STG A a ae 4 — Dic Circults WIT! = @ sci euicetie * ‘ Electrical circee(t sy an ondeveenncl® basic Cireutl ehomen Ces or, © pacrt¥ com inolucky) : Cinol tnevga Aouyces Cuege 7 ven, as Paste cowrh anents 9 a netwrtk !- Civeurt eLemonts are g fom type - Active ¢ Pawlye elements ' Aetive Element = Elena ents fy fewrce whieh pe eee ae ; : ve the ofeyi'ces are cape tle 9 elefiverting gd 4 Lye elements cetive elements: G energy to the Connectacl acKov them wre calle These edomenti Ure basic Aovree : octive elemenb- cixeutt There ore uso type 4 Cenerag pources) =~ (1) Vattage source ai ) Cunsent AOUrte: ale furdéer Lassi fret into ; * These Aources } as ces incle perolent sources £ bape tee ieal ae) (a) Indepenslent ust a pease 27 Eneryg Aource In ahi fermrnet yellage tv? 15 incl epenclené g te iy 7! flowir She he circuit Jermival cuvyent + vottag= Hematas const fs an value 4 bool ste si ybenee Rkome a v cea De Weltane Source a) syne “a representation bh) v-ic axacter ses G) 7 igs enslenf_coorrent source: £ner dourre ockicd, oledivers Q cons tan€ eee rae a) oes ts famines nelepenclert q the vettege Sy? acwots / The, duBut current semalts constant £o eal vake 9 Qoad resistant Ri | Dc sunsrent Soeace ; el | @) rc (b) V-1 choractenstres | presabndo sources: — Sources ushese | ie tereeeeee : Defenclent oY ContaTleol De : output usttoge oY curtxent olepencl e/fhey §0 ! yeltage ov enka 8g ang other element ro fe ciccark 1S collect a deperstert Bowce Be ane class firel jrlo Gow types @) Vetleze alepordlert Votdage Aouree &) Vottee “feperslent Carctent doure A ependent voltage Source (©) Ca td) Cunsent ls endent pee/ Wete Depend Biden Vetter Soumce. © Vadue 4 Usage 2, f Roumce js olefenclert on the vette nots an element, jie, he value Q a ddwice ss Q function g ve7teqe ulegs defencl ent voltage Aovre€ j Vx Ve the clep enclent vara le & k's 4 contdant ki (b ) Mehdage olehedent Curgrent Bouse ce!- Cu Hoven? depp phreol bg Ke Aource IS a function Qvea e a Value 4 BOuree defencls 60 Vige ky Vy ba aa e wat « cenenl s is frac Y e JSOUrCe’ ce depends om He fey value ? cur coe Value 9 the. ol efenclent Aout cartent rae an element; usttege ooure e a qunction 2 ks bx() Current eb erent cunstert AouHce * ( Sak Vad oleBenelent ASOUnCE aleperoll on fe value g c h arctent Horough a9 element, f.€y cartnent pounce 1S 4 forelir J own nent: ky dx 2) Pasctve Efements: The elements ahich canni leLiver powen anol can ont creeive The fou hes axe & ane knoum v passive elements three fgper~ / Cl) Resist CR) OV Tn che ctor, C4) Li) Cop oD) Resivte :- Té fs a bane circerl con fore tL urticd provider nes leFance fo fe circa: Resivlane rs 6 pnpeorty 9 ger sP8Y ey comes ofesi tice to the for @ cuHnent’ Lt ss also Teined cs an clement which, HMPA 8 GE in +e fam J heat uben edectare caret Save Krew? itm hep Vpaase 9 fee sre sts ter oleferots M motertad and shape q fhe concl uch: Rik o park a a fhe conoluchy dhe con eee * He conucrs - acter © A- ke 9 A- anea 9 cnogs-sechan 2 - Spee nesifance x Aexi'rfivity 9HOsi ee ner is hms Cn) @ clef neof ar The net/rdence Youd b he when a cat rort gd one am pene Lows — Unt 1 Ohm rs moter rat hod — - fev Cevninals with one vot apptien/ st | R MM" toy = IR (6hm's lou) Ki hen eusineat J rs passed Jhn ough a mesishs, @) Veith © usp anise Is ae by, V=TR- &) Power toss iy fhe qn 9 heal i's ae bp, P=I'°R Also, Enewgg = Power x Time be = TR xt = ae t al Pe wy) Indu : Tt is a civear€ ebement etic &foues energy in dhe gam nobit Gickl UShen a canyent iS pasxeol prong it: Jhe powperhy the inductsr by ahich it Atortes “ner ina magnetic yield is calledd Faabete ott E) U Sg se oS F—__. | +YOT Crit 2) inchachre vade uy veld IS Hen gee ee d \- jrduced! vot e dijab gale geht 9 conven plat pole f charge 9g coeyront@) ‘inductance ls Qne Heorg if an wductsy © indluces a vSHsge 9 one visit, usken He wn Lac ough the coll cs va rering ot Ke rate g Ampere pew Se concl: Enevga stor eof in an Induckoy Maple? Joules eS yp = 2k TY Cafecrtse ha baric circuck com foo ent hih abner ere in the Gaim 9 elects otetie ene uke ot Ss applicof Kertett (E re gory " fg EY BPH 29°F . " ‘ “ - cay ‘e cifanre H 7 Sa ae dead eobel By called! captor st Gs —A = NV bd dv oy fo et amfere dt € dee L = cunnent Brough the capac lv Jolt = yale Q charge 9 ysl ge c- capacitance - dhe inal cA, Enavey shoved in Th — 2W Wet ev® woh C= oe Prep aieo! beeT BNE thea, Arrakyss Single circents cor Do Lxeilation * Kirche & Carrent daw (ecw) ae daw Ataler Kal “Uo Sam g cansent Cnlorting Into 7 hoote 1 oguad to dum g ARs cunt yreah Pewier'n that hovole P c a ced bkon bo ov mone betanckes ane in bercom : \ at is Vn any Proll circuit, Hho jurcton or ‘ | | | the noole- | z+ Ty Coonsral eri» rcoleP T/+t,+T, -Tyth + 7, => Tj t4t4~Ty7 Fee a~ * Kirchhey's VeHsse Low ve) : ¢ This flow states thet “dhe algeb nar eon § all bnanche vitages anourol any clereof \ Leop (path) In at circea't 1g aloes aides od alt intslands g baie MI % eM, ~My oe EO NaN EVES + VG The bum 9 vel Fage ofn Bertone Be fests will be aquel to the af velheg © 7o or heop Hebe thn’ aid, Vi = ER, 5 v, = FR. Ng = TR Vy = T Ry From Kirchhoff S veHtaye glam » | VeV, VY, 4V3 tVy | v R, tZR, IRs +I Ry CA, +R +R; + hy) : Vv Z Tt Woy 7 = 2, + Rithy Ry8 Woo ch peaitts - VAIT-} oO ph, ee ee? ee ies 1 : A Ooghk era iu Peete eet eh “. 4 1n fhe cfigune: , ty ae Aook,; PPoyin Kv to deh OL); CABEFAD; ~4¥T, —26-)0CI,-1,) +20 7° ne tas =o Tare hy Bee Oo I9L, +lo0 I,-s = © [i =teh =75] ~© Ppplging kve to Lop); CacdEB), pee alent ca Ty, tioCLi- Ta) +27 =o -—G I, -16 -e2, #10T,— 102, +29 = Jol, -242,+/0 = 0 [ie a, 24 ae - 10 ( -@ pee OFLA, TSS OREM =— Nr =|- oA acne eu7A JOS — 0:27 fe eae Ak = -0°ORYFA, J, 20-3814 Carinind frvagh ciffererd nesithos : FAD oenyTA Jou =>- OH EIA Gr Do-ssiya Su Dorryan© Determine Vv, 2 Vv, Jo the cireu't: dowp BCDEB, Lowp AGHCBA, T, =o -2¢(2,-Z,) +2 C4,4+43) +222 —) 21) +2T, +272, +27, 4272 =° —2T,4+6T,+21,=0* [B=6A; * Volage vy Ive i rf, =-3A 2, =3A, 43 = 2 / = 2(1,-1,) = 2 (6-3) = cv | Vetteae Vy = 201, 4%) 2 (6+C-3) ulSits ~ 5? Fad the powes Aupphied by Aigfgere® G Beanees aid Wel anol RVE equations. GA “Pray Ket ak hoole a, i + / ae, =O. “flava ee 21 Va-V, = oes) —— © kd C Kel at hkooleS - Vp -Va HH + fem Mewes Ve #3 2) gis re i ieee + +3 = 6; 21 ar 2 cS 7 a a Se eo V SNe aS ee F aLLe DP 00rVa $0-69Y, OVW ve = -o12| © Applying Kee at Kole c T J L, #8 I+i,t Ly = e-Ve-3] 4 Ve + (-0) =0 } 3 me +¥e feet] =3 +6 SN [a a] 5 > [-ol4V, to-4eve =643( —-@ Selvin equation ®©,© 40) . 2/332 Va = - S824 V5 Ves -0' 29% Maley * Power Sxpplied bey 4A captert source | ie = (V8ttape ACOs ef) current Bourne) x4 | = (Na - drop across 2A)X¥ Cpeva)) = [-36-24 — Crx2)] x4 \ ' * Powex Sepp eof by 4NV vsTtsse source Iny = ¥xty Cv P=va)2) “4x [0:24 +35 2944 TT 21 [By | Pow Owe nt Splice bg CA Cugnect Source) Ney =e Va )* 6 Copevt) =(13-32 438-24 )*6 * Powen opted bey 3Vv vettage Source) hy =3x Cops vt) eax [Merve 2) 2 =54] cate Soe 7 > Pay = EX — ae Psy = -9S2W + Powen meol bq IV vo7Hege Source j Ey cae C7 Pe vi) =f » f= 13) 2 Spe 2 j= Gos ® z [iy = 2620] | . 78a UNIT-/ a Senies Resistive circus: ———— © Sree eee, * Exprvessro of stad mpafieielance mesistaree gd SOmes civcurts— R, Ro Rp Rr Vs Hye dusp acnoss fie neprdences, M=TR, ane TRa, %=IRs---™“ =IR, P pplyina Kv, VeVi 4M) #V34---4Vn Equivadent Circentt = x I Reo =IR, +IR,+TRat ---7R Reg iieneanneninnsastn# oo nenene : PR = Rh test hl * Panalted guesistive chrceuits: * as total equivalent ctrcecd nesi ance a parallel tel civceit:- {PEERweg at ness porcolted cennecteol neti will be same; the cuset ert Brougs tke oo ane Aa by; S v 7,-M 7 =¥ ee ee > rR, ? Rg? R3 Rn A cetrshing fo Kel, alge Srar'e Aum Dia, 43, Soe nD St On te eae Equivalent Circart:- HI : M+ z ee Divino sues Pade: - 7 Wan lage lon ee genres elect bie: cireet. i ane oo kro Consrcley 7 em winds co han each wen ses L/h eneas ver eV? 7s ao at cach nesses Hence, Senier ceul © asa voltage Ai urelenee Rep Res =R, +R, +R; + Ry + Re i: Vv So Oise a SE aE EE Ry Ry +R +Ry tks Alow, vites « pole ere eel MS DR, |= weoRi Ry +Rat Ry thy ths SmiTar ly, eo ee Ry thy thy + HRs it geteaaieh arate tate Ry +R, ERs thy HRs Nee eV pee RAR, Rg ARE ARS MG SS eee een R, +R, Rs thy ReCurvent Divinin Rude This is used aie aCerny ne the value 4 eS Ww Vartous Gana chen fhe ciyeet: Here use ( electvcad circ et’ consicley 4 paralte Ty = a Totad current , re ee ey = Billa) = Ro RFR Ri R, py ® Substinctig the value 9 Vv yrem es nO, e9n® freon 2 T)Ri (Arte) Sonat Ga RiRaa Binary © p, = Tae vee Rit i, @) Loy he ci oY che cigeull calculate, the cumank in Vast 10ud sbrer ches Rep = 34 Cella) co 5.55% ae Trtal cworert, + * ar sss Cuanent Tm resort] 12 aoe = 45-06 xe ytt u ) = )6 39 A e Seen ye nes ett, =J-I, = 45-06-1639Q) Use the dechni gue mesh ano bys's fo evaluate the fhnee unknown mesh Carrer Bkown in figure (t,4h) & : ae 2 D . © Ca4 tt Ts) bn & = E A ppying Ket at cole a, > — - ge @ T,+2,+% °° => 1,+5,%7 7 4f,--?}/ —@ I, +k; oe Ln Bac DHB, Apply! J Kv -2(1,+2,)+31,~- 22 = & SU ti Foi, 212-9" A ppAging kve for the Super mesh ABHDE FGA) se € apply Doe Ig eo fa ae O Segermerhe Cen) Pa 1-64slving 9-0, OO; ee [hi =9a, T,=-¢'SA} Jy -o cA ee ent cuvyent Hreagh |mesh! D> FT, = GA° Merh 2 DCI 41, ) 275% (1444) =2A Q) Fine! the corvrent Hiro cava nestle In the circuit given: Vp 3a 2 8 lea By H + qT, ae Bun “ lon Tiov Paplying KCL al poole A) Dye Ds Se. 3 2 0°833Va -0'S¥a =! -Q@ neele 8) Applying koe al super (ts=%*) Va +6 ( ‘)* 0 2 2r ~orsVAthe Vat OTe = 2 -@ y Apply ing Kye ge oP O aed ep peter Ng Vola oo: = 3) Sélving ans 0, © 1@3 Current {lowing through sun nests hy = V_.-/0 i = 84/910 -—-3.686A e s Ton = 36869 @) Find He vSttege aongu de three resi vances Ahoosn 10 fgue i 10 20 20 L——¢—$ Ts A un ty 2 © (ws / = coe Vpi= a ie Vv Seo) asf f) =co-_/° 5 yee a wae 20420 eee RtRytR, lot2o+20 {Va = / id L a Vp, = IR, = WKIO =I [ie =2N] Nan = 29-¥ Va3 =2K VvCT Lind dhe Current trough all nesrsdees @ in the civeeit: C ! My yy 1s 2% Ty Js | SR Ppply ing eer act nee A 2 tea Ges ae Del ERI Nala ee elle i 2 I Ve HID Va 10, = 150 a 13Va -10V, =150 — ©) Apptying Kel at Avdole By LytIstte« cece | Vi - Va 4 Ye + Ver 7 3 S 1 =(50 = ©) 5Vy —5Va +3, 41S Vy / —5Vg + 23Vb aS 6 -—@ Schving en O £0) [Vas eri vetds | [ve = 10-84 ves | we a = = 11 909K®) Find the ry dasp acHoss each nesives bay e dive der nule: uh. Ny abv Vy, =! kn Ns kw 7 Re ye ee (eee) ev : (Gr e418) x10" 36000 Ny eye 1287 gg, fines a = 12 TSLb05 Bore Ny su 1g0oO CZ 4 =™ LASS. © ge freee) = iy Jeet 36000 Prepared by Charchele leUNIT) : Supetfositien Acorem ! Syn JO SA Teel Adtales Rat « ee Linent ire Compo ring § num dex 9 indefendent say eres the tstal nerponse fet onal Dorahede Me nelook 1S cpus! to tke oly ebrare sun b Bd yreluat aesponse actin alone, hey cons/oler/'n only ove Acurce at a time enol mobing A Hey inolepenclant sources © geno.” = : Keeg One ind eben dant Aource achive and gfhen pourees inactve- 5K [Ove i » avy = «¢ au 1, CN eel eaenisley Stef 2: Refeat Th? above proceduxe fo ~~ a incl pendent Aouree: aa@) Per Gtk Hie = 325A (current oll'wietes 345 = nee) Step: Add ali the age Shlained » Af ier “cons / fern heir vl te e polar tet anol cunmat alinections a “he net boanck mesponse- jhe net ae mies onse fr 3 bnarh'sy > p a f,+h, 2 ops 1215) = s62s5A 7 -o: 625A ees Using Suger ssittien Keorem, determine Me cunkent rougk 30hm mes sfx - 2YF bteB i: Lk | Bi k/hen oy IV fourre js gehve @ i 3H © A Fe Ee taphying nue ts AB EFA, -o2r,-u(h-n)t aan <25,-125, 40D Ft eee 12D, -141, =~ > —)4T, Be re fin=eta]-© Pppdying kve to Sc DEB, “31, 4+12C7, 1) =° -31, +4 -Ph =e joa, -Isd, = ° 41, -5 Te =O -@® Schrag mid OF,Sepa: Iedken only KV Aoure Is active: F E : D Appling KVL jee ABEFA, 2Ty-2CI3-Ly)=0 Ty 12 I, +/rty =e —2 474, =o —® Applying Kve gy Bc DEB, [i +12 CZ3-Iy) =o Bas -% +121, -122y=0 -@ ishing en O4 O Steps: Cunnent through gu sessky ie eo 84-036 = OYA tan =5) Find a. the cusnent Jl awiey Brough 4 thm @ sidence ate Super A e pw om Shearer: Stefi: Step i! When 2o0V Souyre 1S achive: 2 be Re Tassiaiion = Me le 4H 20 ne Canre Knog Zan nesneter “Gly teStep 2 Mien JOA gouyce 7S ocfive- 4a Req = inet = tha a wie = oe coe! iE This telad cayren Ci) is PY) fe c/, aun gon oa A _ 2 T,- 2 eo * = /-F1SA 4+2 iPP pling Ket aot hoole a° Va — + Ya=No ~S =o Ppptying Ke at rocle 6; Vite Ma Ye 20 3 oe IN, —¥Ve + eV, +3%, =0 -@ teeta tilt enna Tao a yim oct I, 7 =o * [igen] cunnent Glowing Posr0 yy Gn men RE = 4/41, 4), = F3RAmK 57) *6 Sousice Diansformatio ae @ he Mecdkocl dnans Sn we ‘ athev iy kre i J ON Bouwee Jncte techn M as source 1Nart{oymetin ec nrgee Thewe ssie tise types g practicod Aources ! Valéase Source ancl carrert Joune Hence, We Con “arty She Aouyce Cnanigermatnr technrguc ter these dtusy Sources to convert one type ta the xFhen- x Rene ae fusd Aource drany matin dechnisues a) VoTtaze Aouree fo current source i? Cantent source te vs7 type -_ Veltege source fo_current Aource: t “tfCanrtent Source te alee ye source: [Ns = Isr sR e) Gravevt a v sttege dSouyee J EV Laue. QO senrer Nest rdance 4 au info an oe Sowree » iy) R=2W 24V = L = R ®) Convevt Ke cunnert Source In the circw't to VoHage Aource: ~~~ a0 - ae RL = our@) VaTR @ = 2X7 = ly volt Jve 14. VS7t | Converting tf Vellape source: — Ram Cony a = Vets source in He circuit to uturent goure ¢ find She cunnent Pm ough Jka newrter Rosr2kh R=! kn Vis = SN Vv. S Tp22-5m) Vs - § = 9 SMA =5]T5=25m R . a : ox —~ r-I _ 0 even ‘s Beoren Und ® * Thevenin's fheorem slates hot ayy Viixesep nefeorrk having active voHog¢ aad cuyrent fost tate hoe Eerminals A #8 can be srefdare eof by an equivalent volley ¢ source Vry and egivad ent nNesidance Pry In dered combination foroning a simple cq uivalert circurL TH rn © Re whens, Vey is Hhe in eveaie vHage acres fhe Eeyminats A an. 8: | Rru is the wivalert serlpfance as Seen fram he termina P anol B ashen the inolebenclent Avouyces we leach vatec! * Procedure fo fied The venin 's Eguielot Civeart % x Ro ws A wi dass vole e Adare e a Knee s1¢s' store 2, Rad m-Sept: To Calrulate Teves) vs Xx Sep ° ¢ a. ‘op % Sbtain rH _ open cites a I N vw © pe (Avs 8 i Nom ts equal do vsllage across Permina bs A and 8, \ins 8 : d “oyna Kv fothe ciycult, s/, - 28, -2h, -¥, 22 pate Sie Chl) aS ey See _@ Rt Ro Noy = Veg = V-28 —-@ Ca botrheh ng eg uation QO ia egn- 5 Be Value § Von cay he cotentateot = -V . Vern =v) a: a ’ oe CAakeas Heh 2 Mo calewete Aru Q a Te © calculate Pru, the ni ¢ Aouwet axe Above cirearlee and cupnen Powe ane Dhen circeet Feof - Ry A a Ray = 2,12, = Rho R,+Ra2- Jhevenio io Equivalent Circeu't ' Rr A Ry Neu B Q) by a Thevenin's Theorem ds d te current 10 [on nen yt A 2 Jove GNite Thevenin *¢ Vertes @, Ven I gird Vin) Memove lon ness SC, Yo Go} S: by LI] |" B Vn = Vag = Volta. = TRyn J= 5_ r- V/p SH3 C ) T=0-62.50 O'625 x3 1 tIsV Tevenin Ms west Manee Ran voller Aouree must Se Phott etveut yar aun 9° acne Jn HeVprke-Thevenin' Ss couivalent ~——— Yo clreert m= gen \V Ly Ry, = fon Carvent flowing Whovough ay Cou); > cee Von reds geo - Fru +R, 6 BIS+10 [ - one] @) Determine the cagrent FT tHeorem - 1 I by sing Thewenia A Be lowe an po-45, ly Jov B * Thovenrn's voHase, Vru -G67,—l=0 F E a MaVoHese aust 6% = 7, Rea =-o0'2 x6 oa DY ONE Ven dy 2-12 412 [Men = roe | TBevenrn 's Fouivalent sen vdence} kry dD x Thevenin's Fguivalet Circus } Brn = 2-4 p 7 Jour Vay = 1o-BY f wv, 10°8 Current J = m 7 Rry ean PF Freuae the [eovenin's equivalent with nepeel | te terminals tage ya the cipcurl givens 20" 4% Mevenin! ee nin's Resiblance Crm) 2owr a GOW 2 ie [Ou ga = C204 J/éo ro) I< 2] Secawe te Areade aeitee consithing 9 50 oo ee out open BOF 60Thev enra |S Ve?depe, Vry CU 7 1,) 2 Ova Apptying ke to Coop FGNEF; 9-S1,-25(1,~-1;)=° to SF, - 262, +251,=0 -30T,4257,4+9=0 30 -1s=9 —@ area 307, - Qsxra)=9 30I,- 48-9 jot, = 54 plying Kve fa Ke dupermerh A BCD ENGA; -20C1,-I,) ~60C4,-7,41,) /0(L1-Ly +3) 425 (I2,-2,) +51, =o -2°C2,~7,)-70(1,-% +z) +25 GS) +52, =° Ryog: : 7°T, 4207, ~Casxrs) =6 ~ FoI, +G20xrg)-/#l = © —~Gol, + 216- It} =0 ~Gor, =F * Capyent flowing thn ough Gow = Cl,-I, +23) =(o-s- Ve +16) = OSA Nga lll= Vor tase acne con nesrrfarc®: = 7x€0 Sos xérv = 30V Vern = sov| 200 (Rm) a 3ov Olu) bwk ‘ a Naston's TLeore wit! @ ——» Nov ben % He orem 4) bey Shat any tro termrnak finear netesctk wih current BOUK ced, Vollese Aourcet anol ses pfancts can Se \ ote flac eal by an eguivalernt Cireast cons/ oon * a eavrent source’ jy Aavallel arth oa peas ewhere fhe valve Q current Aowwre 1S spun lib Be curvent pa sting Through the Afort civewrled terminal ph B @) By usage Notton's Heorem ging te cunrenth the Gn were, n aes n en a 8 U1) Norfen's Current In: Remove en nesivde, anol neplace it with a vyt circa:Reg = B+ (six) Des = CXY dey = 3 ey) deg = = S21 Total carreat Applied 4q fhe Soure ys P= 2 S$ = 0:756A f= Rey S22 Nostsn's cuyyert, I= ee =} (1) Nogden's ne titance, Br ; Replace The vHage source S a Yhort circuse- a ne Ry = 4d (ile)Chreark A Tne on 8 © Cavrent Th 10 ugh 6a ness IS, le BIS cn 7 ea = Ly X= oS s1st& 7 ~ eg 70° 2632A jee ee (current divider pole) Q) Find the current tA! in He civeeut behw usted Noevdeo's theorem: Ow * Shoyt- civewt 20K ste ste ; 10 Ky zTetal é avvent, 7 Vv ae = Re 2o4+ Colle.) 7 2° "ct n08) gotio T's o°72A —= ; | ’ = 7 = Mowten's carrenty Tyr = J (sax) J carted lie sate ) Prefered & chanolralethoa Lime D gin oe Time Dom Pibeteat o) JF ards eg 4 0 RL Civcuy't- * Consiolev dhe pei ° uno civeurt how rn ic . ‘ a 7 : Phi | PPA! KvL) Tine Aorair Ldihd : anolfin D Lipp =v 0 ae Vaid) R = bdi@e apeh ae renee dt = ds = ere. a yb) R 7 "a on bh sides See Svawe 7 D t ‘ - je = - did a ~LCOR oT J poceso | | Stbeb?] hz] ne peepee ener reer eee eetBee = [tn Fis rarag]t a = fn (v-4 aR) - An £ re += Sn va) ‘ yv aR) ce s Rh He ae Ret Vv Poe" = £ODR _ ee ae . 7 it) | * Vettage. an o£ + resis FO Vy (4) = LA) R ee Vg (6) = tls *). ae : oe : “Rit ue aN fee |) + vate aot inact Vv, ae = ide Vt) uf ps Ph I fp be CTH Vioyee, “Alt 4 3) A é / = Riet JV, UW) = Ve d Ale a avg 2 vf “] al ) ah vag (6) = LI- e wae pete eorl R [Ms “=e 7) = ° | VY he vere folie [ov] L’ ach as ghen- circurt at t=0° ~ shes 08; woe fe] Eh oa | i a7 | * Vg (4) = voi tet] Vy, Lt) wv pe] =V [ve *) =V tr OM lé)=ve tet ce ie Iv, co = o| “IKae pi is calle fhe fime- Ms : fa) a e'] fe 06324 [io =0: sar | oe re =vfr-e'f [yw = ezv| alo = Vp = Me = V-8 & # Graph ger g 2+ iwmt 6 @ raph di Vy lO and vy, ):- a Kuyt) - | 01 G32V Ss SL - =) (ictal aaa Time ct attend 9 fee ¢ lyeart '— LES chetned as dhe Hime neq usnesl to neak 632% 2 the steocly Bake meforse- fe ey alia olefrrect as tHe staf7o in cluchance So Suenieeace 2. Phe matke mat cad ed se “ font (i given a2) xprreesion ts . comity dg ve yy t a | | [t=zr 7 oO fine Domain Ana bysts ppeaens : Re trea dé wth Do excibahe 1S histaas rs Applying kvu, we get, V=1LCOR “2 (reodé=e LOR + (edd =V E Dufterenti aking on bsfh sides, ox ca Redk) 4 LC) = > At a Aru) — 1 dé dt BC eee ad on “ Aides, Ai) jue fog o Hy a t An [i aw), 7 i [], ‘ acl, An [ice]- Gen fe t IRfico] -pn CF) 2st y iC eae x a ‘ = € Pate ea vie eee cilae t+ R vfe ) R Vp Gt) = £4) A= Vp 4) = | fa eS Ne * Voltage acon ao ieee ao act Vv Not) = Lr) = — © < (é) Lyre f 5 ° ce aac t = = NV 2 fe Une + x . < 7 Uke — uw feet Ss RC —t]ac =e oe Eafe ae 7 Vette v [r-eteet] a|-M(t )ov (eteew) (vere a R = > Seco ee 2 t 1 Vat Jey (eet) eves Vo) = vf ett] ev fier] ev bre de domes ite) a 2 eae S a= &§ 3 = Vali ev feet] 2 vo = Be Of df 1 At T=t=rRe : il) CS Ng) ee ig Se it) “Fe — vi CE) =v fe eR] ve! = o3&¥ A ee ==* * Time constant Q RC Civcurt!- Gore ph j ' Graph g_ve td) f Ve tt) - Ne w) ; ‘i’ : It vs defineo! aw dhe time daken by the capacitr to attain 63.2% 9 Ateooly Atak e veltey e- f= Re =— Profane! £ Sen