DC electrical circuits

Transcription

1 D elecicl cicuis hpe 8 lecomoive Foce Poenil Diffeences esisos in pllel nd seies icuis wih pcios Beies nd Geneos uen is poduced y pplying poenil diffeence coss conduco (V/). This poenil diffeence is se up y some souce such s ey o geneo. onvenionlly n pplied volge is given he symol (unis: vols). Fo hisoicl esons, his pplied volge is ofen clled he elecomoive foce (emf), even hough i s no foce. Vol s oiginl ey we cloh The Volic Pile Ag Zn Zinc cse elecicl convee......conves chemicl enegy o elecicl enegy on Mixue of Ammonium hloide & Mngnese Dioxide lecicl descipion of ey symol fo ey symol fo esisnce A ey does wok on posiive chges in moving hem o highe poenil. The MF mos pecisely is he wok pe uni chge exeed o move he chges uphill u you cn jus hink of i s n pplied volge. lecicl descipion of ey ey One ls poin: Beies cully hve n inenl esisnce. Ofen we neglec his, u someimes i is impon. uen ound cicui f he cuen poin is Ampee, wh is he cuen poin?... poin c? c

2 The Loop Mehod S ny poin in he cicui. Go ound he cicui in loop. Add up he poenil diffeences coss ech elemen. (Keep he signs sigh!) (using V) So /( ) Kichhoff s Lws Kichhoff devised wo lws h e univeslly pplicle in cicui nlysis:. A ny cicui juncion, cuens eneing mus equl cuens leving (JUNTON o NOD UL).. Sum of ll V s coss ll cicui elemens in loop mus e zeo.(loop UL). n genel Kichhoff s Lws e used in moe complex cicuis. xmple: xmple: ey Fo el ey wih inenl esisnce, wh lod will eceive mximum powe? ey Fo el ey wih inenl esisnce, wh lod will eceive mximum powe? esisos in Seies esisos in Seies V V V V The pi of esisos cn e eplced y single equivlen esiso; one which, given, hs he sme ol volge dop s he oiginl pi. The pi of esisos cn e eplced y single equivlen esiso; one which, given, hs he sme ol volge dop s he oiginl pi. V V V eq We wn o wie his s V eq hence eq

3 esisos in Seies esisos in Seies Given eq, he cuen is /( ) (which gees wih he loop clculion) One cn hen wok ckwds o ge he volge coss ech esiso: Given eq, he cuen is /( ) (which gees wih he loop clculion) One cn hen wok ckwds o ge he volge coss ech esiso: V V esisos in Pllel Agin find he equivlen single esiso which hs he sme V if is given. V esisos in Pllel V Agin find he equivlen single esiso which hs he sme V if is given. Hee he ol splis: V / V/ V(/ / ) V / eq We wn o wie his s: V / eq Hence / eq / / Anlyzing esiso Newoks Ofen you cn eplce ses of esisos sep y sep. Anlyzing esiso Newoks Ofen you cn eplce ses of esisos sep y sep. 6 Ω 6 Ω 6 Ω 6 Ω Ω Ω /6/6/() 5 Ω 5Ω Ω sep sep

4 Find he cuen in he Ω esiso if V vols Find he cuen in he Ω esiso if V vols Ω V Ω Ω V Ω As efoe, find eq fis. Ω V Pllel pllel pllel Ω Ω Ω Ω Find he cuen in he Ω esiso if V vols V Ω Ω pllel As efoe, find eq fis. Ω. Ω Find he cuen in he Ω esiso if V vols V Ω Ω Now use V nd wok ck. Ω Ω V/ V/. Ω 8.6 Α V V Seies V V. Ω Pllel seies Ω pllel. Ω. Ω Find he cuen in he Ω esiso if V vols V Ω Ω Now use V nd wok ck. Find he cuen in he Ω esiso if V vols 8.6 Α V 8.6 Α Ω Ω Now use V nd wok ck. 8.6 Α 8.6 Α Ω 8.6 Α 8.6 Α Ω 8.6 Α V 8.6 Α V. Ω V 8.6 Α V. Ω 8.6 Α. Ω 8.6 Α. Ω

5 Find he cuen in he Ω esiso if V vols 8.6 Α V 8.6 Α Ω Ω Now use V nd wok ck. 8.6 Α Woking ck in seies he cuen is he sme!!! Find he cuen in he Ω esiso if V vols 8.6 Α V 8.6 Α Ω Ω Now use V nd wok ck. 8.6 Α 8.6 Α Ω 8.6 Α 8.6 Α Ω 8.6 Α V 8.6 Α V. Ω V 8.6 Α V. Ω 8.6 Α. Ω 8.6 Α. Ω Volge dop coss he. Ω esiso is V (8.6 A)(. Ω). vols Find he cuen in he Ω esiso if V vols 8.6 Α V 8.6 Α Ω Ω Now use V nd wok ck. 8.6 Α Volge dop coss he Ω (nd ) esiso is he sme s he. Ω esiso, hus. vols V Ω Ω Ω Find he cuen in he Ω esiso if V vols 8.6 Α V 8.6 Α Ω Ω Now use V nd wok ck. 8.6 Α Volge dop coss he Ω (nd ) esiso is he sme s he. Ω esiso, hus. vols V Ω Ω Ω V 8.6 Α Ω 8.6 Α V 8.6 Α. Ω VΩ.V Ω 5. 7 Ω Ω mps 8.6 Α. Ω Volge dop coss he. Ω esiso is V (8.6 A)(. Ω). vols Kichhoff s Lws Kichhoff devised wo lws h e univeslly pplicle in cicui nlysis:. A ny cicui juncion, cuens eneing mus equl cuens leving (JUNTON o NOD UL).. Sum of ll V s coss ll cicui elemens in loop mus e zeo.(loop UL). n genel Kichhoff s Lws e used in moe complex cicuis. xmple: Find he cuen in Ω 5Ω Ω 5 v 5 v 5

6 xmple: Find he cuen in xmple: Find he cuen in Ω 5Ω Ω 5 v 5 v Define/guess cuen diecions nd nodes A nd B. A B Node ule A Node ule B edundn q ns! Thus only use one. Ω 5Ω Ω 5 v 5 v G A D F B Node ule A Loop ule ound ABD Loop ule ound ABFG xmple: Find he cuen in xmple: Find he cuen in Ω 5Ω Ω 5 v 5 v Thee eq ns hee unknowns (,, nd ). We e looking fo..59 mps Negive implies he diecion is opposie fom wh ws ssumed! cicuis: chging cicuis: chging open V V Apply he loop lw: / V / V / When he swich closes, fis high cuen flows: V is ig nd V is smll. As q is soed in, V inceses. This fighs gins he ey nd so deceses. 6

7 cicuis: chging V V / Apply he loop lw: / d Now i s mh polem!, d d () x, dx c e, ( c e Thus, ( ) ( e, dx dx dx () ecomes d, d x x c ln( x ) ln( ), ( c cons. c ), ( ) c e c ( ) ( c e ), ( c ) Boundy ondiion ( ), so ) d c nd of in. ), ( c c ) c ln( ) cicuis: chging V V / Solving we ge: Whee his ssumes h sec he swich is nd hee ws no chge on he AP efoe sec. chge on AP & cuen in cicui. Apply he loop lw: / d e d ( e ) Fom his we ge: Wih he sme ssumpions sec. cicuis: chging V V / V V e ( e ) e e V e / uen Poenil Dop hging / V V / Noe: he plos hve / long he xxis. hs unis of ime! τ, whee τ is he ime consn of he cicui. Poenil Dop / 7

8 xmple: A cpcio chges hough esiso. When does is chge ise o hlf is finl vlue? xmple: A cpcio chges hough esiso. When does is chge ise o hlf is finl vlue? hge on cpcio vies s ( e ) Find he ime fo which / ( e ) ( e e ln( ) e ), e, ln( ) is he ime consn.69 Dischging n cicui Dischging n cicui V V q/ q q chging V o V V q/ q q chging V o V V V q q V o V V q/ q q V o hging cicui, unil AP is fully chged hging cicui, unil AP is fully chged Open cicui, fully chged AP Dischging cicui V V / Afe closing swich Assume swich is s. Dischging n cicui Dischging n cicui Open cicui o o V V uen will flow hough esiso fo while. Powe P V will e dissiped in he esiso (s he) while he cuen flows. venully he cpcio will lose is chge, nd he cuen will go o zeo. Afe closing swich V V / And V V / o e Loop equion: / / e o d o he moun of chge on he AP sec. he cuen in he cicui ny ime fe sec. 8

9 Dischging n cicui Dischging V V / o V e oe V e o e / o / / uen / Poenil Dop V V / xmple: A cpcio dischges hough esiso. () When does is chge fll o hlf is iniil vlue? xmple: A cpcio dischges hough esiso. () When does is chge fll o hlf is iniil vlue? hge on cpcio vies s exp( / ) Find he ime fo which / exp( / ) ln ln (ln ).69 is he ime consn xmple: A cpcio dischges hough esiso. () When does he enegy dop o hlf is iniil vlue? xmple: A cpcio dischges hough esiso. () When does he enegy dop o hlf is iniil vlue? The enegy soed in cpcio is U( ) exp( / ) U exp( / ) We seek he ime fo U o dop o U /: U U exp( / ) ln.5 9