Re: Ohm's Law

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

John M. wrote
> 1. Ohm's law says that the current through a device is directly
> proportional to the applied potential difference.

Well, maybe.

> 2. Ohm's law is not true in general.

Not if you write it that way.

> 4. The resistance of a device is defined by R = delta_V/I

That's unduly narrow.

I think physicists should defer to the electrical
engineers on this one.  In the EE world, resistance
is almost always taken to be
        R = dV / dI

which you can call the small-signal resistance if
you want to remove the last vestige of ambiguity.



If you draw the graph, V/I is the slope of the
_chord_ through the origin, and dV / dI is the
slope of the _tangent_.

R=dV/dI is perfectly well-defined and useful even
if the V(I) characteristic isn't linear.
(To first order, everything is linear :-)
Indeed, if the V(I) curve is nonlinear enough,
you can have regions where the locally-linear
region has negative resistance.  That sounds
weirder than it really is.  It's even useful.
  http://www.tpub.com/neets/book7/26a.htm

=====================

People sometimes grumble that phys-l makes
things more complicated than they need to be.
Obviously dV/dI is more complicated than V/I.
But in the nice linear Ohmic case, the
two expressions are equivalent.  If YOU want
to go beyond the completely linear case, it
is YOUR choice not something the list foisted
on you.

If you've got a non-calculus class, draw the
tangent and call it a "slope" not a derivative.
Or just stick to the fully linear case, which
actually is a remarkably good description of
ordinary wires and resistors.