Capacitors as an energy storage device:

Transcription

1 Capacitos as an enegy stoage evice: It takes wok (i.e. enegy) to chage up a capacito fom zeo chage to (zeo potential to V). V V W ( )V V/C The figue shows a capacito at chage, potential iffeence V (between the plate an the plate). To incease an V, we move a small amount of chage fom the plate to the plate. This euies wok one BY an extenal agent, GINST the electic fiel: EPE WEXT W (one by the electic fiel) ( ) E ( ) V aea of the shae stipe inv vs. gaph

2 Capacitos as an enegy stoage evice: (continue) V V Enegy U aea of tiangle W ( )V ½ V ½ /C V/C To chage a capacito to (, V) fom (,), the total amount of wok aea enclose by the blue tiangle, which is the enegy stoe in the capacito. Enegy U C but CV Enegy U CV

3 3 Example: Paallel plate capacito ea of plates: 4.5m Plate sepaation:.cm Plate chage:.5µc The gap is fille with ai (a) Fin the voltage (potential iffeence) of the capacito. (b) Fin the enegy stoe in this capacito -

4 Example: Paallel plate capacito ea of plates: 4.5m Plate sepaation:.cm Plate chage:.5µc The gap is fille with ai Enegy U C CV (a) Fin the voltage (potential iffeence) of the capacito. (b) Fin the enegy stoe in this capacito.5 (a) V C.99 (b) Enegy U CV / C 9 9 (.5 C F C 4.3 V 9.99 C / J 9 4 (.99 C / J)(.3 V) C) /(.99 9 F).7 J - pplication: Resient Evil? Typical efibillatos have banks of capacitos chage up to ~ V an usually an enegy of up to ~ J is elivee to the patient This means C U/V.4 mf So how o we make capacitance much bigge (appox. 5 )? 4

5 9.5 Capacitos an Dielectics Dielectics ae mateials that can be electically polaize by the application of an extenal electic fiel. Filling the gap of a capacito with a ielectic: the molecules align such that boun chages (that ae not fee to move aoun as chages in a conucto) evelop at the suface. ε E o The inuce suface chages (opposite in sign to the chages on the plates) euce the actual electic fiel insie the mateial. Note: ielectic ia-electic; ia means against (Geek oot) The facto by which the applie fiel E is euce (to E), is calle: THE DIELECTRIC CONSTNT Fiel in absence of ielectic Dielectic constant κ E o E Fiel in pesence of ielectic E E o κ 5

6 9.5 Capacitos an Dielectics The Effect of a Dielectic When a Capacito Has a Constant Chage n empty capacito is connecte to a battey an chage up. The capacito is then isconnecte fom the battey, an a slab of ielectic mateial is insete between the plates. Does the voltage acoss the plates incease, emain the same, o ecease? ε E o Electicfiel in ielectic ( κ > ) : ishel constant E is euce E σ E κ Potential iffeence between plates (iviing out ) : V E V is euce by a facto of κ Paallel plate capacito C fille with ielectic V C inceases κ - fol C κ C E E o κ 6

7 7 Example: Paallel plate capacito in a efibillato (note this is both a high capacitance ND a pecision application) ea of plates:.m (4 x4 : fits in the enclosue) Maximum potential: V. 3 V Maximum enegy stoe: U J The gap is fille with BaTiO 3 (baium titanate) : κ5. 3 Fin the euie plate sepaation an the capacitance C -

8 8 Example: Paallel plate capacito in a efibillato (note this is both a high capacitance ND a pecision application) ea of plates:.m (4 x4 : fits in the enclosue) Maximum potential: V. 3 V Maximum enegy stoe: U J The gap is fille with BaTiO 3 (baium titanate) : κ5. 3 Fin the euie plate sepaation an the capacitance C U CV V V U 3 (5. )[8.85 C V /(N m )](. m ( J) )(. 3 J/C) - C C. 6 m.μm 3 (5. )[8.85 C /(N m 6.x F.398 mf )](. m )

9 9.4 Euipotential Sufaces an Thei Relation to the Electic Fiel n euipotential suface is a suface on which the electic potential is the same eveywhee. In this case they ae fo the point chaeg potential V k The net electic foce oes no wok on a chage as it moves on an euipotential suface. The euipotential sufaces ae analogous to the contous (cuves on the bounaies between iffeent colos instea of sufaces in this pictue) on an elevation map such as this (V is analogous to height) 9

10 9.4 Euipotential Sufaces an Thei Relation to the Electic Fiel The electic fiel ceate by any chage o goup of chages is eveywhee pepenicula to the associate euipotential sufaces an points in the iection of eceasing potential. Euipotential sufaces ae typically awn at eual intevals The electic fiel is always pepenicula to the suface pof a conucto: Conucting sufaces ae euipotential sufaces! (the whole conucto is at the same potential) V k

11 9. Electical Potential Enegy Total Potential enegy of a system of point chages We stat with thee point chages:,, 3 k U EPE of i, j U ij k i ij j U U U3 U 3 k U U 3 3 k 3 3 The oveall potential enegy is the amount of wok euie of an extenal agent to assemble this set of chages this can be one in iffeent ways, fo example: (a) Bing in fom (no cost), W (b) Bing in fom : W U (c) Bing in 3 fom : W 3 U 3 U 3 Total W W W UU U 3 U 3 Can o this in any oe an obtain the SME esult Extening to N point chages k N i i j U i j ij j i k i ij j Thee ae N(N-)/ istinct pais