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capacitors notes

# capacitors notes - CAPACITORS We defined the electric...

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Unformatted text preview: CAPACITORS We defined the electric potential difference between two points as the change in potential energy per unit charge, associated with moving charge between those points. To move charge between the two points takes work equal to the change in potential energy. A charge distribution useful for storing electrostatic energy consists of two isolated conductors carrying equal but opposite charges. Recall that moving a small amount of charge from one conductor to the other results in a net positive charge on one and a net negative charge on the other. This results in an electric field and therefore a potential difference between the conductors. (remember that the more charge that is moved the harder it is to transfer more). To make solving the energy stored an important practical case is to use two parallel plates for the conductors. Charging the plates results in an electric ﬁeld between them. (for closely spaced plates essentially uniform, except near edges). From Gauss's Law the ﬁeld is given as A”: 62 = H _ ._ o 60 The presence of the electric ﬁeld means there is a potential difference betweentheplates. : Ed? = -210 ___ [(641 :9 69W: VJ?) Q Q :9 .1 9f w 2. (,0 75 (ﬂ 2 3o J 0 in g (96.0 ’4 , a M : W : 916.4%Q , Where is this energy stored? It is stored in the electric ﬁeld. The work done in moving charges to create or alter a charge distribution alters the electric field. This becomes the energy stored in the electric field. If that work is positive, the new field contains more energy, if work is negative, the field released energy and the new field contains less energy. Every electric ﬁeld represents stored energy. Because electric forces are primarily responsible for behavior of everyday matter, many seemingly different forms of energy storage really involve electric field energy. When you burn gasoline or metabolize food, you are rearranging the charge distributions (molecules) and a new configuration results whose electric fields contain less energy. The energy stored in an electric field depends on the field strength, which may vary with position therefore it is better to describe the stored energy in terms of energy density, i.e. the energy per unit volume. This energy density is a universal expression that holds for any electric field. _ _ 7. _ i Z _ 7. U -RQA — QQHCEGAE) , ﬁQE/QJ a2 Toidmga Uzgcm —. Show =§ﬁeoEZC€V am (QV : {W (goo/0W Capacitor : - are devices consisting of two conductors called plates, regardless of shape, that are charged one positive and the other negative. These are typically used for short—term energy storage, where it is necessary to release electrical energy quickly. In a capacitor a field develops due the separation of the charges, and energy is stored in this field. The amount of charge placed on the conductors is proportional to the potential difference, i.e. _ : ‘ C_Q/V >Q~CV Uﬂle'f‘lE-‘ZUIQCQ C :: 6,613 I F " "Q E915; that the capacitance depends on the geometry, ( the geometrical arrangements of the two conductors), this makes them ideal transducers. A transducer is a device that converts physical quantities into electrical signals. Various applications include capacitive microphones, where one plate vibrates due to sound waves, effectively changing the capacitance, a computer keyboard, where pushing the key changes the capacitor spacing. Contact or even nearby presence of a conducting object can change the charge distribution on capacitor plates, this principle is why touch sensitive elevator buttons work and touch sensitive lamps, etc.... The stored energy in a capacitor can be given in terms of charge and potential, i.e. , Z : _ Z_ M gov— écv — ﬁg Connecting capacitors. there are only two ways to connect capacitors, parallel and series. welcombinations have conductors of like sign connected together, and noting that there is no potential difference between them since all points are directly connected together and are at the same potential. The other plates of like sign are also connected together. Therefore the potential differences across the two components are equal. 0 l . 5L5 v,=v,.—~v.=v.=~~ I 6) “Q J’Gzl'os’L’W @ Connecting capacitors in parallel amounts to adding their plate areas, giving a larger capacitance. Series combinations: have the same charge on each element. til—‘HHF‘L ©5lQILQtl®3TZ 1”, Cl CL C3 \/S:\/’+V?‘+V3+I|ur L J. i 1 -7l 1' + 4~ ,.. :: C, 0 CL c; Z1 C.- connecting capacitors in series, effectively adds the plate separation yielding a smaller overall capacitance. The space between the plates is frequently filled with an insulating material. Essentially all insulators are dielectric‘s (materials whose molecules behave as dipoles). these serve several purposes: 1. they breakdown less readily than air, meaning that much higher voltages may be applied. 2. they allow plates to be brought much closer together 3. the dielectric itself increases the capacitance by a factor of "k" the dielectric constant. C, 2 KC.) “PM C - go lQ/J F : é; 0“ ,. < On a simple View the capacitor ﬁeld is reduced by the induced ﬁeld in the dielect 'c. . r1 ﬁfe/096:9” I L» %’ MALJidJﬂ ...
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