Xeerarka Kirchhoff

The jirka dadka caanka Jarmal Gustav Robert Kirchhoff (1824 - 1887), ka qalin ah oo ka tirsan Jaamacadda Königsberg, sida madax ka ah physics xisaabeed ee Jaamacadda Berlin, ku salaysan xogta tijaabo iyo sharciga Ohm ayaa helay set oo ah xeerarka in oo noo ogolaadaa in si ay u falanqeeyaan wareeggeedii korontada adag. Sidaas waxaa jiray oo waxaa loo isticmaalaa in ka electrodynamics xeerarka Kirchhoff ee.

Ta hore (caadi ahaan node) waa, in nuxurka, sharciga ilaalinta la'aan lala shardi ah in eedaymaha aan ku dhashay oo ma baabi'i ee kaari ah. Xeerkani wuxuu khuseeyaa noodes ee ku wareeggeedii korontada, i.e. circuit dhibic, taas oo converges saddex ama in ka badan kirishbooyada.

Haddii aan soo qaadanno dhinaca wanaagsan ee hadda ku soo wareegi jiray, taas oo ku haboon yahay in ay node hadda, iyo mid ka mid ah in ka tago - for negative ah, wadarta hadda ee Guntin kasta waa in ay ahaadaan eber, sababtoo ah eedeymaha ma gaari karaan in goobta:

i = n

Σ Iᵢ = 0,

i = l

In si kale loo dhigo, xaddiga lacag u dhigma Guntin ah ee waqtiga unit noqon doonaa siman ay tirada lagu eedeeyay in ka tago hal dhibic siiyey in muddo waqti isku mid ah.

Kirchhoff ee xeerka labaad - guud a sharciga Ohm iyo loola jeedaa in contours xiran jahaysteen silsilad.

In kasta oo circuit xidhan, oo ah sharci darro ah loo doortay in circuit korontada adag, wadarta aljabrada ee alaabta ee ciidamada hadda iyo resistances dhiganta sirqoollada dusha barbareyn doonaa wadarta aljabrada ee emf ee Bannaanka:

i = n₁ i = n₁

Σ Iᵢ Rᵢ = Σ EI,

i = li = l

xeerarka Kirchhoff ayaa inta badan la isticmaalo si loo ogaado qiimaha of xoogga hadda meelaha silsilad adag meesha iska caabin ah oo xuduudaha ka ilaha hadda waxaa la siiyaa. Ka fikir habka codsiga xeerarka in tusaale ahaan circuit xisaabinta. Tan iyo isleegyo, taas oo isticmaalka xeerarka Kirchhoff ee, waa isleeg caadi aljabrada, tirada waa simanyihiin tirada dahsoon. Haddii Bannaanka falanqeeyay kooban qanjidhada n iyo qaybo m (laamaha), ka dibna xukunka ugu horeysay ee la abuuri karaa (m - 1) isleegyo madax banaan oo isticmaalaya xeerka labaad, ka badan (n - m + 1) isleegyo madax banaan.

Action 1. Dooro a random jihada hadda, logu "xukun" loogasoo iyo dheecaanka, Guntin waxaa laga yaabaa in aanay noqon il ama daadi eedeeyay. Haddii aad doorato jihada hadda aad qalad samayso, ka dibna qiimaha hadda tani waxay noqon doontaa xun. Laakiin ilaha meelaha tallaabo hadda ma yihiin aan loo aabo yeelin, waxay loo Yeedhiyaa by hab oo ay ka mid yihiin ulaha.

Tallaabada 2 isla'egta ee hadda ku dhiganta Kirchhoff ugu horeysay ee xukunka, waayo, Guntin b:

I₂ - I₁ - I₃ = 0

Tallaabo 3: The isleegyo u dhiganta xukunkii labaad Kirchhoff ee, laakiin pre-xulo laba wareeggeedii madax banaan. Xaaladdan oo kale, waxaa jira saddex suurtagal: loop bidix {badb}, circuit xaq {bcdb} oo dusha ku wareegsan oo dhan {badcb} silsiladda.

Tan iyo markii ay lagama maarmaan tahay in la helo amperage saddex kaliya, annaga qudhayadu xaddido laba wareeggeedii. jihada qiimaha isku tallaalidda ma laha hadda iyo EMF waxaa loo tixgeliyaa wanaagsan haddii ay la jihada ah isku tallaalidda la cimri tahay. Waxaan u tegi hareeraha dusha {badb} counterclockwise ah, isla'egta uu noqdo:

I₁R₁ + I₂R₂ = ε₁

Wareegii labaad samayn giraan weyn {badcb}:

I₁R₁ - I₃R₃ = ε₁ - ε₂

Tallaabada 4: Hadda ka samaysan nidaamka isleegyo, taas oo waa wax fudud si ay u xalliyaan.

Oo isticmaalaya xeerar Kirchhoff ee, aad qaban karto isla'egta aljabrada halkii adag. Xaaladda waxaa fududeeyey haddii Bannaanka ka kooban yahay xubno ka symmetric gaar ah, haddii ay taasi waxaa laga yaabaa in qanjidhada oo leh awoodo isku mid ah iyo laan silsiladda la hadda loo siman yahay, taas oo si weyn u fududeyneysa isla'egta.

Tusaale A classical xaaladda tani waa dhibaatada go'aaminta ciidamada hadda ka jirta qaab cubic ka kooban resistances isku mid. By circuit dhabanada kartiyo 2,3,6 dhibcood, sidoo kale 4,5,7 dhibcood waa isku mid, waxay la xidhiidhiyo karo, tan iyo ma aysan beddeli eego qaybinta ee hadda jira, laakiin si weyn u fududeeyey jaantuska. Sayidka, sharciga Kirchhoff in wareegga korantada si fudud u qabtaan povolyaet circuit xisaab adag DC.