Week of October 15th

Week of October 15th - Class notes for the week of October...

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Figure e - Figure e - e - a) b) c) -- -- + e - Figure Figure Class notes for the week of October 15 th Capacitors Consider two parallel metal plates that do not touch. Like most things around us, we can assume that the metal plates have an equal number of protons and electrons so that they are electrically neutral. We know that electrons are mobile in metals, so let us consider what happens if we use our very tiny tweezers to grab one electron from one plate and place it on the other plate (Error: Reference source not found). We are moving charge through space; the one electron carried by our tweezers represents a very small current. Clearly, after moving the electron from one plate to the other, it is no longer possible for each plate to have the same number of protons and electrons. One plate will have one too many electrons and the other plate will have one too many protons. This will establish a small electric field between the two plates. So now we have used a small current (the electron in our tweezers) to create a small charge between the plates. If we go back to grab another electron, we will notice that we will have to do some work against the electric field when we move the electron from one plate to the other. When we have moved the second electron, the field will be stronger since now one plate has two excess electrons, while the other has two excess positive charges (protons). With each electron we move, we must do more work against the stronger electric field (Error: Reference source not found). All that work we are doing is not lost, it is being stored in the electric field between the charged plates. We recall that the work per charge is the voltage. With this in mind the equation describing the capacitor makes some sense: . Where Q is the charge stored in the capacitor (the charge on an electron times the number of electrons we moved), V is the voltage across the capacitor and C is a characteristic of the capacitor. The parameter C depends on the area of the metal plates, the material between the plates (if any), and the distance between the plates. The equation tells us that the voltage increases with each electron we transport. KCL and capacitors We have studied Kirchoff’s current law KCL. It states that the sum of currents into a node is zero at every instant. This idea of grabbing electrons with tweezers seems to violate the principle of Kirchoff’s current law. Let us look into the method of conduction through capacitors a little further. A little cartoon, Figure , will help explain the situation. In a) we see an electron entering the capacitor from the left. In b) the electron has arrived
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This note was uploaded on 09/26/2008 for the course ESE 123 taught by Professor Westerfield during the Fall '07 term at SUNY Stony Brook.

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Week of October 15th - Class notes for the week of October...

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