Capacitors A device storing electrical energy

Capacitor A potential across connected plates causes charge migration until equilibrium VV – + –q+q Charge stored q = C  V C = capacitance Unit = C/V = farad = F

Parallel Plate Capacitance Plate area A, separation d d A Capacitance = A  0 /d  0 = 8.85  10 –12 C2C2 N m 2

Circuit Element Symbols Potential Source + – VV Conductor Capacitoror Resistor

At Equilibrium VV C + – Capacitor charges to potential  V Capacitor charge Q = C  V + – VV

Energy in a Capacitor C = Q/  V so  V = Q/C VV Q Work to push charge  Q W =  V  Q = (Q/C)  Q slope = 1/C QQ area = W

Energy in a Capacitor Work to charge to Q is area of triangle W = 1/2 Q(Q/C) = 1/2 Q 2 /C VV Q Q/CQ/C CVCV Work to charge to  V W = 1/2  V (C  V) = 1/2 C(  V) 2

Combining Capacitors and Parallel Series

Parallel Components All have the same potential difference Capacitances add (conceptually add A’s)

Series Capacitors All have the same charge separation Reciprocals are additive (conceptually add d’s)

Gauss’s Law Electric flux through a closed shell is proportional to the charge it encloses.  E = Q in /  0  0 = 8.85  10 –12 C2C2 N m 2

Field Around Infinite Plate With uniform charge density  = Q/A  E = AA 00  00 1 2, so E = = E(2A)

Infinite ||-Plate capacitor Individually –q 1/2  /  0 +q 1/2  /  0 –q+q /0/0 00 Together

Charge of a Capacitor Parallel plates of opposite charge Charge density  = Q/A – + Fields cancel outside d Potential  V = d  /  0 = d Q/(A  0 ) Capacitance C = Q/  V =  0 A/d /0/0

Parallel Plate Capacitance Plate area A, plate separation d Field E =  00 = Q A0A0 Potential  V = Ed = Qd A0A0 Capacitance Q/  V = Q A  0 Qd A0A0 d =

Capacitor with a Dielectric If capacitance without dielectric is C, dielectric is  C.  = dielectric constant 

Dielectric Parameters Dielectric constant  –Dielectric permittivity  =  0 Breakdown voltage –Actually field V/m