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lecture07

Fundamentals of Physics, (Chapters 21- 44) (Volume 2)

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Chapter 25 Capacitance In this chapter we will cover the following topics: -Capacitance C of a system of two isolated conductors. -Calculation of the capacitance for some simple geometries. -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)

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V + V - A system of two isolated conductors, one with a charge and the other - , separated by an insulator (this can be vacuum or air) is known as a "capacitor." The symbol used to indicate a c q q + Capacitance apacitor is two parallel lines. We refer to the conductors as "plates." We refer to the "charge" of the capacitor as the absolute value of the charge on either plate. As shown in the figure, the charges on the capacitor plates create an electric field in the surrounding space. The electric potential of the positive and negative plate are and , respectively. V V + ! We use the symbol for the potential difference between the plates ( would be more appropriate). V V V V + ! ! " If we plot the charge as a function of we get the straight line shown in the figure. The capacitance is defined as the ratio . We define a capacitor of 1 F / a q q V C C V = SI Unit : Farad (symbol F) s one that acquires a charge = 1 C if we apply a voltage difference 1 V between its plates. q V = q C V = ) V q O q = CV (25-2)
Parallel Plate Capacitor A parallel plate capacitor is defined as a capacitor made up from two parallel plane plates of area separated by a distance . The electric field between the plates and away from the plate edges is A d uniform. Close to the plates' edges the electric field (known as "fringing field") becomes nonuniform. A battery is a device that maintains a constant potential difference between its two terminals. These are indicated in the battery symbol using two parallel lines unequal in length. The long V Batteries er line indicates the terminal at higher potential while the shorter line denotes the lower-potential terminal. + - _ V (25-3)

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-q -q +q +q One method to charge a capacitor is shown in the figure. When the switch S is closed, the electric field of the battery drives electrons from the battery negative terminal to the cap Charging a Capacitor acitor plate connected to it (labeled " " for low). The battery positive terminal removes an equal number of electrons from the plate connected to it (labeled " " for high). Initially the potential dif h l ference between the capacitor plates is zero. The charge on the plates as well as the potential difference between the plates increase, and the charge movement from the battery terminals to and from V the plates decreases. All charge movement stops when the potential difference between the plates becomes equal to the potential difference between the battery terminals.
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