Fomula ya Malamulo ya Kirchhoff
Malamulo a Kirchhoff ndi mfundo zazikulu pakusanthula ma circuit amagetsi zomwe zimagwiritsidwa ntchito kuwerengera ma currents ndi ma voltages m'ma circuit amagetsi. Malamulo awa adatchulidwa ndi Gustav Kirchhoff, katswiri wa sayansi ya fizikisi waku Germany yemwe adawapanga mu 1845. Awiri mwa malamulo a Kirchhoff ndi ofunikira kwambiri pakusanthula ma circuit amagetsi: Kirchhoff's Current Law (KCL) ndi Kirchhoff's Voltage Law (KVL). Nkhaniyi ifotokoza mozama malamulo onsewa, kufotokoza momwe amagwiritsidwira ntchito m'mikhalidwe yosiyanasiyana, ndikupereka zitsanzo zosonyeza momwe amagwiritsidwira ntchito.
Lamulo la Pakali pano la Kirchhoff (KCL)
Lamulo la Kirchhoff la Current, lomwe limadziwikanso kuti KCL, limati kuchuluka kwa mafunde olowa mu nthambi yamagetsi ndi kofanana ndi kuchuluka kwa mafunde ochoka mu mfundoyo. Mwa masamu, lamuloli likhoza kufotokozedwa motere:
\[ \sum I_{\text{in}} = \sum I_{\text{out}} \]
kapena
\[ \sum I = 0 \]
Lamuloli likuchokera pa mfundo yosungira mphamvu, yomwe imati mphamvu yamagetsi singathe kupangidwa kapena kuwonongedwa nthawi iliyonse mu dera. Izi zikutanthauza kuti mphamvu iliyonse yomwe imalowa pamalo amenewo iyenera kuchoka.
Chitsanzo cha Lamulo la Pakali pano la Kirchhoff
Tiyerekeze kuti tili ndi nthambi ya mafunde atatu omwe amalowa ndikutuluka. Ngati \( I_1 \) ndi \( I_2 \) ndi mafunde omwe amalowa mu mfundoyo, ndipo \( I_3 \) ndi mafunde omwe amatuluka, ndiye kuti malinga ndi lamulo la Kirchhoff la Current:
\[ I_1 + I_2 = I_3 \]
Mwachitsanzo, ngati \( I_1 = 3 \text{A} \) ndi \( I_2 = 2 \text{A} \), ndiye kuti mphamvu yotulutsa \( I_3 \) ikhoza kuwerengedwa motere:
\[ I_3 = I_1 + I_2 = 3 \malemba{A} + 2 \malemba{A} = 5 \malemba{A} \]
Lamulo la Voltage la Kirchhoff (KVL)
Lamulo la Voltage la Kirchhoff, lomwe limadziwikanso kuti KVL (Lamulo la Voltage la Kirchhoff), limati chiwerengero cha ma voltage onse mu loop yotsekedwa ndi zero. Mwa masamu, lamuloli likhoza kufotokozedwa motere:
\[ \sum V = 0 \]
Lamuloli limachokera pa mfundo yosungira mphamvu, yomwe imati mphamvu yonse mu lupu yotsekedwa iyenera kukhala yokhazikika. Pankhani ya ma circuits amagetsi, izi zikutanthauza kuti kutsika kwa voteji yonse kuzungulira lupu kuyenera kufanana ndi kuchuluka kwa voteji yonse.
Chitsanzo cha Lamulo la Voltage la Kirchhoff
Tiyerekeze kuti tili ndi chizunguliro chotsekedwa chokhala ndi zigawo zitatu: gwero la magetsi \( V \), resistor \( R_1 \) yokhala ndi kutsika kwa magetsi \( V_{R1} \), ndi resistor \( R_2 \) yokhala ndi kutsika kwa magetsi \( V_{R2} \). Malinga ndi Lamulo la Voltage la Kirchhoff:
\[ V – V_{R1} – V_{R2} = 0 \]
Mwachitsanzo, ngati \( V = 12 \text{V} \), \( V_{R1} = 4 \text{V} \), ndi \( V_{R2} = 8 \text{V} \), ndiye kuti lamulo la magetsi la Kirchhoff limatsimikizira kuti:
\[ 12 \malemba{V} – 4 \malemba{V} – 8 \malemba{V} = 0 \]
Kugwiritsa Ntchito Lamulo la Kirchhoff
Malamulo a Kirchhoff amagwiritsidwa ntchito m'njira zosiyanasiyana pofufuza ma circuits amagetsi. Nazi njira zina zomwe zimatsatiridwa pogwiritsira ntchito malamulo awa:
1. Dziwani Malo ndi Ma Loop a Nthambi: Gawo loyamba pakusanthula dera ndikuzindikira malo ndi ma loop onse a nthambi mu dera. Malo a nthambi ndi malo pomwe zigawo ziwiri kapena zingapo zamagetsi zimalumikizana, pomwe malo ndi njira yotsekedwa mu dera.
2. Gwiritsani ntchito Lamulo la Pakadali pano la Kirchhoff: Pa mfundo iliyonse ya nthambi, gwiritsani ntchito Lamulo la Pakadali pano la Kirchhoff kuti mulembe equation ya panopa. Izi zipanga equation imodzi pa mfundo iliyonse ya nthambi.
3. Gwiritsani ntchito Lamulo la Voltage la Kirchhoff: Pa kuzungulira kulikonse mu dera, gwiritsani ntchito Lamulo la Voltage la Kirchhoff kuti mulembe equation ya voltage. Izi zipanga equation imodzi pa kuzungulira kulikonse.
4. Konzani Dongosolo la Ma equation: Gwiritsani ntchito dongosolo la ma equation lomwe latsatira kuti muwerengere mphamvu ndi magetsi mu dera. Izi nthawi zambiri zimaphatikizapo njira zoyambira za algebraic kapena njira zama nambala kuti muthetse ma equation nthawi imodzi.
Zitsanzo za Mafunso Okhudza Kugwiritsa Ntchito Lamulo la Kirchhoff
Tiyeni tiwone chitsanzo cha kugwiritsa ntchito malamulo a Kirchhoff m'njira yosavuta:
Funso:
Popeza pali dera lokhala ndi gwero la magetsi \( V = 10 \text{V} \), ma resistors awiri \( R_1 = 2 \Omega \) ndi \( R_2 = 3 \Omega \), ndi malo a nthambi pomwe mafunde amagawikana kukhala \( I_1 \) kudzera \( R_1 \) ndi \( I_2 \) kudzera \( R_2 \). Werengani mafunde \( I_1 \) ndi \( I_2 \).
Yankho:
1. Dziwani mfundo ndi ma Loop a nthambi:
– Nthambi pomwe nthambi zamakono zimayikidwa mu \( I_1 \) ndi \( I_2 \).
– Chizunguliro chotsekedwa chomwe chili ndi gwero la magetsi \( V \), resistor \( R_1 \), ndi resistor \( R_2 \).
2. Gwiritsani ntchito lamulo la Kirchhoff lomwe likugwiritsidwa ntchito panopa ku nthambi:
\[ Ine = Ine_1 + Ine_2 \]
3. Gwiritsani ntchito lamulo la Kirchhoff la Voltage mu Loop:
\[ V – I_1 R_1 – I_2 R_2 = 0 \]
\[ 10 – 2I_1 – 3I_2 = 0 \]
4. Konzani Dongosolo la Ma Equation:
Ndi ma equation awiri:
\[ Ine = Ine_1 + Ine_2 \]
\[ 10 – 2I_1 – 3I_2 = 0 \]
Tiyerekeze kuti \( I = 2 \text{A} \). Kenako:
\[ 2 = I_1 + I_2 \]
\[ 10 – 2I_1 – 3I_2 = 0 \]
Kuchokera pa equation yoyamba, tikhoza kusintha kuti tipeze \( I_2 \):
\[I_2 = 2 – I_1 \]
Lowetsani \( I_2 \) mu equation yachiwiri:
\[ 10 – 2I_1 – 3(2 – I_1) = 0 \]
\[ 10 – 2I_1 – 6 + 3I_1 = 0 \]
\[ 10 – 6 + I_1 = 0 \]
\[I_1 = -4 \]
Kotero, nthawi yapano \( I_1 \) ndi 4 A.
Mapeto
Malamulo a Kirchhoff ndi zida zofunika kwambiri pakusanthula ma circuit amagetsi. Lamulo la Kirchhoff la Current Law (KCL) ndi Lamulo la Voltage la Kirchhoff (KVL) limapereka maziko owerengera ma current ndi ma voltage m'ma circuit ovuta amagetsi. Pogwiritsa ntchito mfundo izi, titha kuthetsa mavuto osiyanasiyana pakupanga ndi kusanthula ma circuit amagetsi. Kumvetsetsa ndikugwiritsa ntchito malamulo a Kirchhoff kumatithandiza kupanga ma circuit ogwira ntchito bwino komanso ogwira ntchito bwino m'njira zosiyanasiyana, kuyambira pazida zamagetsi za tsiku ndi tsiku mpaka makina akuluakulu amagetsi.
