Mehlala ea Lipotso Mabapi le Melao ea Kirchoff
Melao ea Kirchhoff ke motheo oa bohlokoa tlhahlobong ea potoloho ea motlakase, haholo-holo ha potoloho e ke ke ea rarolloa ho sebelisoa Molao oa Ohm feela. Bophelong ba 'nete, lipotoloho tsa motlakase hangata li na le makala a mangata, mehloli e mengata ea motlakase, le li-resistor tse 'maloa tse hokahaneng. Mona ke moo melao ea Kirchhoff e re thusang ho bala ka mokhoa o hlophisehileng phallo ea hona joale, motlakase le tataiso ea phallo ea hona joale lekaleng ka leng la potoloho. Sengoloa sena se tšohla kakaretso ea likhopolo tsa melao ea Kirchhoff le mathata a 'maloa a tloaelehileng a mehlala, a felletseng ka mehato ea tharollo bakeng sa kutloisiso e bonolo.
Ho Tseba Molao oa Kirchhoff
Ka kakaretso, ho na le Melao e 'meli ea Kirchhoff e sebelisoang hangata:
1. Molao oa I oa Kirchhoff (KCL - Molao oa Hona Joale oa Kirchhoff)
Ka mantsoe a bonolo: kakaretso ea maqhubu a kenang nodeng e lekana le kakaretso ea maqhubu a tsoang nodeng eo.
Ka lipalo:
\[
\kakaretso I_{in} = \kakaretso I_{out}
\]
kapa e ka boela ea ngoloa:
\[
\kakaretso I = 0
\]
ka letshwao le letle bakeng sa hona joale e kenang le le lebe bakeng sa hona joale e tswang (ho ya ka molao o sebedisitsweng).
2. Molao oa Kirchhoff II (KVL - Molao oa Motlakase oa Kirchhoff)
Ka mantsoe a bonolo: kakaretso ea algebraic ea li-voltage tse ka hara selika-likoe se koetsoeng e lekana le lefela.
Ka lipalo:
\[
\ kakaretso V = 0
\]
Sena se bolela hore keketseho yohle ya motlakase (mohlala, ho tswa ho betri) e lekana le ho theoha ha motlakase kaofela (ho pholletsa le resistor kapa karolo e nngwe) ka hara sekgutlo.
Melao ena e 'meli e atisa ho sebelisoa hammoho: KCL ho sekaseka li-node, le KVL ho sekaseka li-loop (meshes).
-
Mohlala oa Potso ea 1 (KCL): Hona joale ho Node
Potso:
Ho node, ho na le maqhubu a mararo a kenang, e leng \(I_1 = 2A\), \(I_2 = 3A\), le \(I_3 = 1A\). Ho tloha nodeng, maqhubu a mabeli a tsoa, e leng \(I_4\) le \(I_5 = 4A\). Fumana boleng ba \(I_4\).
Tharollo:
Sebelisa Molao oa Pele oa Kirchhoff:
\[
Ke_{ka hare} = Ke_{kantle}
\]
Phallo e kenang:
\[
I_1 + I_2 + I_3 = 2 + 3 + 1 = 6A
\]
Phallo e tsoang:
\[
Ke_4 + Ke_5 = Ke_4 + 4
\]
Kahoo:
\[
6 = I_4 + 4
\Motsu o Motle I_4 = 2A
\]
Karabo: \(I_4 = 2A\)
-
Mohlala oa 2 (KVL): Sekotjana se Bonolo se nang le Li-Resistors tsa Letoto
Potso:
Potoloho ea selika-likoe se le seng e na le betri ea 12 V le li-resistor tse peli tsa letoto \(R_1 = 2\Omega\) le \(R_2 = 4\Omega\). Fumana hore na motlakase oa potoloho o fokotseha hakae le hore na motlakase o theoha hakae ho resistor ka 'ngoe.
Tharollo:
Ka lebaka la li-resistor tse se nang sekotjana le tse latellanang, motlakase o tšoana ho pholletsa le likarolo tsohle.
Khanyetso e felletseng:
\[
R_{kakaretso} = R_1 + R_2 = 2 + 4 = 6\Omega
\]
Hona joale ea potoloho:
\[
I = \frac{V}{R} = \frac{12}{6} = 2A
\]
Ho theoha ha motlakase ho pholletsa le \(R_1\):
\[
V_1 = I \cdot R_1 = 2 \cdot 2 = 4V
\]
Ho theoha ha motlakase ho pholletsa le \(R_2\):
\[
V_2 = I \cdot R_2 = 2 \cdot 4 = 8V
\]
Hlahloba KVL:
\[
12 – 4 – 8 = 0
\]
Ho ya ka.
Karabo: \(I = 2A\), \(V_1 = 4V\), \(V_2 = 8V\)
-
Mohlala oa 3 (KVL): Li-Loop tse peli (Mokhoa oa Letlooeng)
Potso:
Ho na le potoloho ea lilulo tse peli. Selulo se ka letsohong le letšehali se na le mohloli oa motlakase \(V_1 = 10V\) le resistor \(R_1 = 2\Omega\). Selulo se ka letsohong le letona se na le mohloli \(V_2 = 5V\) le resistor \(R_2 = 3\Omega\). Lilulo ka bobeli li arolelana resistor e bohareng \(R_3 = 4\Omega\). Fumana maqhubu a letlooeng \(I_a\) (selulo se ka letsohong le letšehali) le \(I_b\) (selulo se ka letsohong le letona).
Tharollo:
Nka hore maqhubu a letlooeng \(I_a\) le \(I_b\) a tsamaellana le oache. Motlakase o ho resistor e tloaelehileng \(R_3\) ke \(I_a – I_b\) (ho latela tataiso ea khopolo-taba).
Tekanyo ea KVL ea Loop e Leqeleng:
\[
10 – (2I_a) – 4(I_a – I_b) = 0
\]
\[
10 – 2I_a – 4I_a + 4I_b = 0
\Motsu o ka letsohong le letona 10 – 6I_a + 4I_b = 0
\Motsu o ka letsohong le letona 6I_a – 4I_b = 10
\]
Tekanyo ea KVL ea Loop e ka ho le Letona:
\[
5 – (3I_b) – 4(I_b – I_a) = 0
\]
\[
5 – 3I_b – 4I_b + 4I_a = 0
\Motsu o ka letsohong le letona 5 + 4I_a – 7I_b = 0
\Motsu o Motle 4I_a – 7I_b = -5
\]
Tlatsa sistimi:
1) \(6I_a – 4I_b = 10\)
2) \(4I_a – 7I_b = -5\)
Atisa equation (1) ka 2:
\[
12I_a – 8I_b = 20
\]
Atisa equation (2) ka 3:
\[
12I_a – 21I_b = -15
\]
Tlosa:
\[
(12I_a – 8I_b) – (12I_a – 21I_b) = 20 – (-15)
\Motsu o ka letsohong le letona 13I_b = 35
\Rightarrow I_b = \frac{35}{13} \hoo e ka bang 2.69A
\]
Kenya sebakeng sa equation (1):
\[
6I_a – 4(2.69) = 10
\Motsu o Motle 6I_a – 10.76 = 10
\Motsu o Motle 6I_a = 20.76
\Rightarrow I_a \hoo e ka bang 3.46A
\]
Karabo: \(I_a \hoo e ka bang 3.46A\), \(I_b \hoo e ka bang 2.69A\)
-
Mohlala oa Potso ea 4 (KCL + KVL): Potoloho ea Lekala le Tšoanang
Potso:
Mohloli oa 12 V o hokahantsoe le makala a mabeli a bapileng. Lekala la 1 le na le \(R_1 = 6\Omega\), lekala la 2 le na le \(R_2 = 3\Omega\). Fumana motlakase lekaleng ka leng le kakaretso ea motlakase.
Tharollo:
Hobane e bapile, motlakase lekaleng ka leng o a tshwana, e leng 12 V.
Lekala la hajoale la 1:
\[
I_1 = \frac{12}{6} = 2A
\]
Lekala la hajoale la 2:
\[
I_2 = \frac{12}{3} = 4A
\]
Ka KCL li-node:
\[
Ke_{kakaretso} = Ke_1 + Ke_2 = 2 + 4 = 6A
\]
Karabo: \(I_1 = 2A\), \(I_2 = 4A\), \(I_{kakaretso} = 6A\)
-
Malebela a ho Rarolla Mathata a Molao a Kirchhoff
1. Fumana ntlha ya hajwale pele. Haeba sephetho sa hajwale se le mpe, ho bolela hore ntlha ya sebele e fapane le kgopolo.
2. Eba le matshwao a (+) le (-) ha o ngola KVL. Keketseho ya motlakase ho tloha mohloding hangata e nkwa e le ntle, athe ho theoha ha motlakase hodima resistor ho le mpe (ho itshetlehile ka tataiso ya sekgoqetsane).
3. Nolofatsa potoloho haeba ho khoneha, mohlala, kopanya li-resistor ka letoto kapa ka tsela e bapileng pele o sebelisa Kirchhoff.
4. Sebelisa mekhoa e hlophisehileng: tlhahlobo ea li-node bakeng sa KCL kapa tlhahlobo ea letlooeng bakeng sa KVL.
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Ho koala
Melao ea Kirchhoff e thusa ho rarolla lipotoloho tse rarahaneng tsa motlakase ka tsela e hlophisitsoeng. Ka ho tseba KCL le KVL hantle, o ka fumana motlakase lekaleng ka leng, ho theoha ha motlakase ho pholletsa le likarolo, le ho utloisisa boitšoaro ba potoloho ka kakaretso. Mehlala e kaholimo e bontša hore senotlolo ke ho theha li-equation tse nepahetseng le ho li rarolla ka hloko. Ka ho ikoetlisa khafetsa, lipaterone li tla ba bonolo ho li lemoha, esita le bakeng sa lipotoloho tse rarahaneng haholoanyane.
Haeba o batla, nka etsa lipotso tse ling tse 10 tsa ho itloaetsa (ntle le puisano kapa puisano e felletseng), kapa ka ngola mofuta o nang le litšoantšo tsa potoloho ka tlhaloso e qaqileng haholoanyane.
