Misalin Dokar Kirchhoff Tambaya ta 1
Dokokin Kirchhoff suna ɗaya daga cikin muhimman ra'ayoyi a cikin nazarin da'irar lantarki. Akwai dokokin Kirchhoff guda biyu: dokar Kirchhoff ta yanzu (KCL) da dokar ƙarfin lantarki ta Kirchhoff (KVL). Wannan labarin zai tattauna dokar Kirchhoff ta farko, ko dokar Kirchhoff ta yanzu (KCL), tare da misalai da dama na matsaloli da mafita don taimaka wa ɗaliban aji na 11 da 12 su fahimta.
Fahimtar Dokar Kirchhoff ta 1
Dokar Kirchhoff ta yanzu (KCL) ta bayyana cewa jimlar kwararar da ke shiga wani wuri a cikin da'irar lantarki daidai take da jimlar kwararar da ke barin wannan wuri. A lissafi, ana iya bayyana wannan doka kamar haka:
\[ \sum I_{in} = \sum I_{out} \]
Wannan yana nufin babu tarin wutar lantarki a wurin; dole ne duk wutar lantarki mai shigowa ta fita.
Ka'idojin Asali na Dokar Kirchhoff 1
1. Node: Wurin da ke cikin da'ira inda abubuwa biyu ko fiye suka haɗu.
2. Ruwan da ke shigowa da wanda ke fita: Ruwan da ke gudana zuwa wani wuri ana ɗaukarsa ruwan da ke shigowa (mai kyau) ne, yayin da ruwan da ke fitowa daga wani wuri ana ɗaukarsa ruwan da ke fita (mara kyau).
Misalin Dokar Kirchhoff Tambaya ta 1
Ga wasu misalai na tambayoyi da ke nuna yadda ake amfani da Dokar Kirchhoff ta 1.
Misali Matsala ta 1: Makulli Mai Sauƙi
Matsala: A wani wuri a cikin da'ira, akwai kwararar ruwa guda uku masu shigowa da kuma kwararar ruwa guda ɗaya mai fita. kwararar ruwa masu shigowa sune \(I_1 = 2 \, \text{A}\), \(I_2 = 3 \, \text{A}\), da \(I_3 = 1 \, \text{A}\). Lissafa kwararar ruwa daga cikin wurin (\(I_{out}\)).
Mafita:
A bisa ga Dokar Farko ta Kirchhoff, jimlar kwararar da ke shigowa daidai take da jimlar kwararar da ke fita. Don haka, muna da:
\[ I_1 + I_2 + I_3 = I_{out} \]
Shigar da ƙimar yanzu:
\[ 2 + 3 + 1 = I_{fita} \]
\[ 6 \, \text{A} = I_{out} \]
Don haka, wutar da ke fitowa daga cikin node ɗin ita ce \(6 \, \text{A}\).
Misali na 2: Node tare da kwararar ruwa mai shigowa da mai fita
Matsala: A wani wuri a cikin da'ira, akwai kwararar ruwa guda biyu masu shigowa, \(I_1 = 5 \, \text{A}\) da \(I_2 = 4 \, \text{A}\), da kwararar ruwa guda biyu masu fita, \(I_3\) da \(I_4 = 6 \, \text{A}\). Lissafa halin yanzu \(I_3\).
Mafita:
A bisa ga Dokar Farko ta Kirchhoff, jimlar kwararar da ke shigowa daidai take da jimlar kwararar da ke fita. Don haka, muna da:
\[ I_1 + I_2 = I_3 + I_4 \]
Shigar da ƙimar halin yanzu da aka sani:
\[ 5 + 4 = I_3 + 6 \]
\[ 9 = I_3 + 6 \]
Domin nemo \(I_3\):
\[ I_3 = 9 – 6 \]
\[ I_3 = 3 \, \rubutu{A} \]
Don haka, \(I_3\) na yanzu shine \(3 \, \text{A}\).
Misali Matsala ta 3: Da'ira tare da Nodes da dama
Tambaya: A cikin da'irar lantarki, akwai maɓallai uku A, B, da C. Current \(I_1 = 2 \, \text{A}\) yana gudana daga A zuwa B, current \(I_2 = 3 \, \text{A}\) yana gudana daga B zuwa C, kuma current \(I_3 = 1 \, \text{A}\) yana gudana daga C zuwa A. Lissafa jimlar current da ke shiga da fita node B.
Mafita:
Ga node B, muna buƙatar ƙididdige jimlar currents ɗin da ke shiga da fita. Daga matsalar, an san cewa current \(I_1\) yana shiga node B kuma current \(I_2\) yana barin node B.
Adadin shigar da na'urar B a halin yanzu:
\[I_{in} = I_1 \]
\[I_{in} = 2 \, \text{A} \]
Jimlar kwararar ruwa da ke barin maɓalli B:
\[ I_{out} = I_2 \]
\[ I_{out} = 3 \, \text{A} \]
A bisa ga Dokar Farko ta Kirchhoff, jimlar kwararar da ke shigowa dole ne ta yi daidai da jimlar kwararar da ke fita. Duk da haka, a cikin wannan matsalar, dole ne mu kuma yi la'akari da kwararar da ke gudana daga kulli C zuwa kulli B, wanda har yanzu ba a bayar da shi a cikin matsalar ba.
Idan muka yi la'akari da yadda wutar lantarki ke gudana daga C zuwa B a matsayin \(I_4\), to za mu iya rubuta lissafin:
\[ I_1 + I_4 = I_2 \]
Domin \(I_1 = 2 \, \text{A}\) da \(I_2 = 3 \, \text{A}\):
\[ 2 + I_4 = 3 \]
\[ I_4 = 1 \, \rubutu{A} \]
Don haka, shigar da na'urar B daga na'urar C a halin yanzu shine \(1 \, \text{A}\), don haka jimlar shigar da na'urar B da ke fita da kuma shigar da na'urar ta kasance daidai da Dokar Kirchhoff ta 1.
Aiwatar da Dokar Kirchhoff ta 1 a cikin Da'irori Masu Rikici
A cikin da'irori masu rikitarwa, sau da yawa muna haɗuwa da maɓallai da yawa da rassan wutar lantarki da yawa. Bari mu dubi wani misali mai rikitarwa don fahimtar amfani da Dokar Farko ta Kirchhoff a cikin zurfi.
Misali Matsala ta 4: Da'irar Hadaka Mai Canje-canje Da Dama
Matsala: A cikin da'irar da ke tafe, akwai nodes guda huɗu (A, B, C, D) tare da currents \(I_1 = 4 \, \text{A}\) daga A zuwa B, \(I_2 = 5 \, \text{A}\) daga B zuwa C, \(I_3 = 3 \, \text{A}\) daga C zuwa D, da kuma \(I_4 = 2 \, \text{A}\) daga D zuwa A. Lissafa hasken da ke fitowa daga node A.
Mafita:
Muna buƙatar ƙididdige jimlar wutar lantarki da ke shiga da kuma barin kowace ƙulli. Da farko, bari mu dubi ƙulli A.
A kan node A, na yanzu \(I_4\) yana shiga kuma na yanzu \(I_1\) yana fita.
\[ \sum I_{in} = I_4 \]
\[ \sum I_{out} = I_1 \]
Shigar da ƙimar halin yanzu da aka sani:
\[ I_4 = 2 \, \rubutu{A} \]
\[ I_1 = 4 \, \rubutu{A} \]
Tunda \(I_1\) ya fi \(I_4\) girma, wannan yana nufin akwai ƙarin maɓalli na barin wutar lantarki A wanda dole ne ya fito daga wani maɓalli na wutar lantarki da ba a ambata ba. Bari mu kalli ɗayan maɓalli na wutar lantarki a maɓalli na A:
Ƙarin wutar lantarki shine \(I_5\):
\[ I_5 = I_1 – I_4 \]
\[ I_5 = 4 – 2 \]
\[ I_5 = 2 \, \rubutu{A} \]
Don haka, akwai ƙarin kwararar \(2 \, \text{A}\) da ke fitowa daga node A.
Kammalawa
Dokar Farko ta Kirchhoff kayan aiki ne mai mahimmanci a nazarin da'irar lantarki. Ta hanyar fahimtar da amfani da wannan doka, za mu iya tantance kwararar da ke gudana ta cikin maɓallai daban-daban a cikin da'irar mai rikitarwa. Ta hanyar misalai da yawa na matsaloli da aka gabatar, za mu iya ganin yadda Dokar Farko ta Kirchhoff ke taimaka mana mu fahimta da magance matsaloli a cikin da'irar lantarki. Ci gaba da yin aiki tare da matsaloli irin waɗannan zai taimaka wa ɗalibai su ƙarfafa fahimtar wannan ra'ayi kuma su yi amfani da shi yadda ya kamata a cikin nazarin kimiyyar lissafi.
