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Class notes #3
Ohm’s law
We have discussed the nature of conductivity, and we described three classes of
materials, conductors, semiconductors, and insulators. As you might expect, this is
something of an oversimplification. For example, not all metals conductor equally well.
This is due to the probability of the electron being scattered by collisions while traveling
through the metal and is very different for the different metals. Similarly, insulators are
not perfect, and a few electrons can slip through them, helped along by impurities or
unlikely probabilities. So we need to describe conductivity a little more precisely.
In 1827 Georg Ohm published an empirical rule that defines conductivity. Much later
with the discovery of quantum mechanics, it was found that Ohm’s law depends on the
statistical probabilities of electron motion and holds only on the average. Real resistors
are subject to random electron motions, not described by Ohm’s law, that introduce some
random error or
noise
in the circuit. This resistor noise is small and we will ignore it in
this course. Despite the fact that Ohm’s law is only a statistical approximation to the
underlying
quantum
mechanics,
it
works
very
well
for
different
materials
with
conductivities that vary over a range of 25 orders of magnitude (i.e. a factor of 10
25
). We
will use Ohm’s law in the following form:
where
V
is the voltage across the resistor,
I
is the current through the device and
R
is the
resistance of the device. Resistance is thus defined to be:
We find that resistance has units of volt per amp which is used so often that a derived unit
ohm
was created to save us from having to constantly write ‘volt per amp’. Probably
because of the similar sound, a capital Greek letter omega (
Ω
) is also used to signify the
ohm unit. In electrical engineering, it is more common to discuss resistance as opposed to
conductance. The two quantities are related with conductivity being the reciprocal of
resistance and having units of amp per volt or the
derived unit
siemen
(S). The term mho (ohm spelled
backwards) was once used as a unit for conductivity,
and is sometimes still seen.
Ohm’s law requires that the voltage and current be
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 Fall '07
 Westerfield

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