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*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.

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