notes%203 - Class notes #3 Ohms law We have discussed the...

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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, semi-conductors, 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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notes%203 - Class notes #3 Ohms law We have discussed the...

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