Van,
As one of my professor used to say "Ohm's Law is a bad law because
it works for a limited class of materials over a limited temperature range,
but it is the foundation upon which electrical engineering is built."
Historically it wasn't even Ohm who first discovered it.
Among others Henry Cavendish was measuring the resistance of salt
solutions almost a century earlier. He used Lyden Jars for his source of
"current" and his own sense of the intensity of the shock to get the
potential. He charged matching Jars to same potential and then changed the
length of the path in one solution relative to another until the shock felt
the same. Won't our students love this for a lab. Comparing his results with
this setup with modern calculations show he was capable of measuring
relative resistance to within about 5%.
As a law it is very comparable to Hooke's law. But also the other
relations we have in electricity. As Ludwik like to point out Q = CV as a
definition of capacitance isn't that good a definition either, and the
definition of inductance is much worse as real coils have both measurable
resistance and capacitance!
As a bit bordering on heresy, all laws in physics are generalization
of things that look to be true, but can't be proven. Some of them are more
"true" then others, but the game we are constantly playing in this field is
to stretch them as far as we can and see were they fail. My favorite
definition of science is that it is the search for truth and the distrusting
of it.
One last note: electrical engineers like to define resistance as:
R = dV/dI. Thus avoiding our whole problem.
Gary
Gary Karshner
St. Mary's University
San Antonio, Texas
KARSHNER@STMARYTX.EDU