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Re: Definition of Capacitance

• 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

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.