Re: Series, Parallel, and Resistivity Equations

["John S. Denker" <jsd@MONMOUTH.COM>]

Larry Woolf wrote:
> I like the pinball machine analogy best.  ....
>
> Balls - conduction electrons
> Pins - scattering centers in a solid
> Slope of pinball machine - electric field
> Height difference of back and front of machine - voltage
> Horizontal length of machine - length of resistor

This has the advantage of
 -- being a constructive suggestion, and
 -- capturing the basic physics correctly in considerable
    detail.

The only problem is that it doesn't answer the
question.  It doesn't produce Ohm's law.  You
have separate control of the voltage (the height
difference) and the current (the rate at which
you inject pinballs).

In some sense, that's because the pinballs aren't
charged.  They don't repel each other the way
real electrons do.

But there is still a lot of virtue in this model.

Suggestion:  Lay the model flat and populate it
with a pretty significant number of carriers.
Then suddenly tilt it.  Watch how many carriers
tumble out the bottom.  Do _not_ watch what is
happening at the top, because the model does not
correctly represent what is happening at that
part of a real resistor.  Cover that section
if you need to.

This models several additional physical facts:
 *) Resistance inversely proportional to
    carrier density.  Current goes up when
    you've got lots of carriers.
 *) Resistance inversely proportional to
    width.  Current goes up when you've got
    resistances (or should I say conductances)
    in parallel.
 *) Electrons in the conductor don't have any
    strong long-range interactions.  Short range,
    yes, but not long ranged.  The metal (or
    whatever) they're moving through provides
    dielectric screening.  (Unless there is a
    Kirchhoff-law-violating gross excess of
    carriers, in which case the model is incorrect,
    as previously mentioned.)