
preran

vidyut vahakachi, tyatoon vahana vidyutpravahatil badalala virodh karanyachi pravrutti mhanje preran. vidyut pravahacha pravah vahakachya bhovati chumbakeey kshetra tayar karato. kshetrachi takad hii pravahachya parimanavar avalambun asate aanee pravahatil konatyahi badalanche anusaran karate. farradechya preran niyamapramane, paripathadvare chumbakeey kshetratil konatahi badal vahkamadhye vidyut prerak shakti (eae. emm. eff.) (voltage) prerit karato, hii prakriya vidyutchumbakiy preran mhanoon olakhali jaate. badalatya pravahadvare nirman jhalelya yaa prerit vidyutdabat vidyutpravahatil badalala virodh karnyacha parinam hoto. heey lenzchya niyamanusar sangitale jaate aanee voltagela "back eae. emm. eff." mhanatat.
inductancechi vyakhya, prerit voltageche aanee tyala karanibhoot asalelya vidyutpravahatil badalachya darache gunottar mhanoon kelee jaate. haah eka pramanbaddh ghatak aahe joou paripath vahakanchya bhoomitivar aanee jawalchya samgrichya chumbakeey pargamyatevar avalambun asato. paripathat preran jodanyasathi tayar kelelya electronic ghatkala prerak mhanatat. tyat samanyatah taranchi gundali kinwa helics asate.
inductance' haah shabd meey 1884 madhye oliver havicidene tayar keela hota. bhautikshastradnya heinrich lenz yanchya sanmanarth inductancesathi '1' heey chinh sootra vaparanyachi pratha aahe. ess. aay. pranalimadhye, inductance ekak heey heinry (etch) aahe, jeey inductance praman aahe jyamule eka volt voltage hote, jevha current prati sekand eka ampearchya darane badalat asato. yala joseph heinryche naav denyat aale aahe, jyane faradepasoon swatantrapane preran shodhale.
itihas.
vidyutchumbakiy preranacha itihas, vidyutchumbakiyatecha eka pailu, pracheen kalatil nirikshanansah suru jhalah vidyutbhar kinwa sthir veej (emberver resheem ghasane), vidyut pravah (veej) aanee chumbakeey aakarshan (loadestone). nisargachya yaa shaktinchi ekata samajoon ghene aanee vidyutchumbakiyatecha vaidnyanik siddhant 18 vya shatkachya uttaradhat suru jhaala.
vidyutchumbakiy preran pratham 1831 madhye michael farrade yanni varnan kele. farradechya prayogat, tyanni lokhandi ringchya viruddha bajunna done taar gundalalya. tyala ashee apeksha hotee qee, jevha eka taratoon pravah vahoo lagel, tevha eka prakarchi laat ringmadhun jaeel aanee ulatya bajula kahee vidyut parinam hoil. galvanometercha vapar karoon, pratyek velee jevha battery pahilya koilpasoon jodali gelee kinwa disconnect kelee gelee tevha tyane vayarchya dusya coilmadhye kshanik pravah pahila. battery jodali gelee aanee jodani todali gelee tevha jhalelya chumbakeey pravahatil badalamule haah pravah prerit jhaala. farrade yanna vidyutchumbakiy prerananchi itar anek abhivyakti sapadali. udaharanarth, jevha tyane taranchya gundalit baar chumbak patkan sarkavale aanee baher kadhale tevha tyala kshanik pravah disale aanee tyane sliding electrical lead (farradechi disk) saha baar chumbkajaval tambe disk firvoon sthir (dc) pravah nirman keela.
preran srot.
vahakatoon vahanare vidyutpravah sootra _ 2 vahakbhovati chumbakeey kshetra nirman karate, jyache varnan ampearchya parighiy niyamane kele aahe. paripathatoon ekoon chumbakeey pravah sootra _ 3 heey chumbakeey pravah ghanatechya lumb ghatakachya aanee vartaman margavar pasarlelya prushthbhagachya kshetrafalachya gunakarasarkhe asate. jarr pravah badalat asel tarr paripathatoon yenare chumbakeey pravah sootra _ 3 badalate. farradechya preran niyamanusar, paripathatoon vahana pravahatil konatahi badal, pravahatil badalachya darachya pramanat, paripathatil vidyut prerak shaktila (eae. emm. eff., sootra _ 5) prerit karato.
sootra _ 6
samikaranatil nakaratmak chinh soochit karate qee prerit voltage asha dishene aahe jeey teey nirman karananya pravahatil badalala virodh karate; yala lenzcha niyam mhanatat. tyamule sambhavyates back eae. emm. eff. mhanatat. jarr vidyutpravah vadhat asel tarr vahakachya shevati vidyutpravah sakaratmak asato jyadvare vidyutpravah pravesh karato aanee jyadvare too baher padato tyaa shevati nakaratmak asato, jyamule vidyutpravah qamee hoto. jarr vidyutpravah qamee hott asel tarr jyachyadvare vidyutpravah vahkala sodato tyaa shevati vidyutpravah sakaratmak asato, jyamule vidyutpravah tikavoon thevanyachi pravrutti asate. self-inductance, jyala samanyatah fakt inductance mhanatat, sootra _ 1 heey prerit voltage aanee karantchya badalachya daramadhil gunottar aahe.
sootra _ 8
asha prakare, preran haah vahak kinwa paripathcha eka gunadharm aahe, kaaran tyachya chumbakeey kshetramule, jeey paripathatoon pravahat honanya badalanna virodh karato. ess. aay. pranalitil preran ekak heey heinry (etch) aahe, jyala joseph heinryche naav denyat aale aahe, jeey preran praman aahe jeey eka voltche voltage tayar karate jevha pravah prati sekand eka ampearchya darane badalat asato.
serve vahakanmadhye kahee pramanat preran asate, jyache vyavharik vidyut upkarnanmadhye ektar vanchhaniy kinwa hanikarak parinam houu shakatat. paripathatil preran heey vartaman margachya bhoomitivar aanee jawalchya samgrichya chumbakeey pargamyatevar avalambun asate; vahkajavalil lohasarkhya uchch pargamyata asalelya lohchumbakiy samagrimule chumbakeey kshetra aanee preran vadhate. dilelya pravahadvare utpadit honanya paripathatoon pravah (ekoon chumbakeey kshetra) vadhavna paripathatil konatahi badal, preran vadhavato, kaaran preran dekhil chumbakeey pravah aanee pravah yanchya gunottaraitakech asate.
sootra _ 9
inductor haah vidyut ghatak aahe jyamadhye chumbakeey pravah vadhavanyasathi, paripathat preran jodanyasathi vahak aakarat asato. samanyatah tyat gundali kinwa heliksmadhye eka taar asate. gundallelya taramadhye samaan lambichya saral tarapeksha jaast preran asate, kaaran chumbakeey kshetrachya resha paripathatoon anek vela jaatat, tyat anek pravah jodanya asatat. purn pravah jodani gruheet dharoon, inductance haah coilmadhil valananchya sankhyechya vargala pramanbaddh asato.
madhyabhagi asalelya chhidramadhye lohchumbakiy samagricha chumbakeey gabha thevun gundalicha preran vadhavta yeto. coilche chumbakeey kshetra koarchya samagriche chumbakiyakaran karate, tyachya chumbakeey kshetranna sanrekhit karate aanee koarche chumbakeey kshetra coilmadhye jodate, jyamule coilmadhun pravah vadhato. yala pheromagnetic coor inductor mhanatat. chumbakeey gabha gundalicha preran hajaro patine vadhavu shakato.
jarr anek vidyut paripath ekmekanchya jawal asateel tarr ekache chumbakeey kshetra dusyamadhun jaau shakate; yaa prakaranat paripathanna 'prerakpane jodalele' mhatale jaate. farradechya inductionchya niyamamule, eka paripathatil pravahatil badalamule dusya paripathatil chumbakeey pravahat badal houu shakato aanee asha prakare dusya paripathatil voltage prerit houu shakato. yaa prakaranat, circuit sootra _ 11 chey paraspar preran sootra _ 10 aanee circuit sootra _ 12 heey circuit sootra _ 12 madhye prerit voltageche praman aanee circuit sootra _ 11 madheel karantchya badalachya darache gunottar mhanoon paribhashit karoon preran sankalpaneche samanyikaran kele jaau shakate. heey "transformer" chya magche tattva aahe. eka vahakachya swatahvareel parinamache varnan karananya gunadharmala adhik tantotant 'self-inductance' mhanatat aanee jawalchya vahakanvar badalatya pravahasah eka vahakachya parinamanche varnan karananya gunadharmanna 'mutual inductance' mhanatat.
swayam-preran aanee chumbakeey urja.
jarr prerak asalelya vahakadvare pravah vadhat asel tarr vahakatil vidyutpravah sootra _ 15, vahkamadhye vidyutpravahala virodh karananya dhruviyatesaha prerit kele jaate-vahakachya pratikaramule honanya konatyahi vidyutpravahatil ghasaranivyatirikt. paripathatoon vahanare charge sambhavya urja gamavatat. yaa 'sambhavya tekadivar' maat karnyasathi aavashyak asaleli bahya paripathatil urja vahakachya sabhovatalachya vadhiv chumbakeey kshetrat sathavali jaate. mhanoon, prerak tyachya chumbakeey kshetrat urja sathavato. konatyahi velee sootra _ 16 madhye chumbakeey kshetrat vahanare urja sootra _ 17, jeey sathavalelya urja sootra _ 18 chya badalachya darachya barobariche aahe, heey vahkavar vartaman sootra _ 19 aanee voltage sootra _ 15 chey gunakar aahe.
sootra _ 21
(1) varr
sootra _ 22
jevha vidyutpravah nasato, tevha chumbakeey kshetra nasate aanee sathavaleli urja shoonya asate. pratirodhak nukasanakade durlaksh karoon, urja sootra _ 18 (jyulmadhye, ess. aay. madhye mojale jaate) heey tyachyadvare vartaman sootra _ 24 saha preranadvare sathavale jaate, jeey shunyapasoon preranadvare pravah sthapit karnyasathi aavashyak asalelya kamachya pramanachya barobariche aahe aanee mhanoon chumbakeey kshetra. heey asey dile jaateh
sootra _ 25
jarr inductance sootra _ 26 vartaman shrenivar sthir asel tarr sathavaleli urja aahe
sootra _ 27
tyamule dilelya pravahasathi chumbakeey kshetrat sathavalelya urjechya pramanat dekhil preran asate. joparyant pravah sthir rahato toparyant hii urja sathavali jaate. jarr pravah qamee jhaala tarr chumbakeey kshetra qamee hote, jyamule vahkamadhye viruddha dishene voltage nirman hote, jyachyadvare pravah pravesh karato tyaa shevati nakaratmak aanee jyachya madhyamatoon too baher padato tyaa shevati sakaratmak. heey bahya paripathat sathavaleli chumbakeey urja parat karate.
jarr lohchumbakiy padarth vahkajaval asateel, jase qee chumbakeey gabha asalelya prerkamadhye, tarr vareel sthir preran samikaran keval chumbakeey pravahachya resheey kshetransathi vaidh aahe, jyaa patalivar lohchumbakiy padarth santrupt hoto tyaa patalichya khalee asalelya pravahanvar, jethe preran andaje sthir asate. jarr prerkatil chumbakeey kshetra coor jyaa patalivar santrupt hote tyaa patalichya jawal pohochale tarr pravahasah preran badaloo lagate aanee avibhajya samikaran vaparale jaane aavashyak aahe.
prerak pratikriya.
jevha cyanucidal ulternating current (essie) resheey preranatoon jaat asato, tevha prerit back-dekhil cyanucidal asato. jarr inductancemadhun vahanara current sootra 28 asel, tarr tyachya palikade asalelya voltage (1) varr aahe
sootra _ 29
jethe sootra _ 30 heey ampearmadhil cyanucidal currentche amplitude (shikhar moolya) aahe, sootra _ 31 heey paryayi currentchi koneey varanvarta aahe, sootra _ 32 heey heartzmadheel tyachi varanvarta aahe aanee sootra _ 1 heey preran aahe.
asha prakare inductancechya palikade voltageche amplitude (shikhar moolya) aahe
sootra _ 34
prerak abhikriya mhanje paryayi pravahala prerakcha virodh hoy. tyachi vyakhya pratirodhakatil vidyut pratirodhapramanech kelee jaate, ghatakatil vidyutpravah aanee paryayi vidyutdabchya amplitudeche (shikhar moolya) gunottar mhanoon.
sootra _ 35
abhikriyeche ohmache ekak asatat. heey pahile jaau shakate qee inductorchi prerak pratikriya frequency sutrasah pramananusar vadhate, mhanoon frequency vadhalyane dilelya lagoo kelelya essie voltagesathi inductor qamee current chalavato. kaaran jevha vidyutpravah vadhat asato tevha prerit vidyutpravah sarvat motha asato, vidyutpravah aanee vidyutpravah lahari heey tappyabaher asatat; vidyutpravah shikhar pratyek chakrat vidyutpravah shikharanpeksha lavkar yetat. vidyutpravah aanee prerit vidyutpravah yanchyatil tappyatil farak sootra 37 radian kinwa 90 ansh aahe, jeey darshavite qee aadarsh prerkamadhye vidyutpravah vidyutpravahapeksha 90 anshanni mage aahe.
preran ganana.
sarvat samanya babatit, maxwellchya samikarananvarun preran ganana kelee jaau shakate. saralikaranacha vapar karoon anek mahattvachi prakarane sodavali jaau shakatat. jethe uchch varanvarta pravahancha vichar keela jaato, tvachechya prabhavasah, prushthbhagavaril pravah ghanata aanee chumbakeey kshetra laplas samikaran sodavun prapt kele jaau shakate. jethe vahak patal taar asatat, tethe swayam-preran ajunahi taar trijya aanee taratil pravahachya vitarnavar avalambun asate. itar lambichya pramananpeksha khoopach lahan asalelya taar trijyesathi heey vidyutpravah vitaran andaje sthir (prushthbhagavar kinwa tarchya aakarmanat) asate.
saral ekach tarcha preran.
vyavharik baab mhanoon, lamb taranmadhye adhik preran asate aanee jaad taranmadhye qamee asate, jeey tyanchya vidyut pratikarshaktishi samaan asate (jaree sambandh resheey nasale taree aanee lambi aanee vyasachya pratirodhshaktishi asalelya sambandhanpeksha bhinn asale taree).
paripathatil itar bhaganpasun taar vegale kelyane konatyahi sutranchya nikalanmadhye kahee apariharya truti udbhavtat. yaa inductansna byavachada "aanshik inductance" mhanoon sambodhale jaate, anshatah vagalalelya sampoorn-paripath inductancemadhil itar yogdanacha vichar karnyas protsahit karnyasathi.
vyavharik sutre.
khaleel sutranchya vyutpattisathi, rosa (1908) pahaa.
saral taranchi ekoon qamee varanvarta preran (aateel aanee bahya) ashee aaheh
sootra _ 38
kuthe? 
sthirank 0.75 heey anekanmadhye fakt eka mapdand moolya aahe; bhinn varanvarta shreni, bhinn aakar kinwa atyant lamb wire lambisathi thoda vegala sthirank aavashyak asato (khalee pahaa). haah parinam yaa gruhitkavar aadharit aahe qee trijya sootra _ 41 heey lambichya sootra _ 12 peksha khoopach qamee aahe, jeey taar aanee rodsathi samanya prakaran aahe. disk kinwa jaad cylinderchi sutre thodi vegali asatat.
puresha uchch varanvartesathi tvachechya prabhavanmule aateel pravah nahise hotat, vahak prushthbhagavar fakt pravah uratat; paryayi pravahasathi preran, sootra _ 47 nantar agadi samaan sutradvare dile jaateh
sootra _ 48
jethe chull sootra _ 12 aanee sootra _ 41 varilpramanech aahet; varr 0.75 varoon aata badalaleli sthir sandnya 1 nondwa.
dainandin anubhavavarun eka udaharanat, 18 aii. doubleu. jee. taranni banalelya divyachya dorkhandachya lamb vahakanpaiki fakt eka vahakacha, saral pasarlyasach sumare eka preran asel.
done samantar saral tarancha paraspar preran.
vichar karnyasathi done prakarane aaheth
taranmadhil pravah jaree samaan asale pahijet asey nahee, jaree teey bahutekda, sampoorn paripathapramane, jethe eka taar srot aahe aanee dusari parat yete.
done taranchya loopscha paraspar preran.
samaan qamee varanvarta pravah vahoon nenanya pratiman done-loop dandgolakar gundaliche heey samanyikrut prakaran aahe; loop swatantra bund paripath aahet jyachi lambi bhinn asoo shakate, avkashatil konatihi disha asoo shakate aanee bhinn pravah vahoon neuu shakate. tathapi, trutichya sandnya, jyaa avibhajyamadhye samavisht kelya jaat naheet, tyaa keval chhotya asatat jarr loopchi bhoomiti bahutek gulgulit aanee bahirmukh aselah tyanchyat khoop jaast kink, tikshna kopare, coil, crossover, samantar vibhag, avtal pokali kinwa itar sthanikdrushtya "jawal" vikrutee nasavyat. tri-aayami bahugunit ektrikaran sutrala duheri vakr avibhajya mhanoon qamee karnyasathi eka aavashyak vidhey mhanje vartaman marg philamentary circuits aahet, i.eae. jyaa patal taranchi trijya tyachya lambichya tulanet nagany asate.
philamentary circuit sutravar philamentary circuit sootra _ 51 dware paraspar preran _ 52 heey duheri avibhajya "neuman sootra" dware dile jaate."
kuthe?
vyutpatti.
sootra _ 63
kuthe?
sootra _ 70
kuthe?
tisya samanatechya payarisathi stokesche pramey vaparale gele aahe. shevatchya samanatechya payarisathi, aapan formula _ 71 sathee mand sambhavya abhivyakti vaparali aanee aapan mand velechya prabhavakade durlaksh karato (asey gruheet dharoon qee circuitchi bhoomiti teey vahoon nett asalelya karantchya tarangalambichya tulanet pureshi lahan aahe). hii pratyakshat eka andaje payari aahe aanee keval patal taranni banavalelya sthanik paripathansathi vaidh aahe.
wire loopche swayam-preran.
aupcharikpane, wire loopcha self-inductance vareel samikaranadvare sootra _ 72 saha deela jaeel, tathapi, yethe sootra _ 73 anant hote, jyamule laghuganakinusar bhinn avibhajya hote.
yasathi taar trijya sootra _ 74 aanee taratil vidyut pravahache vitaran vicharat ghene aavashyak aahe. serve muddyanvar aanee durustichya mudativar avibhajya yogdan rahate,
kuthe?
solenoidcha preran.
solenoid hii eka lamb, patal gundali asate; i.eae.eka gundali jyachi lambi tyachya vyasapeksha khoop jaast asate. yaa paristhitit, aanee konatyahi chumbakeey samagricha vapar naan karata, gundalitil chumbakeey pravah ghanata sootra _ 88 vyavharikdrushtya sthir aahe aanee heey khalilpramane dile jaateh
sootra _ 89
jethe sootra _ 56 haah chumbakeey sthirank aahe, sootra _ 91 heey valananchi sankhya, sootra _ 2 heey vidyutpravah aanee sootra _ 93 heey gundalichi lambi aahe. antim parinamankade durlaksh karoon, pravah ghanata sootra _ 88 laa cross-section kshetra sootra _ 95 neey gunakar karoon gundalitun ekoon chumbakeey pravah prapt keela jaatoh
sootra _ 96
jevha heey inductance sootra _ 97 chya vyakhyeshi jodale jaate, tevha solnoidcha inductance khalilpramane deela jaatoh
sootra _ 98
mhanoon, air-coor koilsathi, inductance heey coil bhoomiti aanee valananchi sankhya yanche karya aahe aanee teey karantpasoon swatantra aahe.
samakshiy kebalacha preran.
aateel vahkala trijya sootra 99 aanee pargamyata sootra 100 asoo dya, aateel aanee bahya vahkamadhil paravartaniyata sootra 101 asoo dya aanee bahya vahkala aateel trijya sootra 102, bahya trijya sootra 103 aanee pargamyata sootra 56 asoo dya. tathapi, eka vishisht samakshiy reshechya anuprayogasathi, aaplyala varanvartevar (dii. see. nasalele) sanket paas karnyat rus aahe jyasathi pratirodhak tvachechya prabhavakade durlaksh kele jaau shakat nahee. bahutansh prakarananmadhye, aateel aanee bahya vahak sandnya nagany asatat, asha paristhitit ekhada andaje asoo shakato.
sootra _ 105
bahustareey gundalyancha preran.
bahutek vyavharik air-coor inductors heey valananmadhil sarasari antar qamee karnyasathi chauras cross-sections bahustareey dandgolakar coil asatat (golakar cross-section adhik changle parantu tayar karane katheen asel).
chumbakeey coor.
anek prerkanmadhye valananchya madhyabhagi kinwa anshatah sabhovatalacha chumbakeey gabha samavisht asato. puresha mothya shreneet heey chumbakeey sampruktatesarkhya prabhavansah eka araikhik pargamyata pradarshit karatat. saturation parinami yenanya inductancela lagoo kelelya currentche karya banavate.
pravah gananet secont kinwa mothya-signal inductancecha vapar keela jaato. tyachi vyakhya ashee aaheh
sootra _ 106
dusarikade, voltagechi ganana karnyasathi vibhedak kinwa lahan-signal inductancecha vapar keela jaato. tyachi vyakhya ashee aaheh
sootra _ 107
farradechya niyamane aanee gananechya sakhali niyamane darshavilyapramane, nonlinear inductorsathi circuit voltage heey vibhedak inductancedware prapt kele jaate.
sootra _ 108
nonlinear mutual inductancesathi samaan vyakhya midavata yeu shakatat.
paraspar preran.
paraspar preran mhanje eka loop kinwa coilmadhye prerit eae. emm. eff. madheel gunottar aanee dusya loop kinwa coilmadhye karantchya badalachya darache gunottar. paraspar preran heey prateek dile jaate.
paraspar preran vyutpatti.
vareel preran samikarane hii maxwellchya samikaranancha parinam aahet. patal taranchya vidyut paripathanchya mahattvachya prakaranasathi, vyutpatti saral aahe.
sootra _ 109 wire loopchya pranalimadhye, pratyekane eka kinwa anek wire valane asalele, loop sootra _ 51, sootra _ 111 chey fluxes linkage, dware dile jaate
sootra _ 112
yethe sootra _ 113 heey loop sootra _ 51 madheel valananchi sankhya darshavate; sootra _ 115 heey loop sootra _ 51 dware chumbakeey pravah aahe; aanee sootra _ 117 heey khalee varnan kelele kahee sthirank aahet. heey samikaran ampearchya niyamapramane aaheh "chumbakeey kshetre aanee pravah hii pravahanchi resheey karye aahet". farradechya preran niyamanusar, aamchyakade aahe
sootra _ 118
jethe sootra _ 119 heey paripath sootra _ 51 madhye prerit voltage darshavate. jarr gunank sootra _ 117 heey prerananchya gunankansah olakhale gele tarr heey vareel prerananchya vyakhyeshi sahmat aahe. kaaran ekoon pravah sootra _ 122 heey sootra _ 115 madhye yogdan dete, teey dekhil tyaa sutrache anusaran karate jeey _ 117 heey valan sootra _ 125 chya gunakaras pramanbaddh aahe.
paraspar preran aanee chumbakeey kshetra urja.
vareel 'vm' sathichya samikaranala 'IMdt' neey gunakar kelyane aanee 'm' varr berries kelyas, 'dt' yaa velechya madhyantarat pranalimadhye hastantarit keleli urja milate.
sootra _ 126
heey vidyutpravahamule honanya chumbakeey kshetrachya urjechya, "doubleu" chya badalashi sahmat asale pahije. ekatmata sthitee
sootra _ 127
lm, n = ln, m" aavashyak aahe. inductance matricks, "lm, n", asha prakare samamiteey aahe. urja hastantaranacha avibhajya bhag mhanje vidyutpravahanche karya mhanoon chumbakeey kshetra urja,
sootra _ 128
heey samikaran dekhil maxwellchya samikarananchya reshatmakatecha thet parinam aahe. badalatya vidyut pravahanna chumbakeey kshetrachya urjechya vadhishi kinwa ghatashi jodane upayukt tharate. sambandhit urja hastantaranasathi voltage aavashyak asate kinwa nirman hote. k" = 1 prakaranatil chumbakeey kshetra urjeshi yantrik sadrushya (1/2) "Li" 2 mhanje vastuman "m", veg "u" aanee gatij urja (1/2) "mu" 2 asalela padarth. veg (pravah) chya badalacha darr vastumanane (preran) gunakar kelyas shakti (vidyut vidyutdab) aavashyak asate kinwa nirman hote.
jevha eka prerkatil pravahatil badal jawalchya dusya prerkamadhye vidyutpravah prerit karato tevha paraspar preran hote. transformer jyaa yantranedvare karya karatat tee yantrana mhanoon heey mahatvache aahe, parantu yamule paripathatil vahakanmadhye avanchhit jodani dekhil houu shakate.
paraspar preran, sootra _ 129, heey dekhil done prerkanmadhil jodaniche mojmap aahe. circuit sootra _ 65 varr circuit sootra _ 2 dware paraspar preran duheri avibhajya "neuman sootra" dware dile jaate, ganana tantre pahaa
paraspar preranamadhye dekhil sambandh aaheh
sootra _ 132
kuthe?
ekada mutual inductance, sootra _ 133, nishchit jhaale qee, tyacha vapar paripathatil vartanacha andaj lavnyasathi keela jaau shakatoh
sootra _ 134
kuthe?
vartaman sootra _ 135 aakrutimadhye paribhashit kele aahe yaa arthamule vaja chinh udbhavate. donhi pravah bindunmadhye jaanyas paribhashit kele asalyas sootra _ 133 chey chinh sakaratmak asel (tyaeivaji samikaran adhik chinhasah vachale jaeel).
jodani gunank.
jode gunank heey open-circuit vastavik voltage gunottar aanee gunottar yanche gunottar aahe jeey serve pravah eka chumbakeey paripathatoon dusya chumbakeey paripathat jodale gele tarr prapt hoil. jodani gunank khaleel prakare paraspar preran aanee swayam preran yanchyashi sambandhit aahe. too-poort matrixmadhye vyakt kelelya done ekach velee samikarananvarun open-circuit voltage gunottar asey aadhalateh
sootra _ 137
kuthe?
jarr serve pravah jodale gele tarr gunottar heey valananche gunottar aahe, mhanoon inductancechya vargmoolache gunottar
sootra _ 138
tyamule,
sootra _ 139
kuthe?
coupling gunank haah eka soyiskar marg aahe jyamule inductorschya vishisht abhimukhata aanee aniyantrit inductance yanchyatil sambandh spasht keela jaato. bahutek lekhak shrenichi vyakhya ashee karatat, parantu kahijan tyachi vyakhya sootra _ 11 chya nakaratmak moolyanna parvanagi dett coil jodanyanchya tappyatil ulatya aanee valananchi disha capture karatat.
matrixche pratinidhitva.
paraspar jodalelya inductorsche varnan too-poort network parameter matrixchya konatyahi pratinidhitvadvare kele jaau shakate. sarvat thet aahet zed mapdand, jeey dware dile jaatat
sootra _ 141
jethe sootra _ 142 heey jatil varanvarta chull aahe, sootra _ 143 aanee sootra _ 144 heey anukrame prathamik aanee duyyam gundaliche preran aahet aanee sootra _ 133 heey gundalyanmadhil paraspar preran aahe.
samatulya paripath.
tii-circuit.
paraspar jodalele inductors darshavilyapramane inductorschya tii-sarkitdware samaan ritine darshavile jaau shakatat. jarr jodani majboot asel aanee prerak asman mulyanche asateel tarr payari-khalee bajuvaril malika prerak nakaratmak moolya gheu shakato.
yache vishleshan too poort network mhanoon kele jaau shakate. kahee aniyantrit pratibadhesah samapt jhalelya outputs, sootra _ 146, voltage geena, sootra _ 147, dware dile jaate,
sootra _ 148
jethe formula _ 11 haah coupling sthirank aahe aanee formula _ 142 haah varr namood kelyapramane complexes frequency variable aahe.
ghatt jodalelya inductorsasathi jethe heey qamee hote
sootra _ 151
jeey bhaar pratibadha pasoon swatantra aahe. jarr inductors ekach koarvar aanee samaan bhoomitisah vran kelele asateel, tarr heey samikaran done inductorschya valanachya gunottarasarkhe aahe kaaran inductance heey valanachya gunottaranchya vargala pramanbaddh aahe.
jaalyacha input pratibadha hyadvare deela jaato,
sootra _ 152
yasathi qamee
sootra _ 153
asha prakare, pudhil aut asalyashivay current geena, sootra _ 154 heey bharapasoon swatantra nahee
sootra _ 155
tee purn hote, asha paristhitit,
sootra _ 156
aanee
sootra _ 157
π-circuit.
vaikalpikaritya, pratyek bandaravar paryayi aadarsh parivartakansah 'π' samatulya paripath vaparoon done jodalele prerak model kele jaau shakatat. tii-sarkitpeksha circuit adhik klisht asale taree, donpeksha jaast jodalelya inductors asalelya circuitsathi tyache samanyikaran kele jaau shakate. samatulya paripath ghatakanche sootra _ 158, sootra _ 159 chaa bhautik arth aahe, joou jodani marganche anukrame chumbakeey anichha aanee galatee marganche chumbakeey anichha yanche pratirupan karate. udaharanarth, yaa ghatakanmadhun vahanare vidyut pravah jodani aanee galatee chumbakeey pravahanshi sambandhit aahet. ganiteey sutre sopee karnyasathi aadarsh parivartak serve swayam-prernes 1 henarimadhye samanya karatat.
samatulya paripath ghatak mulyanchi ganana sahgunak jodanyavarun kelee jaau shakate
sootra _ 160
jethe jodani gunank matricks aanee tyache sahghatak ashee paribhashit kelee jaatat
done jodalelya prerkansathi, hii sutre sopee karatat
aanee teen jodalya gelelya prerkansathi (fakt sootra _ 165 aanee sootra _ 166 sathee darshavilelya sankshiptatesathi)
anunadit parivartak.
jevha capacitor transformerchya eka valanavar jodala jaato, jyamule valanala eka tune kelele circuit (anunad circuit) banate, tevha tyala single-tune transformer mhanatat. jevha pratyek valanavar capacitor jodala jaato, tevha tyala duheri tune kelele transformer mhanatat. heey "anunad transformer" anunad paripathasarkhich dolan karnari vidyut urja sathavu shakatat aanee asha prakare bandpass filter mhanoon karya karoo shakatat, jyamule tyanchya anunad varanvartechya jawalil varanvarta prathamik teey duyyam valanakade jaau shakate, parantu itar varanvarta avarodhit karatat. done valananmadhil paraspar preran praman, paripathatil q ghatkashi miloon, varanvarta pratisad vakrareshecha aakar nirdharit karate. duheri tune kelelya transformercha fayda assa aahe qee tyat sadhya tune kelelya sarkitpeksha vistrut bandwidth asoo shakate. duheri-tune kelelya paripathanchya jodaniche varnan coupling gunank sootra _ 11 chya mulyanusar sail-, gambhir-kinwa atee-jode mhanoon kele jaate. jevha done tune kelelya paripathanna paraspar preranadvare shithilpane jodale jaate, tevha bandwidth arund asate. paraspar preran praman vadhat asatana, bandwidth vadhatach jaate. jevha paraspar preran heey gambhir jodanichya palikade vadhavale jaate, tevha varanvarta pratisad vakrareshetil shikhar done shikharanmadhye vibhagale jaate aanee jasjase jodani vadhate tastashi done shikharn aanakhi vegale hotat. yala over coupling mhanatat.
madhyam shrenitil antaravaril (done meetarparyant) upkarnanmadhye wireless veej hastantaranasathi stangley-coupled self-resonent coilcha vapar keela jaau shakato. uchch takkevarichya shaktichya hastantaranasathi majboot jodani aavashyak aahe, jyamule varanvarta pratisadache sarvoch vibhajan hote. 
aadarsh parivartak.
jevha sootra _ 170 asate, tevha prerkala jawalun jodalele mhanoon sambodhale jaate. yavyatirikt, jarr swayam-preran anantaparyant gele, tarr prerak eka aadarsh transformer banato. yaa prakaranat, vidyutpravah, pravah aanee valananchi sankhya khaleel prakare sambandhit asoo shakateh
sootra _ 171
kuthe?
ulat vartamanah
sootra _ 172
kuthe?
eka prerkadvare milanari shakti hii dusya prerkadvare milananya shaktiitakich asate. hii samikarane vidyutpravah srot kinwa vidyutpravah strotandvare konatyahi baljabarikade durlaksh karatat.
patal taranchya aakaranche swa-preran.
khaleel taktyat patal dandgolakar vahakanni (taar) banavalelya vividh sopya aakaranchya swayam-preranasathi sutranchi yadee aahe. samanyatah heey keval tevhach achook asatat jevha taar trijya sootra _ 173 aakarachya parimananpeksha khoopach lahan asel aanee jarr konatehi lohchumbakiy sahitya jawal nasel (chumbakeey gabha nasel).
sootra _ 174 heey 0 aanee 1 darmyanche andaje sthir moolya aahe jeey taratil pravahachya vitarnavar avalambun asateh jevha pravah keval tarchya prushthbhagavar vahato (sampoorn tvacha prabhav), jevha pravah samaan ritine tarchya cross-sectionvar pasarato (thet pravah). goal taransathi, rosa (1908) samatulya sootra deteh
sootra _ 175
kuthe?
sootra _ 176 heey lahan shabdanche pratinidhitva karate jeey sutratoon vagalale gele aahet, jenekarun teey sope hoil. adhik lahan sudharana jyaa sootra _ 177 chya kramanusar badaltat" ashee sandnya vacha (mothe oo sanketan pahaa).