ever used
have a characteristic impedance that is
-- independent of frequency, and
-- non-reactive.
Specifically, Z = sqrt(L0 / C0) where L0 is the inductance per unit
length and C0 is the capacitance per unit length.

Typical laboratory cables have Z = 50 ohms and have BNC connectors
on the end. Typical home video cables have Z = 75 ohms and have
F connectors on the end.

Thirdly, consider the analogy between an LC circuit and
a mass on a spring. ...

The way I've usually seen it is
L d2i/dt2 + R di/dt + (1/C) i = f(t)
L -> mass
R -> drag
1/C -> spring constant

Let's call that the "series" version.

That form of equation would be improved by writing Q instead
of i as the key variable.
Q -> position
Then all the terms have dimensions of voltage. (You can take the
voltage equation and differentiate both sides w.r.t time, but it's
not an improvement.)

In any case, wider experience and/or deeper thought should convince
you that there is no scientific basis for preferring the series
version over the parallel version, to wit:
C -> mass
G -> drag
1/L -> spring constant
Phi -> position

If you have never worked out this version, now would be a good
time. It'll give you some perspective on what's fundamental
and what's not.

Once again, using C' = 1/C seems pretty logical and consistent.

Only if you ignore half the data, or more. For every electronic
argument in favor of 1/C, there is a mirror-image electronic
argument in favor of C ... unless you are going to argue that
series circuits are somehow normal and parallel circuits are
somehow abnormal. Are we going to have another holy war between
the little-endians and the big-endians?
http://www.jaffebros.com/lee/gulliver/bk1/chap1-4.html

The physics argument points pretty strongly to L and C as the
extensive variables.