Re: Definition of Capacitance

[John Clement <clement@HAL-PC.ORG>]

I would vote for the converse solution.  Go with conductance and then define
an inverse inductance (outductance?, niductance?...)
The then means that the quantities are related in a simple way analogous to
position, velocity, acceleration.

The quantity capacitance has a very easily pictured meaning as the amount of
charge for a given voltage.
Similarly the conductance is also easily pictured as the amount of flow of
charge (current) for a given voltage.  This also makes it correspond to
experiments where students vary the voltage and measure the current.  It
might make teaching much easier.  Resistance is probably conceptually a much
harder concept.

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.  Then we could help students
conceptually because the current would be in the same direction as the
electron flow.

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.

John M. Clement
Houston, TX

> We, as physicists, often seem to be stuck with various conventions and
> definitions.  These conventions are often not the most convenient or most
> logical, but once they get ingrained, they seem almost impossible to
> adjust.
>
>
> 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)
>
> 2) Similar geometry (at least for "standard" geometries):
>   C' =    (1/e0) l/A  (l = length; 1 = one)
>   R  =     (rho) l/A
>   L  = (mu0 N^2) l/A
>
> 3) Similar addition rules:
>   For all three - in series, you simply add values
>                 - in parallel, you add inverses.
>
>
> I can't think of a single case where this definition is inferior (except,
> of
> course, for historical inertia).  Think of all the time and confusion we
> could save our students.  Now we just need to hire a good ad agency and/or
> grease the palms of a few textbook editors ;-)
>
> Tim Folkerts