Su'aalo Tusaale ah oo ku saabsan Sharciyada Kirchoff
Shuruucda Kirchhoff waa aasaas muhiim ah oo ku saabsan falanqaynta wareegga korantada, gaar ahaan marka wareegga aan lagu xallin karin iyadoo la adeegsanayo Sharciga Ohm oo keliya. Nolosha dhabta ah, wareegyada korontadu waxay inta badan ka kooban yihiin laamo badan, ilo koronto oo dhowr ah, iyo dhowr iska caabin oo isku xiran. Halkan waa meesha sharciyada Kirchhoff ay naga caawiyaan inaan si nidaamsan u xisaabinno hadda, danabka, iyo jihada socodka hadda ee laan kasta oo wareegga ah. Maqaalkani wuxuu ka hadlayaa soo koobid ku saabsan fikradaha sharciyada Kirchhoff iyo dhowr dhibaato oo tusaale ah oo caadi ah, oo dhammaystiran oo leh tallaabooyin xallin si loo fahmo si fudud.
Barashada Sharciga Kirchhoff
Guud ahaan, waxaa jira laba Sharci oo Kirchhoff ah oo inta badan la isticmaalo:
1. Sharciga 1aad ee Kirchhoff (KCL – Sharciga hadda ee Kirchhoff)
Si fudud marka loo eego: wadarta qulqulka soo galaya godka waxay la mid tahay wadarta qulqulka ka baxaya godkaas.
Xisaab ahaan:
\[
\sum I_{in} = \sum I_{out}
\]
ama sidoo kale waxaa loo qori karaa:
\[
\ wadarta I = 0
\]
oo leh calaamad togan oo ah hadda soo socota iyo calaamad taban oo ah hadda soo baxaysa (sida waafaqsan heshiiska la isticmaalay).
2. Sharciga Kirchhoff II (KVL – Sharciga Korantada ee Kirchhoff)
Si fudud: wadarta aljabrada ee danabyada ku jira wareegga xiran waxay la mid tahay eber.
Xisaab ahaan:
\[
\ wadarta V = 0
\]
Taas macnaheedu waa in wadarta guud ee faa'iidada danabka (tusaale ahaan batteriga) ay la mid tahay wadarta guud ee hoos u dhaca danabka (oo dhan iska caabbinta ama qayb kale) ee wareegga.
Labadan sharci ayaa badanaa la wada isticmaalaa: KCL si loo falanqeeyo qanjidhada, iyo KVL si loo falanqeeyo wareegyada (meshes).
-
Tusaalaha Su'aasha 1aad (KCL): Hadda ku sugan Node
Su'aal:
Barta, waxaa jira saddex durdur oo soo socda, kuwaas oo kala ah \(I_1 = 2A\), \(I_2 = 3A\), iyo \(I_3 = 1A\). Laga bilaabo barta, laba durdur ayaa ka baxa, kuwaas oo kala ah \(I_4\) iyo \(I_5 = 4A\). Go'aami qiimaha \(I_4\).
Xalka:
Isticmaal Sharciga Koowaad ee Kirchhoff:
\[
I_{in} = I_{out}
\]
Socodka soo galaya:
\[
I_1 + I_2 + I_3 = 2 + 3 + 1 = 6A
\]
Socodka Baxaya:
\[
I_4 + I_5 = I_4 + 4
\]
Markaa:
\[
6 = I_4 + 4
\Foolka Midig I_4 = 2A
\]
Jawaab: \(I_4 = 2A\)
-
Su'aal Tusaale 2 (KVL): Wareeg Fudud oo leh Iska caabin Taxane ah
Su'aal:
Wareeg hal wareeg ah wuxuu ka kooban yahay baytari 12 V ah iyo laba iska caabin taxane ah \(R_1 = 2\Omega\) iyo \(R_2 = 4\Omega\). Go'aami qulqulka wareegga iyo hoos u dhaca danabka ee ku jira iska caabin kasta.
Xalka:
Sababo la xiriira hal wareeg iyo iska caabin taxane ah, hadda waa isku mid dhammaan qaybaha.
Wadarta iska caabinta:
\[
R_{wadarta} = R_1 + R_2 = 2 + 4 = 6\Omega
\]
Korontada wareegga:
\[
I = \frac{V}{R} = \frac{12}{6} = 2A
\]
Hoos u dhaca danabka oo dhex mara \(R_1\):
\[
V_1 = I \cdot R_1 = 2 \cdot 2 = 4V
\]
Hoos u dhaca danabka oo dhex mara \(R_2\):
\[
V_2 = I \cdot R_2 = 2 \cdot 4 = 8V
\]
Hubi KVL:
\[
12 – 4 – 8 = 0
\]
Sida waafaqsan.
Jawaab: \(I = 2A \), \(V_1 = 4V\), \(V_2 = 8V\)
-
Tusaale 3 (KVL): Laba Wareeg (Habka Mesh)
Su'aal:
Waxaa jira wareeg laba wareeg ah. Wareegga bidix wuxuu leeyahay isha danab \(V_1 = 10V\) iyo iska caabin \(R_1 = 2\Omega\). Wareegga midig wuxuu leeyahay isha \(V_2 = 5V\) iyo iska caabin \(R_2 = 3\Omega\). Labada wareegba waxay wadaagaan iska caabin dhexe \(R_3 = 4\Omega\). Go'aami socodka shabagga \(I_a\) (wareegga bidix) iyo \(I_b\) (wareegga midig).
Xalka:
U qaado in hirarka shabagga \(I_a\) iyo \(I_b\) ay saacad u socdaan. Hadda ku jira iska caabbinta caadiga ah \(R_3\) waa \(I_a – I_b\) (iyadoo ku xiran jihada mala-awaalka).
Wareegga Bidix ee Isle'egta KVL:
\[
10 - (2I_a) - 4 (I_a - I_b) = 0
\]
\[
10 – 2I_a – 4I_a + 4I_b = 0
\Midigta fallaadha 10 – 6I_a + 4I_b = 0
\Midigta 6I_a – 4I_b = 10
\]
Wareegga Midig ee KVL Isle'egta:
\[
5 - (3I_b) - 4 (I_b - I_a) = 0
\]
\[
5 – 3I_b – 4I_b + 4I_a = 0
\Midigta fallaadha 5 + 4I_a – 7I_b = 0
\Midigta fallaadha 4I_a – 7I_b = -5
\]
Dhammaystir nidaamka:
1) \(6I_a – 4I_b = 10\)
2) \(4I_a – 7I_b = -5\)
Ku dhufo isla'egta (1) 2:
\[
12I_a – 8I_b = 20
\]
Ku dhufo isla'egta (2) 3:
\[
12I_a – 21I_b = -15
\]
Ka jar:
\[
(12I_a – 8I_b) – (12I_a – 21I_b) = 20 – (-15)
\Foolka Midig 13I_b = 35
\Midigta I_b = \frac{35}{13} \qiyaastii 2.69A
\]
Ku beddel isla'egta (1):
\[
6I_a – 4(2.69) = 10
\Midigta 6I_a – 10.76 = 10
\Foolka Midig 6I_a = 20.76
\Midigta I_a \ qiyaastii 3.46A
\]
Jawaab: \(I_a \qiyaastii 3.46A\), \(I_b \qiyaastii 2.69A\)
-
Tusaalaha Su'aasha 4aad (KCL + KVL): Wareegga Laamaha Isbarbar socda
Su'aal:
Ilo 12 V ah ayaa ku xiran laba laamood oo is barbar socda. Laanta 1 waxay ka kooban tahay \(R_1 = 6\Omega\), laanta 2 waxay ka kooban tahay \(R_2 = 3\Omega\). Go'aami hadda ku jira laan kasta iyo wadarta hadda.
Xalka:
Maadaama ay is barbar socoto, danabku waa isku mid, waana 12 V.
Hadda laanta 1aad:
\[
I_1 = \frac{12}{6} = 2A
\]
Hadda laanta 2aad:
\[
I_2 = \frac{12}{3} = 4A
\]
Iyadoo KCL ku taal qanjidhada:
\[
I_{wadarta} = I_1 + I_2 = 2 + 4 = 6A
\]
Jawaab: \(I_1 = 2A\), \(I_2 = 4A\), \(I_{wadarta} = 6A\)
-
Talooyin ku saabsan Xalinta Dhibaatooyinka Sharciga Kirchhoff
1. Marka hore go'aami jihada hadda jirta. Haddii natiijada hadda jirtaa ay taban tahay, waxay la macno tahay in jihada dhabta ahi ay ka soo horjeeddo mala-awaalka.
2. La jaanqaad calaamadaha (+) iyo (-) marka aad qorayso KVL. Kororka danabka ee ka imanaya isha waxaa badanaa loo arkaa mid togan, halka hoos u dhaca danabka ee ka gudba iska caabinta uu yahay mid taban (iyadoo ku xiran jihada wareegga).
3. Fududee wareegga haddii ay suurtogal tahay, tusaale ahaan isku dar iska caabinta taxane ah ama isbarbar socda ka hor intaadan isticmaalin Kirchhoff.
4. Adeegso habab nidaamsan: falanqaynta qanjidhada ee KCL ama falanqaynta mesh ee KVL.
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Xiritaanka
Shuruucda Kirchhoff waxay gacan ka geystaan xallinta wareegyada korantada ee adag si habaysan. Markaad barato KCL iyo KVL, waxaad go'aamin kartaa qulqulka laan kasta, hoos u dhaca danabka ee qaybaha, oo aad fahmi kartaa dhaqanka guud ee wareegga. Tusaalooyinka kor ku xusan waxay muujinayaan in furaha uu yahay in la abuuro isla'egyada saxda ah oo si taxaddar leh loo xalliyo. Iyadoo la adeegsanayo ku celcelin joogto ah, qaababku waxay noqon doonaan kuwo si fudud loo aqoonsan karo, xitaa wareegyada aadka u adag.
Haddii aad rabto, waxaan sameyn karaa 10 su'aalood oo dheeraad ah oo ku saabsan tababarka (iyada oo aan la yeelan dood ama dood dhammaystiran), ama waxaan qori karaa nooc leh jaantusyo wareeg ah oo sharraxaad faahfaahsan leh.
