Summary: Introduction of simple conduction, including the basic ideas and models of conductor.

Our initial studies will more or less be a review of topics in electricity that you may have seen before in physics. However, if experience is any guide, there is no great harm in going back over this material, for it seems that for many students, the whole concept of just how electricity actually works is just a little hazy. Considering that you hope to be called an electrical engineer one of these days, this might even be a good thing to know!

Most of the "laws" of how electricity behaves are really just mathematical representations of a number of empirical observations, based on some assumptions and guesses which were made in attempt to bring the "laws" into a coherent whole. Early investigators (Faraday, Gauss, Coulomb, Henry etc....all those guys) determined certain things about this strange "invisible" thing called electricity. In fact, the electron itself was only discovered a little over 100 years ago. Even before the electron itself was observed, people knew that there were two kinds of electric charge, which were called positive and negative. Like charges exhibit a repulsive force between them and opposite charges attract one another. This force is proportional to the product of the absolute value of positive and negative charge, and varies inversely with the square of the distance between them. Different charge carriers have different mass, some are very light, and others are significantly heavier. Electrical charges can experience forces, and can move about. Since force times distance equals work, a whole system of energy (potential as well as kinetic) and energy loss had to be described. This has lead to our current system of electrostatics and electrodynamics, which we will not review now but bring up along the way as things are needed.

Just to make sure everyone is on the same footing however, let's define a few quantities now, and then we will see how they interact with one another as we go along.

The total charge in some region is defined by the symbol

Since charge can be distributed throughout a region with varying
concentrations, we will also talk about the charge
density,

We know that when we apply an electric field to a charge that
there is a force exerted on it, and that if the charge is able
to move it will do so. The motion of charge gives rise to an
electric current, which we call

It will be helpful if we have some kind of model of how electricity flows in a conductor. There are several approaches which one can take, some more intuitive than others. The one we will look at, while not correct in the strictest sense, still gives a very good picture of how electrical conduction works, and is perfectly fine to use in a variety of situations. In the Drude theory of conduction, the initial hypothesis consists of a solid, which contains mobile charges which are free to move about under the influence of an applied electric field. There are also fixed charges of polarity opposite that of the mobile charges, so that everywhere within the solid, the net charge density is zero. (This hypothesis is based on the model of the atom, with a positively charged nucleus and negatively charged electrons surrounding it. In a solid, the atoms are fixed in position in the lattice, but it is assumed that some of the electrons can break free of their "host" atom and move about to other places within the solid.) In our model, let us choose the polarity of the mobile charges to be positive; this is not usually the case, but we can avoid a lot of "minus ones" this way, and have a better chance of ending up with the right answer in the end.

The electric field will exert a force on the movable charges (And the fixed ones too for that matter, but since they can not go anywhere, nothing happens to them). The force is given simply as the product of the electric field strength times the charge

Note that Equation 13 tells us that the resistance
of the sample is proportional to its length (the longer the
sample, the higher the resistance) and inversely proportional to
its cross sectional area (the fatter the sample, the lower the
resistance). The sample resistance is also inversely
proportional to the conductivity

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