Imithetho Kirchhoff

Yamachiza odumileyo German Gustav Robert Kirchhoff (1824 - 1887), owaphumelela kwiYunivesithi Königsberg, njengosihlalo ophanda zezibalo kwiYunivesithi Berlin, ngenxa yokuba data uvavanyo kunye nomthetho Ohm kaThixo ifumene iseti yemithetho evumela ukuba ukuhlalutya iisekethe zombane entsonkothileyo. Ngoko kwakukho kwaye zisetyenziswa kule electrodynamics lwemithetho Kirchhoff kaThixo.

Eyokuqala (idla node) kukuthi, eneneni, umthetho yolondolozo kwentlawulo kunye nemeko ukuba izityholo hayi bezalwa musa zinyamalale umqhubi. Lo mgaqo usebenza yindawo iisekethe zombane, ngamanye circuit indawo apho converges abaqhubi ezintathu okanye ngaphezulu.

Xa sithatha ulwalathiso ezakhayo ngoku kwisekethe, leyo efanelekileyo ukuze esiludumbo yangoku, kunye nalowo uyahamba - kuba ezingakhiyo, udibaniso imisinga nangaliphi na elisisiseko kufuneka zero kuba izityholo angakhuli kwisiza:

i = n

Σ Iᵢ = 0,

i = l

Ngamanye amazwi, isixa kwentlawulo ezihambelana udumbo kwixesha unit iya kulingana nenani iintlawulo ukuba emke kwindawo enikwe ngexesha elifanayo.

ulawulo yesibini Kirchhoff kaThixo - isiphetho yomthetho Ohm yaye libhekisela yakhiwe ezivaliweyo branched chain.

Kuyo nayiphi na wesekethe evaliweyo, i ngokuqgibeleleyo ezikhethiweyo kwindawo yombane esimbaxa, isixa aljibra iimveliso imisinga imikhosi kunye resistances esihambelanayo lucinga nentaba iya kulingana inani aljibra ye-EMF kwisekethe:

i = n₁ i = n₁

Σ Iᵢ Rᵢ = Σ Ei,

i = li = l

imithetho Kirchhoff bakaThixo amaninzi zisetyenziswa ukugqiba amaxabiso amandla yangoku kwimimandla chain entsonkothileyo apho bokuxhathisa kwaye parameters ze nemithombo ngoku banikwa. Cinga indlela ukusebenzisa imithetho ukuya umzekelo ukubala wesekethe. Ekubeni zibalo apho ukusetyenziswa imithetho Kirchhoff, andibi quadratic eziqhelekileyo aljibra, inani kufuneka zilingane inani angaziwa. Ukuba wesekethe yacazululwa iquka n ezalathelwe kunye neenxalenye m (amasebe), ngoko ke umthetho wokuqala kuyilwa (m - 1) quadratic ezizimeleyo usebenzisa ulawulo yesibini, ngaphezulu (n - m + 1) quadratic ezizimeleyo.

Action 1. Khetha indlela yangoku random, ukugcina "lulawulo" ekungeneni kunye kuphuma, esiludumbo isenokungabi umthombo okanye uwutshise iintlawulo. Ukuba ukhetha kwicala yangoku wenze impazamo, ngoko ke ixabiso le yangoku iya kuba mibi. Kodwa ke imithombo iindawo eziza kuthathelwa amanyathelo ngoku ngaba aliqonde; kokuba lilawulwe ngendlela kuquka izibonda.

Inyathelo 2 lenxaki le imisinga ehambelana umthetho wokuqala Kirchhoff kaThixo ophawulwe njengomgca woyilo b:

I₂ - I₁ - I₃ = 0

Inyathelo lesi-3: Ezi zibalo ehambelana ulawulo i Kirchhoff wesibini, kodwa pre-khetha iziphaluka ezibini ezizimeleyo. Kule meko kukho amathuba amathathu: ndzhendzheleko ekhohlo {badb}, ekunene beesekethe {bcdb} kwaye aya ujikeleze lonke {badcb} chain.

Ekubeni kuyimfuneko ukufumana kul ezintathu kuphela, sinikela thina kwiziphaluka ezimbini. ixabiso esa indlela akukho imisinga EMF kuthathwa HIV ukuba kudibane ngokomyalelo ukudlula. Siya emhlabeni aya {badb} ebalwa, i equation uba:

I₁R₁ + I₂R₂ = ε₁

Umjikelo wesibini abazinikezele isangqa esikhulu {badcb}:

I₁R₁ - I₃R₃ = ε₁ - ε₂

Inyathelo lesi-4: Ngoku ukwenza i inkqubo zibalo, nto leyo kakhulu ilula ukuyisombulula.

Ukusebenzisa imithetho Kirchhoff, unako ukwenza equation kunokuba nzima algebra. Le meko lula ukuba wesekethe iqulethe izinto ezithile twatsa, kulo mzekelo kusenokubakho iindawo kunye nekhono efanayo kwaye isebe chain namanzi alinganayo, leyo lula kakhulu equation.

Umzekelo classical yale meko ingxaki emisela imikhosi zangoku enembonakalo cc owakhiwa ngayo resistances ezifanayo. Besifunda lohlukanisa nekhono amanqaku 2,3,6, kwakunye iingongoma 4,5,7 ayafana, ukuba nibe kuwumbi, kuba akukho kutshintsha ngokwemiqathango lonikezelo lwangoku, kodwa lula kakhulu umzobo. Ngenxa yoko, Kirchhoff umthetho ukuya yombane povolyaet ngokulula ukwenza ubalo yesekethe ezintsonkothileyo DC.