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*From*: John Denker <jsd@AV8N.COM>*Date*: Fri, 13 Feb 2004 15:20:53 -0800

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

Today's inconvenient convention is capacitance (and I bet I could come up

with one a day for the next month). There are two obvious ratios we could

consider:

C = Q/V

C' = V/Q

The first, of course, is the standard definition of capacitance, but the

second is much more logical because it then matches R & L:

1) similar definitions:

C' = V / Q

R = V / (dQ/dt)

L = V / (d2Q/dt2)

But as BC pointed out, C agrees with G (conductance) so there

is an equally good (or equally bad) argument for leaving C and

G alone and using the set {G, C, 1/L} ... all of which are

additive for components in parallel.

I can't think of a single case where this definition is inferior (except, of

course, for historical inertia).

For starters, think about the frequency dependence: the

relevant quantities are (omega L) and (omega C).

Secondly, when you are working with the wave equation for a

coax, you find that the coax has a certain inductance per

unit length and a certain capacitance per unit length.

Thirdly, consider the analogy between an LC circuit and

a mass on a spring. You have your choice of which

electrical variable plays the role of position. One

choice leads to 1/C playing the role of spring constant

in the potential-energy term. Another equally reasonable

choice leads to C (not 1/C) playing the role of mass in

the kinetic energy term. The equivalence of these two

choices is an example of a contact transformation; for

details see any generic classical mechanics book.

====

Inverse resistance shows up a lot, and has its own name

(conductance) and its own unit (mho) and symbol (G).

Inverse capacitance shows up quite a lot, but AFAIK it

has never been honored with a proper name, conventional

symbol, or unit. Folks just call it inverse capacitance.

Yes, you need inverse capacitance. But you need capacitance

also. Neither is going to supplant the other, not in a

million years.

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