Muenzaniso weMutemo waKirchhoff Mubvunzo 1
Mitemo yaKirchhoff ndeimwe yepfungwa huru mukuongorora magetsi. Kune mitemo miviri yaKirchhoff: mutemo waKirchhoff wemazuva ano (KCL) uye mutemo wemagetsi waKirchhoff (KVL). Chinyorwa chino chichakurukura mutemo wekutanga waKirchhoff, kana mutemo waKirchhoff wemazuva ano (KCL), pamwe nemibvunzo yakawanda uye mhinduro dzekubatsira vadzidzi vegiredhi rechi11 nerechi12 kunzwisisa.
Kunzwisisa Mutemo waKirchhoff 1
Mutemo waKirchhoff wepari zvino (KCL) unoti huwandu hwemagetsi anopinda muchikamu chemagetsi hwakaenzana nehuwandu hwemagetsi anobuda muchikamu ichocho. Pamasvomhu, mutemo uyu unogona kutsanangurwa seizvi:
\[ \sum I_{in} = \sum I_{out} \]
Izvi zvinoreva kuti hapana kuungana kwemagetsi panzvimbo yacho; magetsi ese anouya anofanira kubuda.
Nheyo Dzekutanga dzeMutemo waKirchhoff 1
1. Node: Nzvimbo iri mudunhu panosangana zvinhu zviviri kana kupfuura zvedunhu.
2. Mafurenzi Anopinda Neanobuda: Mafurenzi anoyerera akananga kupfurenzi anoonekwa semafurenzi anouya (akanaka), nepo mafurenzi anobuda mupfurenzi achionekwa semafurenzi anobuda (asina kunaka).
Muenzaniso weMutemo waKirchhoff Mubvunzo 1
Heano mimwe mienzaniso yemibvunzo inoratidza kushandiswa kweMutemo wekutanga waKirchhoff.
Muenzaniso Dambudziko 1: Nyore Knot
Dambudziko: Panode iri mudunhu, pane macurrents matatu anouya uye rimwe chete rinobuda. Macurrents anouya ndeaya \(I_1 = 2 \, \text{A}\), \(I_2 = 3 \, \text{A}\), uye \(I_3 = 1 \, \text{A}\). Verengai macurrents ari kunze kwenode (\(I_{out}\)).
Mhinduro:
Zvinoenderana nemutemo wekutanga waKirchhoff, huwandu hwemafungu anouya hwakaenzana nehuwandu hwemafungu anobuda. Saka, tine:
\[I_1 + I_2 + I_3 = Ini_{kunze} \]
Isa kukosha kwazvino:
\[ 2 + 3 + 1 = Ini_{kunze} \]
\[ 6 \, \text{A} = I_{out} \]
Saka, magetsi anobuda mu node ndi \(6 \, \text{A}\).
Muenzaniso 2: Node ine Incoming neOutgoing Currents
Dambudziko: Pa node iri mudunhu, pane ma currents maviri anouya, \(I_1 = 5 \, \text{A}\) uye \(I_2 = 4 \, \text{A}\), uye ma currents maviri anobuda, \(I_3\) uye \(I_4 = 6 \, \text{A}\). Verenga ma current \(I_3\).
Mhinduro:
Zvinoenderana nemutemo wekutanga waKirchhoff, huwandu hwemafungu anouya hwakaenzana nehuwandu hwemafungu anobuda. Saka, tine:
\[I_1 + I_2 = I_3 + I_4 \]
Isa ma "current values" anozivikanwa:
\[ 5 + 4 = I_3 + 6 \]
\[ 9 = I_3 + 6 \]
Kuti uwane \(I_3\):
\[I_3 = 9 – 6 \]
\[ I_3 = 3 \, \mashoko{A} \]
Saka, \(I_3\) iripo ikozvino \(3\, \text{A}\).
Muenzaniso Dambudziko rechitatu: Dunhu rine MaNode Akawanda
Mubvunzo: Mudunhu remagetsi, mune ma node matatu A, B, na C. Current \(I_1 = 2 \, \text{A}\) inoyerera kubva kuA kuenda kuB, current \(I_2 = 3 \, \text{A}\) inoyerera kubva kuB kuenda kuC, uye current \(I_3 = 1 \, \text{A}\) inoyerera kubva kuC kuenda kuA. Verenga huwandu hwe current inopinda neinobuda node B.
Mhinduro:
Kune node B, tinofanira kuverenga huwandu hwema currents anopinda nekubuda. Kubva padambudziko iri, zvinozivikanwa kuti current \(I_1\) inopinda node B uye current \(I_2\) inosiya node B.
Huwandu hwechinhu chinopinda nemagetsi B:
\[ Ini_{mu} = Ini_1 \]
\[ I_{in} = 2 \, \text{A} \]
Huwandu hwemafungu anosiya node B:
\[ Ini_{kunze} = Ini_2 \]
\[ I_{out} = 3 \, \text{A} \]
Sekureva kwemutemo wekutanga waKirchhoff, huwandu hwemagetsi anouya hunofanira kuenzana nehuwandu hwemagetsi anobuda. Zvisinei, mudambudziko iri, tinofanirawo kufunga nezvemagetsi anoyerera kubva panode C kuenda panode B, ayo asati apihwa mudambudziko iri.
Kana tikafunga nezvemvura inoyerera kubva kuC kuenda kuB se \(I_4\), tinogona kunyora equation:
\[I_1 + I_4 = I_2 \]
Nekuti \(I_1 = 2 \, \text{A}\) uye \(I_2 = 3 \, \text{A}\):
\[ 2 + I_4 = 3 \]
\[ I_4 = 1 \, \mashoko{A} \]
Saka, node B inopinda panguva ino kubva panode C i \(1 \, \text{A}\), saka huwandu hwese hwemagetsi hunopinda nekubuda panode B hunoramba huchienderana neMutemo waKirchhoff 1.
Kushandiswa kweMutemo wekutanga waKirchhoff muMatunhu Akakombama
Mumacircuit akaomarara, tinowanzo sangana nema node akawanda uye matavi akawanda emagetsi. Ngatitarisei muenzaniso wakaomarara kuti tinzwisise mashandisirwo eMutemo wekutanga waKirchhoff zvakadzama.
Muenzaniso Dambudziko rechina: Dunhu Rakaomarara rine Mavheti Akawanda
Dambudziko: Mudunhu rinotevera, kune ma node mana (A, B, C, D) ane ma currents \(I_1 = 4 \, \text{A}\) kubva kuA kusvika kuB, \(I_2 = 5 \, \text{A}\) kubva kuB kusvika kuC, \(I_3 = 3 \, \text{A}\) kubva kuC kusvika kuD, uye \(I_4 = 2 \, \text{A}\) kubva kuD kusvika kuA. Verenga magetsi anobuda mu node A.
Mhinduro:
Tinofanira kuverenga huwandu hwema currents anopinda nekubuda mu node yega yega. Kutanga, ngatitarisei node A.
Panodhi A, current \(I_4\) inopinda uye current \(I_1\) inopinda.
\[ \sum I_{in} = I_4 \]
\[ \sum I_{out} = I_1 \]
Isa kukosha kwazvino kunozivikanwa:
\[ I_4 = 2 \, \mashoko{A} \]
\[ I_1 = 4 \, \mashoko{A} \]
Sezvo \(I_1\) iri huru kupfuura \(I_4\), izvi zvinoreva kuti pane imwe current inosiya node A inofanira kubva kune imwe current isina kutaurwa. Ngatitarisei imwe current iri pa node A:
Iyo yekuwedzera current ndeye \(I_5\):
\[I_5 = I_1 – I_4 \]
\[I_5 = 4 – 2 \]
\[ I_5 = 2 \, \mashoko{A} \]
Saka, kune imwe current ye \(2 \, \text{A}\) inobuda mu node A.
Mhedziso
Mutemo wekutanga waKirchhoff chishandiso chakakosha mukuongorora dunhu remagetsi. Nekunzwisisa nekushandisa mutemo uyu, tinogona kuona kuti magetsi ari kufamba sei kuburikidza nemanode akasiyana-siyana mudunhu rakaoma. Kuburikidza nematambudziko akati wandei anoratidzwa, tinogona kuona kuti Mutemo wekutanga waKirchhoff unotibatsira sei kunzwisisa nekugadzirisa matambudziko mudunhu remagetsi. Kuramba tichidzidzira nematambudziko akadai kuchabatsira vadzidzi kusimbisa kunzwisisa kwavo pfungwa iyi uye kuishandisa zvinobudirira muzvidzidzo zvavo zvefizikisi.
