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Lecture 6 02-0410 with notes

# Lecture 6 02-0410 with notes - Lecture 6 February 4 2010...

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Lecture 6 February 4, 2010 Capacitors

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Consider a spherical conductor of radius R with charge Q. Where is the potential equal to zero? 1 2 3 4 5 0% 0% 0% 0% 0% 1. At the center of the sphere 2. On the surface of the sphere 3. Depends on the size of Q 4. At infinity 5. We are free to set V=0 anywhere.
Key concepts Capacitance of two isolated conductors Capacitance for some simple geometries Methods of connecting capacitors (in series , in parallel) Equivalent capacitance Energy stored in a capacitor Capacitor filled with dielectric materials Gauss’ law in the presence of dielectrics (25 - 1)

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V + V - A system of two isolated conductors separated by an insulator (this can be vacuum or air) one with a charge and the other - is known as a "capacitor" The symbol used to indicate a capacit q q Capacitance or 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 the positive and negative plate is 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 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 / s q V q V C C SI Unit : Farad (symbol F) one which acquires a charge = 1 C if we apply a voltage difference 1 V between its plates q V q C V (25 - 2) V q O q = CV
A capacitor is said to “have a charge Q”. The actual charge on its plates are: 1 2 3 4 5 0% 0% 0% 0% 0% 1. Q, Q 2. Q/2, Q/2 3. Q, -Q 4. Q/2, -Q/2 5. Q, 0

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Parallel Plate Capacitor A parallel plate capacitor is defined as 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 uniform. Cl A d ose to the plates edges the electric field (known as "fringing field") becomes non-uniform. 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)
-q -q +q +q One method to charge a capacitor is show n in the figure. When the switch S is closed , the electric field of the battery drives electrons fr om the battery negative terminal to the cap Charging a Capacitor acitor plate connected to it (labeled " " for low). The battery po sitive terminal removes an equal number of elec trons from the plate connected to it (labeled " " fo r high). Initially the potential dif h ference between the capacitor plates is zero. The charge on the plates as well as the potential difference betw een the plates increase, and the charge movement from t he battery terminals to and from V the plates decreases.

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