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# Re: Definition of Capacitance

Responding to John & John:

I would vote for the converse solution.

I could go for either (C',R,L) or (C,G,L')as a starting point. Either of
these shows a fine level of self-consistency - a major consideration when
evaluating any convention.

Whether or not such a rationalization of the system would help
students can only be ultimately decided by experiment. Does
anyone know of any good experiments that relate to this issue.

Can the experiment be done? Does it need to be done? On the one hand, even
if students after 1 semester do better, you really want to know how they
would do "down the road", but you could never do a controlled experiment
over the intervening years. On the other hand, isn't the self-consistency
sufficient to guarantee that it would be an improvement?

Of course if we are really willing to reform things
then we need to consider Ben Franklin's mistake that
saddled us with + and - because he did not know which
way the charge was usually transferred.

That would have been Day Two of my month's worth of "inconvenient,
inconsistent, or just plain incorrect conventions". ;-)

For starters, think about the frequency dependence: the
relevant quantities are (omega L) and (omega C).

X(L) = (omega L) X(C) = 1 / (omega C)
vs.
X(L) = (omega) L X(C') = (1/omega) C'

The frequency dependences are more opposite than they are the same. The
second seems just as logical and self-consistant to me as the first.

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.
Perhaps it is better not to have these sound so similar.

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

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

Yes, you need inverse capacitance. But you need capacitance
also. Neither is going to supplant the other, not in a
million years.

Certainly, for any ratio that is useful, the inverse of the ratio will also
be useful. But usually, one form is considered standard: rho = m/V, C =
Q/dT, E = F/q. Do you need a name for the inverse of these? Do you need a
name for both Q/V and V/C?

Tim