Fomura yeMutemo yaKirchhoff
Mitemo yaKirchhoff ndiyo misimboti mikuru mukuongorora macircuit emagetsi inoshandiswa kuverenga ma currents nema voltages muma circuit emagetsi. Mitemo iyi yakatumidzwa zita raGustav Kirchhoff, nyanzvi yefizikisi yekuGermany yakaigadzira muna 1845. Mitemo miviri yaKirchhoff inonyanya kukosha mukuongorora macircuit emagetsi: Kirchhoff's Current Law (KCL) neKirchhoff's Voltage Law (KVL). Chinyorwa chino chichakurukura mitemo yese iri miviri zvakadzama, kutsanangura mashandisirwo ayo mumamiriro akasiyana-siyana, uye kupa mienzaniso inoratidza kushandiswa kwayo.
Mutemo waKirchhoff weParizvino (KCL)
Mutemo waKirchhoff weParizvino, unozivikanwawo seKCL, unoti huwandu hwemagetsi anopinda panzvimbo yebazi mudunhu remagetsi hwakaenzana nehuwandu hwemagetsi anopinda panzvimbo iyoyo. Pamasvomhu, mutemo uyu unogona kutsanangurwa seizvi:
\[ \sum I_{\text{in}} = \sum I_{\text{out}} \]
kana
\[ \sum I = 0 \]
Mutemo uyu wakavakirwa panheyo yekuchengetedza chaji, iyo inotaura kuti chaji yemagetsi haigone kugadzirwa kana kuparadzwa chero panguva ipi zvayo mudunhu. Izvi zvinoreva kuti chaji chero ipi inopinda panzvimbo iyoyo inofanira kubuda.
Muenzaniso weMutemo waKirchhoff weParizvino
Ngatitii tine poindi yebazi ine mafungu matatu anopinda nekubuda mairi. Kana \( I_1 \) uye \( I_2 \) ari iwo mafungu anopinda panzvimbo yacho, uye \( I_3 \) ari iwo mafungu anobuda mairi, saka maererano neMutemo waKirchhoff weCurrent:
\[I_1 + I_2 = I_3 \]
Semuenzaniso, kana \( I_1 = 3 \text{A} \) uye \( I_2 = 2 \text{A} \), saka kubuda kwezvino \( I_3 \) kunogona kuverengerwa seizvi:
\[ I_3 = I_1 + I_2 = 3 \chinyorwa{A} + 2 \chinyorwa{A} = 5 \chinyorwa{A} \]
Mutemo weVoltage waKirchhoff (KVL)
Mutemo weVoltage waKirchhoff, unozivikanwawo seKVL (Mutemo weVoltage waKirchhoff), unoti huwandu hwemavoltage ese ari muchikamu chakavharwa hwakaenzana ne zero. Pamasvomhu, mutemo uyu unogona kutsanangurwa seizvi:
\[ \sum V = 0 \]
Mutemo uyu wakavakirwa panheyo yekuchengetedza simba, iyo inoti simba rose riri mudenderedzwa rakavharwa rinofanira kugara risingachinji. Panyaya yemagetsi, izvi zvinoreva kuti kudonha kwemagetsi ese kutenderedza denderedzwa kunofanira kuenzana nekuwedzera kwemagetsi ese.
Muenzaniso weMutemo weVoltage waKirchhoff
Ngatitii tine jira rakavharwa rine zvikamu zvitatu: tsime remagetsi \( V \), resistor \( R_1 \) ine kudonha kwemagetsi \( V_{R1} \), uye resistor \( R_2 \) ine kudonha kwemagetsi \( V_{R2} \). Sekureva kweMutemo weVoltage waKirchhoff:
\[ V – V_{R1} – V_{R2} = 0 \]
Semuenzaniso, kana \( V = 12 \text{V} \), \( V_{R1} = 4 \text{V} \), uye \( V_{R2} = 8 \text{V} \), mutemo wemagetsi waKirchhoff unoita kuti:
\[ 12 \text{V} – 4 \text{V} – 8 \text{V} = 0 \]
Kushandiswa kweMutemo waKirchhoff
Mitemo yaKirchhoff inoshandiswa mumhando dzakasiyana dzemashandisirwo ekuongorora macircuit emagetsi. Heano mamwe matanho akajairika anoteverwa mukushandisa mitemo iyi:
1. Kuziva Nzvimbo dzeBazi neMarobho: Danho rekutanga mukuongorora dunhu nderekuona nzvimbo dzese dzebazi nemarabhobho mudunhu. Nzvimbo yebazi inzvimbo apo zvikamu zviviri kana kupfuura zvemagetsi zvinobatana, nepo jira riri nzira yakavharwa mudunhu.
2. Shandisa Mutemo waKirchhoff weParizvino: Pachikamu chimwe nechimwe chebazi, shandisa Mutemo waKirchhoff weParizvino kuti unyore chiyero chazvino. Izvi zvinogadzira chiyero chimwe chete chechikamu chimwe nechimwe chebazi.
3. Shandisa Kirchhoff's Voltage Law: Pachitenderedzo chega chega chiri mudunhu, shandisa Kirchhoff's Voltage Law kunyora voltage equation. Izvi zvinogadzira equation imwe chete pachitenderedzo chega chega.
4. Gadzirisa Sisitimu yeMaequations: Shandisa sisitimu yemaequations inobuda kuti uverenge magetsi nemagetsi ari mudunhu. Izvi zvinowanzo sanganisira matekiniki ekutanga ealgebraic kana nzira dzekuverenga kuti ugadzirise maequations panguva imwe chete.
Mienzaniso yeMibvunzo pamusoro peKushandiswa kweMutemo waKirchhoff
Ngatitarisei muenzaniso wekushandisa mitemo yaKirchhoff muchikamu chakareruka:
Mubvunzo:
Zvichipiwa dunhu rine source yevoltage \( V = 10 \text{V} \), ma resistors maviri \( R_1 = 2 \Omega \) uye \( R_2 = 3 \Omega \), uye branch point apo ma currents anopatsanuka kuita \( I_1 \) kuburikidza ne \( R_1 \) uye \( I_2 \) kuburikidza ne \( R_2 \). Verenga ma currents \( I_1 \) uye \( I_2 \).
Mhinduro:
1. Ziva Mapoinzi eBazi uye Marobho:
– Nzvimbo yebazi apo matavi aripo ari mu \(I_1 \) uye \(I_2 \).
– Chitenderedzo chakavharwa chinosanganisira sosi yemagetsi \( V \), resistor \( R_1 \), uye resistor \( R_2 \).
2. Shandisa Mutemo waKirchhoff wePari Zvino paBazi reBazi:
\[ Ini = Ini_1 + Ini_2 \]
3. Shandisa Mutemo weVoltage waKirchhoff muLoop:
\[ V – I_1 R_1 – I_2 R_2 = 0 \]
\[ 10 – 2I_1 – 3I_2 = 0 \]
4. Gadzirisa Sisitimu yeMaequations:
Nemaequation maviri:
\[ Ini = Ini_1 + Ini_2 \]
\[ 10 – 2I_1 – 3I_2 = 0 \]
Ngatitii \( I = 2 \text{A} \). Zvadaro:
\[ 2 = I_1 + I_2 \]
\[ 10 – 2I_1 – 3I_2 = 0 \]
Kubva pa equation yekutanga, tinogona kuronga kuti tiwane \( I_2 \):
\[I_2 = 2 – I_1 \]
Isa \( I_2 \) muequation yechipiri:
\[ 10 – 2I_1 – 3(2 – I_1) = 0 \]
\[ 10 – 2I_1 – 6 + 3I_1 = 0 \]
\[10 – 6 + I_1 = 0 \]
\[I_1 = -4 \]
Saka, ikozvino \( I_1 \) i4 A.
Mhedziso
Mitemo yaKirchhoff maturusi akakosha mukuongorora macircuit emagetsi. Mutemo waKirchhoff weParizvino (KCL) neMutemo weVoltage waKirchhoff (KVL) zvinopa hwaro hwekuverenga macurrents nemavoltage mumacircuit emagetsi akaomarara. Tichishandisa misimboti iyi, tinogona kugadzirisa matambudziko akasiyana-siyana mukugadzira nekuongorora macircuit emagetsi. Kunzwisisa nekushandisa mitemo yaKirchhoff kunotibvumira kugadzira macircuit anoshanda zvakanaka uye anoshanda zvakanaka mumashandisirwo akasiyana-siyana, kubva kumidziyo yemagetsi yemazuva ese kusvika kumasisitimu makuru esimba.
