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Re: Series, Parallel, and Resistivity Equations



At 17:43 2/18/02 -0500, David Bowman wrote:
...
The water-in-a-pipe analogy is *not* particularly accurate in terms
of modeling the behavior of electric current in an ohmic resistive
medium. The problem is not with the resistance being proportional to
the path length, but with it being inversely proportional to the
cross section area of the flowing current.
...if we
change our analogy from that of flow through a pipe to that of fluid
flow through a fine porous medium, such as water through a sponge or
filter, or ground water or petroleum through rocks, then the analogy
with electric current is much better. In this later case the fluid
flow is governed by D'Arcy's Law where the pressure gradient *is*
locally (here 'locally' means not quite *so* fine scale that the
medium's manifest inhomogeneity is apparent) proportional to the
current density, and this kind of flow really *is* mathematically
analogous to DC electric current flow through a conducting medium
(at least from the point of view of the macroscopic equations
describing the steady state flow).

David Bowman
David_Bowman@georgetowncollege.edu


As usual, I found David's insight commanding. THIS time,
I found it comprehensible too. You will appreciate this is no criticism
of David's
expositions, but rather of my [lack of] mathematical sophistication.