Piv txwv ntawm Kirchhoff Txoj Cai Lus Nug 1
Cov kev cai lij choj Kirchhoff yog ib qho ntawm cov ntsiab lus tseem ceeb hauv kev tshuaj xyuas hluav taws xob. Muaj ob txoj kev cai lij choj Kirchhoff: Kirchhoff txoj cai tam sim no (KCL) thiab Kirchhoff txoj cai voltage (KVL). Tsab xov xwm no yuav tham txog Kirchhoff txoj cai thawj zaug, lossis Kirchhoff txoj cai tam sim no (KCL), nrog rau ntau qhov piv txwv teeb meem thiab kev daws teeb meem los pab cov tub ntxhais kawm qib 11 thiab 12 nkag siab.
Kev Nkag Siab Txog Txoj Cai Kirchhoff 1
Kirchhoff txoj cai tam sim no (KCL) hais tias qhov sib npaug ntawm cov hluav taws xob nkag mus rau hauv lub node hauv lub voj voog hluav taws xob yog sib npaug rau qhov sib npaug ntawm cov hluav taws xob tawm hauv lub node ntawd. Hauv lej, txoj cai no tuaj yeem piav qhia li:
\[ \sum I_{in} = \sum I_{out} \]
Qhov no txhais tau tias tsis muaj kev sib sau ua ke ntawm cov hluav taws xob ntawm lub node; txhua qhov hluav taws xob nkag los yuav tsum tawm mus.
Cov Ntsiab Cai Tseem Ceeb ntawm Kirchhoff Txoj Cai 1
1. Node: Lub ntsiab lus hauv ib lub voj voog uas ob lossis ntau lub voj voog sib ntsib.
2. Cov Hluav Taws Xob Tuaj thiab Tawm: Cov hluav taws xob uas ntws mus rau ib qho node raug suav hais tias yog cov hluav taws xob tuaj (zoo), thaum cov hluav taws xob uas ntws tawm ntawm ib qho node raug suav hais tias yog cov hluav taws xob tawm (tsis zoo).
Piv txwv ntawm Kirchhoff Txoj Cai Lus Nug 1
Nov yog qee cov lus nug piv txwv uas piav qhia txog kev siv Kirchhoff's 1st Law.
Piv txwv teeb meem 1: Knot yooj yim
Teeb Meem: Ntawm ib lub node hauv ib lub circuit, muaj peb lub incoming currents thiab ib lub outgoing current. Cov incoming currents yog \(I_1 = 2 \, \text{A}\), \(I_2 = 3 \, \text{A}\), thiab \(I_3 = 1 \, \text{A}\). Xam qhov tam sim no tawm ntawm lub node (\(I_{out}\)).
Kev daws teeb meem:
Raws li Kirchhoff Txoj Cai Thawj Zaug, qhov sib npaug ntawm cov dej ntws tuaj yog sib npaug rau qhov sib npaug ntawm cov dej ntws tawm. Yog li, peb muaj:
\[ Kuv_1 + Kuv_2 + Kuv_3 = Kuv_{\tau} \]
Sau cov nqi tam sim no:
\[ 2 + 3 + 1 = Kuv_ { tawm} \]
\[ 6 \, \text{A} = Kuv_{out} \]
Yog li, tam sim no tawm ntawm lub node yog \(6 \, \text{A}\).
Piv txwv 2: Node nrog Cov Hluav Taws Xob Tuaj thiab Tawm
Teeb Meem: Ntawm ib lub node hauv ib lub circuit, muaj ob lub incoming currents, \(I_1 = 5 \, \text{A}\) thiab \(I_2 = 4 \, \text{A}\), thiab ob lub outgoing currents, \(I_3\) thiab \(I_4 = 6 \, \text{A}\). Xam qhov tam sim no \(I_3\).
Kev daws teeb meem:
Raws li Kirchhoff Txoj Cai Thawj Zaug, qhov sib npaug ntawm cov dej ntws tuaj yog sib npaug rau qhov sib npaug ntawm cov dej ntws tawm. Yog li, peb muaj:
\[ Kuv_1 + Kuv_2 = Kuv_3 + Kuv_4 \]
Sau cov nqi tam sim no uas paub:
\[ 5 + 4 = I_3 + 6 \]
\[ 9 = I_3 + 6 \]
Yuav nrhiav tau \(I_3\):
\[ I_3 = 9 – 6 \]
\[ I_3 = 3 \, \text{A} \]
Yog li, tam sim no \(I_3\) yog \(3 \, \text{A}\).
Piv txwv teeb meem 3: Circuit nrog ntau lub Nodes
Lus Nug: Hauv ib lub voj voog hluav taws xob, muaj peb lub nodes A, B, thiab C. Tam sim no \(I_1 = 2 \, \text{A}\) ntws los ntawm A mus rau B, tam sim no \(I_2 = 3 \, \text{A}\) ntws los ntawm B mus rau C, thiab tam sim no \(I_3 = 1 \, \text{A}\) ntws los ntawm C mus rau A. Xam tag nrho tam sim no nkag thiab tawm ntawm node B.
Kev daws teeb meem:
Rau node B, peb yuav tsum xam tag nrho cov hluav taws xob nkag thiab tawm. Los ntawm qhov teeb meem, nws paub tias hluav taws xob \(I_1\) nkag mus rau node B thiab hluav taws xob \(I_2\) tawm ntawm node B.
Tus nqi ntawm tam sim no nkag mus rau node B:
\[ Kuv_{in} = Kuv_1 \]
\[ Kuv_{in} = 2 \, \text{A} \]
Tus nqi ntawm cov dej ntws tawm ntawm node B:
\[ Kuv_{\tau} = Kuv_2 \]
\[ Kuv_{out} = 3 \, \text{A} \]
Raws li Kirchhoff Txoj Cai Thawj Zaug, qhov sib npaug ntawm cov dej ntws los yuav tsum sib npaug rau qhov sib npaug ntawm cov dej ntws tawm. Txawm li cas los xij, hauv qhov teeb meem no, peb kuj yuav tsum xav txog qhov dej ntws los ntawm node C mus rau node B, uas tseem tsis tau muab rau hauv qhov teeb meem.
Yog tias peb xav txog qhov tam sim no ntws los ntawm C mus rau B ua \(I_4\), ces peb tuaj yeem sau qhov sib npaug:
\[ Kuv_1 + Kuv_4 = Kuv_2 \]
Vim tias \(I_1 = 2 \, \text{A}\) thiab \(I_2 = 3 \, \text{A}\):
\[ 2 + I_4 = 3 \]
\[ I_4 = 1 \, \text{A} \]
Yog li, qhov tam sim no nkag mus rau ntawm node B los ntawm node C yog \(1 \, \text{A}\), yog li ntawd tag nrho cov tam sim no nkag mus thiab tawm hauv node B tseem nyob raws li Kirchhoff Txoj Cai 1.
Kev siv Kirchhoff txoj cai thib 1 hauv Complex Circuits
Hauv cov voj voog uas nyuaj dua, peb feem ntau ntsib ntau lub nodes thiab ntau ceg tam sim no. Cia peb saib ib qho piv txwv nyuaj dua kom nkag siab txog kev siv Kirchhoff Txoj Cai Thawj Zaug kom tob dua.
Piv txwv teeb meem 4: Lub voj voog nyuaj nrog ntau lub qhov siab
Teeb Meem: Hauv lub voj voog hauv qab no, muaj plaub lub nodes (A, B, C, D) nrog cov hluav taws xob \(I_1 = 4 \, \text{A}\) los ntawm A mus rau B, \(I_2 = 5 \, \text{A}\) los ntawm B mus rau C, \(I_3 = 3 \, \text{A}\) los ntawm C mus rau D, thiab \(I_4 = 2 \, \text{A}\) los ntawm D mus rau A. Xam qhov hluav taws xob uas tawm ntawm lub node A.
Kev daws teeb meem:
Peb yuav tsum xam tag nrho cov dej ntws uas nkag thiab tawm ntawm txhua lub node. Ua ntej, cia peb saib ntawm node A.
Ntawm node A, qhov tam sim no \(I_4\) nkag mus thiab qhov tam sim no \(I_1\) tawm mus.
\[ \sum I_{in} = I_4 \]
\[ \sum I_{out} = I_1 \]
Sau tus nqi tam sim no uas paub:
\[ I_4 = 2 \, \text{A} \]
\[ I_1 = 4 \, \text{A} \]
Vim tias \(I_1\) loj dua \(I_4\), qhov no txhais tau tias muaj ib qho hluav taws xob ntxiv tawm ntawm node A uas yuav tsum los ntawm lwm qhov hluav taws xob uas tsis tau hais txog. Cia peb saib lwm qhov hluav taws xob ntawm node A:
Tus tam sim no ntxiv yog \(I_5\):
\[ Kuv_5 = Kuv_1 – Kuv_4 \]
\[ I_5 = 4 – 2 \]
\[ I_5 = 2 \, \text{A} \]
Yog li, muaj ib qho ntxiv tam sim no ntawm \(2 \, \text{A}\) tawm ntawm node A.
Xaus
Txoj Cai Thawj Zaug ntawm Kirchhoff yog ib qho cuab yeej tseem ceeb hauv kev tshuaj xyuas hluav taws xob. Los ntawm kev nkag siab thiab siv txoj cai no, peb tuaj yeem txiav txim siab qhov tam sim no ntws los ntawm ntau lub nodes hauv lub voj voog nyuaj. Los ntawm ntau qhov teeb meem piv txwv uas tau nthuav tawm, peb tuaj yeem pom tias Txoj Cai Thawj Zaug ntawm Kirchhoff pab peb nkag siab thiab daws cov teeb meem hauv cov voj voog hluav taws xob li cas. Kev xyaum txuas ntxiv nrog cov teeb meem zoo li no yuav pab cov tub ntxhais kawm txhim kho lawv txoj kev nkag siab txog lub tswv yim no thiab siv nws kom zoo dua hauv lawv cov kev kawm txog physics.
