Kev cai Kirchhoff

Lub npe nrov German physicist Gustav Robert Kirchhoff (1824 - 1887), ib tug kawm tiav ntawm lub University of Königsberg, raws li lub rooj zaum ntawm zauv physics ntawm lub University of Berlin, nyob rau lub hauv paus ntawm cov ntaub ntawv thiab Ohm txoj cai tau txais ib co kev cai uas tso cai rau peb mus txheeb xyuas complex hluav taws xob circuits. Yog li ntawd muaj thiab yog siv nyob rau hauv lub electrodynamics ntawm Kirchhoff cov kev cai.

Tus thawj (feem ntau yog ntawm) yog, nyob rau hauv essence, cov kev cai lij choj ntawm kev txuag xwb nyob rau hauv nrog cov mob uas tus nqi yog tsis tau yug los thiab tsis ploj nyob rau hauv ib tug neeg xyuas pib. Qhov no txoj cai siv rau lub pob hlav ntawm qhov hluav taws xob circuits, i.e. point Circuit Court nyob rau hauv uas converges peb lossis ntau tshaj conductors.

Yog hais tias peb coj txoj kev coj ntawm cov tam sim no nyob rau hauv lub Circuit Court, uas yog haum rau tam sim no nkees heev, thiab ib tug uas ncaim - rau qhov tsis zoo, tus lej ntawm cov currents thaum twg ntawm yuav tsum pes tsawg vim hais tias cov nqi yuav tsis noog nyob rau hauv lub site:

kuv = n

Σ Iᵢ = 0,

kuv = l

Nyob rau hauv lwm yam lus, tus nqi ntawm cov xwb uas sib haum mus rau ib tug node nyob rau hauv chav tsev lub sij hawm yuav sib npaug zos rau cov xov tooj ntawm cov nqi uas mus los ntawm ib tug muab point nyob rau hauv tib lub sij hawm lub sij hawm.

Kirchhoff tus thib ob txoj cai - ib tug generalization ntawm Ohm txoj cai thiab yog hais txog mus rau lub kaw nkhaus branched saw.

Nyob rau hauv txhua kaw Circuit Court, ib tug arbitrarily xaiv nyob rau hauv ib tug complex hluav taws xob Circuit Court, lub algebraic sum ntawm cov khoom ntawm currents rog thiab resistances coj contour plots yuav sib npaug rau hauv lub algebraic sum ntawm cov emf nyob rau hauv lub Circuit Court:

kuv = n₁ kuv = n₁

Σ Iᵢ Rᵢ = Σ EI,

kuv = li = l

Kirchhoff cov kev cai yog feem ntau siv los mus txiav txim rau qhov tseem ceeb ntawm qhov tam sim no lub dag lub zog nyob rau hauv lub complex saw tej qhov chaw uas kuj thiab tsis ntawm qhov tam sim no qhov chaw yuav muab. Xav txog cov qauv ntawm cov ntawv thov cov kev cai rau lub xam Circuit Court piv txwv. Txij li thaum lub sib npaug nyob rau hauv uas ntawm kev siv ntawm Kirchhoff cov kev cai, muaj ntau algebraic equations, tus xov tooj yuav tsum yog tib lub xov tooj ntawm unknowns. Yog hais tias lub analyzed Circuit Court muaj n o thiab m feem (ceg), ces tus thawj txoj cai yuav tsum tsim nyob rau (m - 1) ywj siab sib npaug siv ib tug thib ob txoj cai, ntau (n - m + 1) ywj siab sib npaug.

Action 1. Xaiv ib tug random kev taw qhia tam sim no, tsom kwm "txoj cai" inflow thiab outflow, lub node tej zaum yuav tsis tau rau qhov chaw los yog ntws nqi. Yog hais tias koj xaiv qhov tam sim no cov kev taw qhia koj ua yuam kev, ces tus nqi ntawm no tam sim no yuav tsum tau tsis zoo. Tab sis lub qhov chaw ntawm tam sim no txiav txim qhov chaw yog tsis arbitrary, lawv yog dictated los ntawm txoj kev ntawm xws li cov tug.

Kauj ruam 2 Tus kab zauv ntawm lub currents coj mus rau tus thawj Kirchhoff tus txoj cai rau ntawm b:

I₂ - I₁ - I₃ = 0

Kauj ruam 3: Cov sib npaug sib nug xov mus rau lub thib ob Kirchhoff tus txoj cai, tab sis pre-xaiv ob ywj siab circuits. Nyob rau hauv cov ntaub ntawv no muaj peb possibilities: sab laug lub voj {badb}, txoj cai Circuit Court {bcdb} thiab lub contour nyob ib ncig ntawm tag nrho {badcb} saw.

Txij li thaum nws yog tsim nyog los nrhiav tau xwb peb amperage, peb txwv tsis pub peb tus kheej rau ob circuits. bypass nqi kev taw qhia muaj tsis muaj dej tsaws ntxhee thiab EMF pom tau hais tias zoo yog hais tias lawv coincide nrog cov kev taw qhia ntawm cov bypass. Peb mus nyob ib ncig ntawm lub contour {badb} counterclockwise, kab zauv yuav:

I₁R₁ + I₂R₂ = ε₁

Qhov thib ob puag ncig kuas nyuas siv zug ib tug loj nplhaib {badcb}:

I₁R₁ - I₃R₃ = ε₁ - ε₂

Kauj ruam 4: Tam sim no ua li lub system ntawm equations, uas yog yooj yim heev los daws kom tau.

Siv Kirchhoff cov kev cai, koj yuav ua tau es nyuab algebraic kab zauv. Qhov teeb meem no yog yooj yim zog yog hais tias tus Circuit Court muaj tej yam zoo ib yam hais, nyob rau hauv cov ntaub ntawv no tej zaum yuav muaj ntshav nrog ib tug tib potentials thiab lub saw ceg nrog sib npaug dej tsaws ntxhee, uas zoo heev simplifies kab zauv.

Ib tug classical piv txwv ntawm qhov teeb meem no yog qhov teeb meem ntawm kev txiav txim tam sim no rog nyob rau hauv ib tug nyhav zoo li ntawm zoo tib yam resistances. Los ntawm symmetry Circuit Court potentials 2,3,6 cov ntsiab lus, raws li tau zoo raws li 4,5,7 cov ntsiab lus yog tib yam, lawv yuav tsum tau tuaj koom, vim nws tsis hloov nyob rau hauv cov nqe lus ntawm qhov tam sim no muab faib rau, tab sis ho yooj yim zog daim duab. Yog li, Kirchhoff txoj cai mus rau lub qhov hluav taws xob Circuit Court povolyaet yooj yim ua txoj kev xam Circuit Court DC.