The difference between voltage and potential difference

Transcription

1 Slavko Vjevć 1, Tonć Modrć 1 and Dno Lovrć 1 1 Unversty of Splt, Faclty of electrcal engneerng, mechancal engneerng and naval archtectre Splt, Croata The dfference between voltage and potental dfference

2 Introdcton (1) dfferent defntons of potental dfference, voltage and electromotve force confson wth some basc notons there s a dfference between voltage and potental dfference, dependng on what s or observaton pont statc electrc felds conservatve felds the electromotve force for any closed crve s zero tme-varyng electrc feld s not a conservatve feld the electromotve force ndced n the closed crve can be expressed n terms of partal tme dervatve of the magnetc flx and t s dfferent from zero

3 Introdcton (2) what voltmeter measres, whether the poston of observed ponts or poston of the voltmeter leads affects the voltmeter readngs? transmsson lne model the voltage depends on the path of ntegraton transversal voltage s a specal case of voltage eqal to the potental dfference electrcal crct analyss branch voltages are nqe and eqal to dfference of nodal voltages (nodal potentals)

4 Statc felds (1) statc felds do not change wth tme the smplest knd of felds electrostatc felds prodced by statc electrc charges statonary crrents assocated wth free charges movng along closed condctor crcts magnetostatc felds de to moton of electrc charges wth nform velocty (drect crrent) or statc magnetc charges (magnetc poles) the electrc feld generated by a set of fxed charges can be wrtten as the gradent of a scalar feld electrc scalar potental φ E E electrc feld ntensty electrc scalar potental

5 Statc felds (2) nqe voltage B can be defned for any par of ponts and B ndependent of the path of ntegraton between them B B E d ; B C Stokes theorem Maxwell eqaton for statc electrc felds: C E d E 0 S E ds 0

6 Statc felds (3) the work done on the partcle when t s taken arond a closed crve s zero, so the voltage arond any contor C can be wrtten as: E d 0 ; C C

7 Tme-varyng felds (1) can be generated by accelerated charges or tme-varyng crrent db B E v B Maxwell eqaton for tme-varyng felds dt t v relatve velocty beetween magnetc feld and medm B magnetc flx densty B - magnetc vector potental E v B t the electrc feld ntensty for tme-varyng felds E E stat E nd total electrc feld ntensty E nd E stat Etr Em v B t

8 Closed crves: e ndced INDS 11 & ISTET 11 S. Vjevć, T. Modrć, D. Lovrć Tme-varyng felds (2) E d E d E C electromotve force C stat 0 C nd d ee for any contor C, voltage s eqal to ndced electromotve force e: C C e E d E d C voltage and ndced electromotve force depend on the ntegraton path transformer electromotve force, e tr, can be expressed as negatve of partal tme dervatve of the magnetc flx Φ throgh the contor C over the srface S : etr d B ds t t t C C S nd tr e m

9 Tme-varyng felds (3) Open crves: voltage between any par of ponts and B can be defned as: B B E d B E stat d B e B E d B e nd trb e mb B B e B dfference between tme-varyng voltage and potental dfference s evdent and these two concepts are not eqvalent potental dfference between any two ponts s ndependent of the ntegraton path voltage and ndced electromotve force between any two ponts are not eqal and depend on the ntegraton path

10 C voltmeter readng (1) conventonal crct analyss wthot tme-varyng felds Ohm law and Krchhoff voltage law tme-harmonc electromagnetc feld Ohm law and Krchhoff voltage law extend wth Faraday law the voltmeter readngs are path dependent the measred voltage depends on the rate of change of magnetc flx throgh the srface defned by the voltmeter leads and the electrcal network tme-harmonc electrcal network crrents and crrent throgh the voltmeter, connected between ponts and B, wll ndce a transformer electromotve force: j phasor of thendced electromotve force phasor of the magnetc flx throgh the contor

11 C voltmeter readng (2) Thevenn eqvalent conssts of Thevenn electromotve force and Thevenn mpedance and represents the electrcal network between ponts and B Thevenn electromotve force E T, ndced electromotve force ε, magnetc flx Φ and crrent throgh the voltmeter are phasors wth magntdes eqal to effectve vales voltmeter readng s eqal to effectve vale of voltage on voltmeter mpedance U V U V I Z V Z T ET Z V Z L Z V

12 Transmsson lne model (1) two-condctor transmsson lne model voltage and crrent along the lne: t L R x t C G x n tme-varyng electromagnetc feld, voltage between two ponts depends on ntegratng path transversal voltage s a specal case of voltage eqal to the potental dfference d E dx x d E

13 Transmsson lne model (2) sngle-condctor representaton of the two-condctor transmsson lne of length l, wth nformly dstrbted per-nt-length parameters R, L, C and G: transversal voltages 1 and 2 are eqal to the potentals φ 1 and φ 2

14 Electrcal crct theory (1) s an approxmaton of electromagnetc feld theory that can be obtaned from Maxwell eqatons actve crct elements: crrent and voltage sorces passve crct elements: resstance, ndctance and capactance n drect crrent, tme-harmonc and transent electrcal crct analyss, voltage s nqe and eqal to dfference of nodal voltages (nodal potentals)

15 Smmary only n the statc felds, voltage s dentcal to the potental dfference (de to conservatve natre of statc felds, voltage does not depend on the ntegraton path between any two ponts) n the tme-varyng felds voltage and potental dfference are not dentcal; potental dfference between two ponts s nqe; voltage and ndced electromotve force depend on the ntegraton path n the transmsson lne model the tme-varyng voltage between two ponts depends on the path of ntegraton voltage s ambgos transversal voltage s a specal case of voltage eqal to the potental dfference n electrcal crct analyss voltage s nqe and eqal to dfference of nodal voltages (nodal potentals)

16 Thank yo!