PHY2049_05-20-11

PHY2049_05-20-11 - Chapter 25 HITT An electron moves from...

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5/20/2011 1 Chapter 25 Capacitance-II In the last lecture: we calculated the capacitance C of a system of two isolated conductors. We also calculated the capacitance for some simple geometries. In this chapter we will cover the following topics: -Methods of connecting capacitors (in series , in parallel). -Equivalent capacitance. -Energy stored in a capacitor. -Behavior of an insulator (a.k.a. dielectric) when placed in the electric field created in the space between the plates of a capacitor. -Gauss’ law in the presence of dielectrics. (25 - 1) HITT A. the work done by the field is positive and the potential energy of the electron-field system increases B. the work done by the field is negative and the potential energy of the electron-field system increases C. the work done by the field is positive and the potential energy of the electron-field system decreases D. the work done by the field is negative and the potential energy of the electron-field system decreases E. the work done by the field is positive and the potential energy of the electron-field system does not change An electron moves from point i to point f, in the direction of a uniform electric field. During this displacement: i j This means that if we apply the same voltage across the capacitors in fig.a and fig.b (either right or left) by connecting to a battery, the same charge is provided by the battery. Alternatively, i V q f we place the same charge on plates of the capacitors in fig.a and fig.b (either right or left), the voltage across them is identical. This can be stated in the following manner: If we place the q V capacitor combination and the equivalent capacitor in separate black boxes, by doing electrical mesurements we cannot distinguish between the two. Consider the combination of capacitors shown in the figure to the left and to the right (upper part). We will substitute these combinations of capacitor with a single capacitor eq C Equivalent Capacitor that is "electrically equivalent" to the capacitor group it substitutes. (25 - 9) The fig.a we show three capacitors connected in parallel. This means that the plate of each capacitor is connected to the terminals of a battery of voltage . We will substitute V Capacitors in parallel the parallel combination of fig.a with a single equivalent capacitor shown in fig.b which is also connected to an identical battery 1 1 1 2 2 2 3 3 3 1 2 3 1 The three capacitors have the across their plates. The charge on is: . The charge on is: . The charge on is: . The net charge C q CV C q C V C q C V q q q q C = = = = + + = same potential difference V ( ( 29 2 3 1 2 3 1 2 3 1 2 1 The equivalent capacitance For a parallel combination of n capacitors is given by the expression: ... n e n eq q j j C C V C C C C C C C C V q C C C C V V = = + + + + = = = + + + + + = 1 2 3 eq C C C C = + + (25 - 10) The fig.a we show three capacitors connected in series.

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