325_Sp2011_7_Capacitors

325_Sp2011_7_Capacitors - 7 Capacitors EE325 Mikhail Belkin...

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© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin 1 7. Capacitors EE325 Mikhail Belkin

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© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin 2 Capacitors Ceramic disc capacitor Electrolytic capacitor Electrolytic capacitor, inside Coaxial cable (we will need to know its capacitance per unit length to calculate signal propagation there)
© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin 3 Conductor/vacuum example: parallel plates consider two conductive parallel plates that are much wider than the distance by which they are separated assume we have charged these two plates, top plate with –Q and bottom plate with +Q pretty much all the charge will be on the inside faces of the plates ρ surf ~ Q/plate area conductor conductor + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - d ε o gaussian surface S = ρ surf · S D = ρ surf E = ρ surf / ε o D = ε o E gaussian surface, no charge inside S = 0 D = 0 E = 0 surface Q A ρ =

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© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin 4 Conductor/dielectric example: parallel plates now what happens if we carefully add a slab of dielectric that completely fills the gap between the plates? assuming there are no other connections to the outside world, the charge on the two plates does not change so D does not change since ρ surf ~ Q/(plate area) did not change but E DOES change, in fact it is REDUCED by ε r compared to the original value with “vacuum” ε o : E = E = ρ surf / ε o with dielectric: E = ( ρ surf / ε r ε o ), REDUCED as expected conductor conductor + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - d ε r ε o gaussian surface S = ρ surf · S D = ρ surf E = ρ surf / ε r ε o D = ε r ε o E surface Q A ρ =
© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin 5 Potential difference between the two plates integrate between bottom and top notice that here the ratio of charge to voltage is a function only of geometry (plate area A and plate separation d) and the dielectric constant ε surface r o E ρ ε ε = A surface AB B r o r o Q d V E dl d A = = = r r surface r o A AB B E dS A Q V d E dl ε = = r r r r

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© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin 6 Capacitance for two oppositely charged conductors the ratio of charge to potential difference is the “capacitance” of the system the capacitance is a function only of the geometry and the dielectric constant(s) measured in farads [F]; [F]=[Coul/V] surface A AB B E dS Q C function of geometry V E dl ε = = = r r r r
© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin 7

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325_Sp2011_7_Capacitors - 7 Capacitors EE325 Mikhail Belkin...

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