Mitemo Kirchhoff

The akakurumbira yefizikisi yokuGermany Gustav Robert Kirchhoff (1824 - 1887), kudzidza paYunivhesiti Königsberg, sezvo chair kwemasvomhu wefizikisi paUniversity of Berlin, pahwaro experimental mashoko uye mutemo Ohm akagamuchira mitemo unobvumira kuti tiongorore zvakaoma magetsi matunhu. Saka pakanga uye zvinoshandiswa mune electrodynamics mitemo Kirchhoff vake.

Wokutanga (kazhinji raiva pedyo nebundu), chaizvoizvo, mutemo kuchengetedza muripo pavanoparidza ezvinhu kuti zvaipomerwa hatiberekwi uye regai inonyangarika ari kondakita. mutemo uyu kwomunguva nodes pakati magetsi nematunhu, i.e. pfungwa redunhu mune converges conductors nhatu kana kupfuura.

Kana isu kutora yakanaka inoenda kuitika mudunhu, inova dzakakodzera kuitika raiva pedyo nebundu, uye uya anoendazve - nokuti akaipa, Verengai dzenzvimbo chero raiva pedyo nebundu anofanira kuva razero nokuti mhosva havagoni kuunganidza iri nzvimbo:

Ini = N

Σ Iᵢ = 0,

I = L

Nemamwe mashoko, uwandu muripo dzinoenderana kuti raiva pedyo nebundu iri chikwata nguva ichava akaenzana nokuwanda kupomera kuti aende kubva apa pfungwa iyoyo nguva.

Kutonga Kirchhoff kechipiri - mumwe zvavo mutemo Ohm uye rinoreva namahwindo contours mapazi cheni.

In redunhu chero namahwindo, ane pamadiro vakasarudzwa muna kunzwisisa magetsi dunhu, nyika algebraic uwandu zvibereko dzenzvimbo mauto uye resistances zvinoenderana gandiwa kwokurangana richafanana ari algebraic Verengai emf mudunhu:

Ini = n₁ Ini = n₁

Σ Iᵢ Rᵢ = Σ Ei,

Ini = he = L

Mitemo Kirchhoff vari zvinowanzoshandiswa kuona tsika nesimba kuitika mune kunzwisisa munzvimbo cheni apo nemishonga uye parameters pakati magetsi zvinyorwa dzinopiwa. Funga nzira kushandisa mitemo kuti kuverenga redunhu muenzaniso. Sezvo equations umo kushandisa mitemo Kirchhoff vaJehovha, nevakawanda algebraic equations, nhamba anofanira kuenzana nokuwanda unknowns. Kana vakaongorora redunhu unotora N nodes uye M migove (matavi), ipapo ushe wokutanga inogona kuumbwa (m - 1) akazvimirira equations kushandisa mutemo wechipiri, zvakawanda (n - mamita + 1) akazvimirira equations.

Action 1. Sarudzai anongoitika mirayiridzo kuitika, vachichengeta "kutonga" inflow uye water drainage, kuti raiva pedyo nebundu angasava kwaibva kana wopedza mhosva. Kana wasarudza mirayiridzo razvino ukakanganisa, ipapo kukosha ichi kuitika achava asina kunaka. Asi kunobva ano chiito nzvimbo hazvisi, ivo zvinosiyana nzira kusanganisira matanda.

Step 2 mukana wokuti vanhu vanga pamusoro dzenzvimbo zvakafanana mutemo wokutanga Kirchhoff kuti raiva pedyo nebundu B:

I₂ - I₁ - I₃ = 0

Danho 3: The equations chaienzanirana wechipiri Kirchhoff kutonga, asi kufanosarudza maviri akazvimirira matunhu. Muchiitiko ichi pane vatatu zvingangoitika: kuruboshwe loop {badb}, zvakarurama wedunhu {bcdb} uye gandiwa akapoteredza yose {badcb} cheni.

Sezvo zvakafanira kuwana matatu chete amperage, isu vanamatai isu pakupotereka maviri. yokunzvenga ukoshi mirayiridzo haana dzenzvimbo uye EMF vanoonekwa zvakanaka kana ivo uwirirane achitungamirirwa yokunzvenga. We vapoterere gandiwa {badb} counterclockwise, mukana wokuti vanhu vanga kunova:

I₁R₁ + I₂R₂ = ε₁

Rwakapoteredza chechipiri zvipire rin'i guru {badcb}:

I₁R₁ - I₃R₃ = ε₁ - ε₂

Danho 4: Zvino vanoumba negadziriro equations, riri nyore kugadzirisa.

Kushandisa mitemo Kirchhoff raMwari, unogona kuita nani zvakaoma algebraic mukana wokuti vanhu vanga. Mamiriro acho ezvinhu nyore kana redunhu rine zvimwe symmetric okunze, muchiitiko ichi pangava nodes ane chete potentials uye cheni bazi zvakaenzana dzenzvimbo, izvo nyore zvikuru mukana wokuti vanhu vanga.

A venguva Muenzaniso uyu mamiriro ezvinhu ndiwo dambudziko kuziva kuitika mauto ari cubic chimiro rinoumbwa dzakafanana resistances. By symmetry redunhu potentials 2,3,6 pfungwa, uyewo 4,5,7 pfungwa ndiwo chete, vanogona kuva vakabatana, sezvo haachinji tichitarisa zviri kuitika nokuparadzirwa, asi yekudyidzana nyore chati. Saka, Kirchhoff mutemo kuti magetsi wedunhu povolyaet nyore kuita kunzwisisa kukarukureta redunhu DC.