Lecture09_Kim

Lecture09_Kim - 2/8/2012 1 Lecture 9-1 ( Ideal )...

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Unformatted text preview: 2/8/2012 1 Lecture 9-1 ( Ideal ) Parallel-Plate Capacitor (Review) b b a a V V V E dl Ed =- =- = a a 1. Put charges +q and q on plates of area A and separation d . 2. Calculate E by Gausss Law q E A = 3. Calculate V by 4. Divide q by V a b q q q A C V Ed d q d A = = = = q is indeed prop. to V C is prop. to A C is inversely prop. to d 5. Energy stored (Q=q) 2 2 2 1 1 1 2 2 ( / ) 2 Q Q Q U d C A d A = = = Lecture 9-2 Capacitors in Parallel Equivalent Capacitor: V is common 1 2 3 1 2 3 q q q V C C C = = = eq q C V = where 1 2 3 q q q q = + + 1 2 3 1 2 3 1 2 3 1 2 3 ( ) eq eq C C C C A A A d C A A q q q V A A A d + + = + + = + + = = + + = A C A d = Lecture 9-3 Capacitors in Series Equivalent Capacitor: eq q C V = where 1 2 3 V V V V = + + 1 2 3 3 1 2 1 2 3 1 2 3 1 2 3 1 1 1 1 1 eq eq eq C C C C d A A d d C C A V V V q A A d d d d d d d d = + + = + + = = + + = + + + + = Consistent with parallel- plate capacitor result of 1 1 A C d d or d C = 1 1 2 2 3 3 q C V C V C V = = = q is common Lecture 9-4 Summary The equivalent capacitance for n capacitors in parallel is The equivalent capacitance for n capacitors in series is 1 n eq i i C C = = 1 n eq i i C C = = 1 1 1 n i eq i C C = = 1 1 1 n i eq i C C = = = = 1 2 3 1 2 3 eq A A C d d d d d d d d = = + + = + + 1 2 3 eq C A A A A A d = = + + 2/8/2012 2 Lecture 9-5 Capacitors with Dielectrics So far, we have discussed capacitors with air or vacuum between the plates. However, most real-life capacitors have an insulating material, called a dielectric , between the two plates. The dielectric serves several purposes: Provides a convenient way to maintain mechanical separation between the plates Provides electrical insulation between the plates Increases the capacitance of the capacitor Lecture 9-6 Parallel Plate Capacitor with Dielectric Placing a dielectric between the plates of a parallel plate capacitor modifies the electric field as (decreases) Placing a dielectric between the plates of a capacitor increases the capacitance by (dielectric constant)...
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Lecture09_Kim - 2/8/2012 1 Lecture 9-1 ( Ideal )...

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