Nā lula o Kirchhoff - nā pilikia a me nā hoʻonā
1. He aha ke kikowaena anakahi uila o ka pila i loko o ka huakai kaapuni ma lalo?
pāʻoihana
emf = electromotive force = ka ʻokoʻa hiki ma waena o nā kikowaena ke ʻole ʻikena kahe i kahi kaapuni waho.
ʻO ke anakahi uila (V) = ka ʻokoʻa hiki ke hana ma waena o nā kikowaena ke kahe ke au mai ka pila.
Inā ʻaʻohe au i huki ʻia mai ka pila, ua like ka volta o ke kikowaena me ka emf.
ʻIke ʻia:
Kū'ē 1 (R1) = 2 Ω
Kū'ē 2 (R2) = 4 Ω
Palekana 3 (R3) = 4 Ω
emf 1 (E1) = 20 Volt
emf 2 (E2) = 15 Volt
Makemake ʻia: ʻO ke anakahi uila (V)
Pāʻoihana 1:
ʻO ke anakahi uila:
V = E1 – ʻE2 = 20 – 15 = 5 Volt
Pāʻoihana 2:
E helu i ke kahe o ke au i loko o ke kaapuni (I)
Ka mua, E koho i ke kuhikuhi o kēlā me kēia au. Hiki ke koho ʻia ke kuhikuhi me ka manaʻo ʻole: inā aia ke au ma ke kuhikuhi ʻē aʻe, e puka mai ia me kahi hōʻailona minus i ka hopena.
A laila, e hoʻomaka ana ma kekahi wahi o ke kaapuni, ke noʻonoʻo nei mākou e hele ana a puni kahi loop, e hoʻohui ana i nā emfs a me nā huaʻōlelo IR i ko mākou hiki ʻana iā lākou.
Ka lua, Ke hele mākou ma waena o kahi kumu ma ke kuhikuhi mai – a i +, ua manaʻo ʻia ka emf he maikaʻi; ke hele mākou mai + a i -, ua manaʻo ʻia ka emf he maikaʻi ʻole.
Ke kolu, Ke hele mākou ma waena o kahi resistor ma ke kuhikuhi like me ke au i manaʻo ʻia, he maikaʻi ʻole ka huaʻōlelo IR no ka mea ke hele nei ke au ma ke kuhikuhi o ka hiki ke emi. Ke hele mākou ma waena o kahi resistor ma ke kuhikuhi ʻē aʻe i ke au i manaʻo ʻia, he maikaʻi ka huaʻōlelo IR no ka mea ke hōʻike nei kēia i ka piʻi ʻana o ka hiki.
Ua koho ʻia ke kuhikuhi o ke au e like me ke kuhikuhi o ka ʻaoʻao uaki:
E1 – IR1 – IR2 – IR3 – ʻE2 = 0
20 – I(2) – I(4) – I(4) – 15 = 0
20 – 15 – ʻAu (2) – ʻAu (4) – ʻAu (4) = 0
5 – 10 I = 0
5 = 10 ʻI
ʻO wau = 5/10
ʻO I = 0.5 Amperes
ʻO ke au uila e kahe ana i loko o ke kaapuni he 0.5 Ampere. ʻO ke au uila i hōʻailona ʻia he maikaʻi ke ʻano o ke kuhikuhi o ke au uila e like me ke kuhikuhi ʻana o ka uaki.
E helu i ke kū'ē like (R):
Mea kū'ē 1 (R1), kū'ē 2 (R2) a pale kū'ē 3 (R3) ua hoʻopili ʻia ma ke ʻano moʻo. ʻO ke kū'ē like:
R = R1 + R2 + R3 = 2 Ω + 4 Ω + 4 Ω = 10 Ω
ʻO ke ana wela hope i loko o ke kū'ē R (V)
V = IR = (0.5)(10) = 5 Volts
2. Ma ke kaapuni e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei, e ʻike i ka mana i hoʻokahe ʻia i loko ka Pale kū'ē 3-Ω.
Lōlā:
ʻIke ʻia:
Mea kū'ē 1 (R1) = 2 Ω 
Mea kū'ē 2 (R2) = 3 Ω
Kū'ē 3 (R3) = 4 Ω
emf 1 (E1) = 8 Volt
emf 2 (E2) = 10 Volt
Makemake: Ua hoʻopau ʻia ka mana i loko ka 3-Ω resistor
Lōlā:
ka mana hoʻopuehu ʻia i loko ka 3-Ω resistorr:
P = VI
P= mana, V = ka voltage ma kēlā ʻaoʻao ka 3-Ω resistor, I = ke kahe nei ke au ma o ka 3-Ω resistor
E helu i ke au uila (I) maalo ae ka 3-Ω resistor
Ua koho ʻia ke kuhikuhi o ke au e like me ke kuhikuhi o ka ʻaoʻao uaki:
E1 – IR1 – IR2 – IR3 + E.2 = 0
8 – I(2) – I(3) – I(4) + 10 = 0
18 – 9 I = 0
18 = 9 ʻI
I = 18 / 9
ʻO I = 2 Amperes
ʻO ke au uila e kahe ana i loko o ke kaapuni 2 ʻAmpere. ʻO ke au uila i hōʻailona ʻia he maikaʻi ke ʻano o ke kuhikuhi o ke au uila e like me ke kuhikuhi ʻana o ka uaki.
Hoʻopili ʻia nā kaapuni ma ke ʻano he moʻo i hiki ai i ke au uila e kahe ana i loko o ke kaapuni = hele ke au uila ma o 3-Ω pale pale = 2 Amperes.
E helu i ke ana uila (V) ma'ō aku 3-Ω pale pale
V = IR2 = (2 A)(3 Ω) = 6 Volt
Ua hoʻopau ʻia ka mana i loko ka 3-Ω mea kū'ē:
P = VI = (6 Volt)(2 Ampere) = 12 Volt Ampere = 12 Watt
3. Ma muli o ke kaapuni e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei, he aha ka ʻokoʻa hiki ma waena o nā kiko A a me B.
ʻIke ʻia:
Kū'ē 1 (R1) = 2 Ω 
Kū'ē 2 (R2) = 3 Ω
Kū'ē 3 (R3) = 4 Ω
emf 1 (E1) = 8 Volt
emf 2 (E2) = 10 Volt
Makemake ʻia: ʻO ka ʻokoʻa hiki (V) ma waena o ke kiko A a me B
Lōlā:
E helu i ke au uila (I) ke kahe nei i loko o ka 3-Ω pale pale
Ua koho ʻia ke kuhikuhi o ke au e like me ke kuhikuhi o ka ʻaoʻao uaki:
– ʻE1 – IR1 – IR2 – ʻE2 – IR3 = 0
– 8 – ʻAu (2) – ʻAu (3) – 10 – ʻAu (4) = 0
– 18 – 9 I = 0
– 18 = 9 ʻU
ʻO wau = -18 / 9
ʻO I = – 2 Amperes
ʻO ke au uila e kahe ana i loko o ke kaapuni 2 Ampere. Ua kau inoa ʻia ke au uila maikaʻi ' ʻo ia hoʻi ke kuhikuhi o ke au uila loankuhikuhi ʻana ma ka ʻaoʻao uaki.
Hoʻopili ʻia nā kaapuni ma ke ʻano he moʻo i hiki ai i ke au uila e kahe ana i loko o ke kaapuni = hele ke au uila ma o 3-Ω pale pale = 2 Amperes.
E helu i ka ʻokoʻa hiki (V) ma waena o ka 3-Ω mea pale:
V = IR2 = (2 A)(3 Ω) = 6 Volt
4. Ma muli o ke kaapuni e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei, he aha ka ʻokoʻa hiki ke hana ma waena o R3 mea pale.
ʻIke ʻia:
Kū'ē 1 (R1) = 2 Ω 
Kū'ē 2 (R2) = 4 Ω
Kū'ē 3 (R3) = 3 Ω
emf 1 (E1) = 6 Volt
emf 2 (E2) = 9 Volt
Makemake ʻia: ʻO ka ʻokoʻa hiki ma waena o R3 pale pale
Lōlā:
E helu i ke au uila (I) hele ma ka R3 pale pale
Ua koho ʻia ke kuhikuhi o ke au e like me ke kuhikuhi o ka ʻaoʻao uaki:
E1 – IR1 – ʻE2 – IR2 – IR3 = 0
6 – 2I – 9 – 4I – 3I = 0
6 – 9 – 2I – 4I – 3I = 0
-3 – 9I = 0
-3 = 9I
ʻO wau = -3/9
ʻO wau = -1/3
ʻO ke au uila e kahe ana i loko o ke kaapuni 1/3 Ampere. Ua kau inoa ʻia ke au uila maikaʻi ' ʻo ia hoʻi ke kuhikuhi o ke au uila loankuhikuhi ʻana ma ka ʻaoʻao uaki.
Hoʻopili ʻia nā kaapuni ma ke ʻano he moʻo i hiki ai i ke au uila e kahe ana i loko o ke kaapuni = ke kahe nei ke au uila ma o ka R3 pale pale = 1/3 ʻAmepere.
E helu i ka ʻokoʻa hiki (V) ma'ō aku R3 pale pale
V = IR3 = (1/3)(3) = 1 Volt
5. ʻO ka uila hiki ke loaʻa ma waena o nā kiko C a me D = 4 Volts, e ʻimi iā R!
ʻIke ʻia:
Kū'ē 1 (R1) = 2 Ω 
Kū'ē 2 (R2) = 2 Ω
Kū'ē 3 (R3) = R
emf 1 (E1) = 8 Volt
emf 2 (E2) = 4 Volt
ʻO ka ʻokoʻa hiki ma waena C a D (VCD) = 4 Volt
Makemake ʻia: R
Lōlā:
VCD = IR
4 = IR
R = 4 / I
...……… ...
E helu i ke au uila (I) hele ma waena o ke kū'ē R
Ua koho ʻia ke kuhikuhi o ke au e like me ke kuhikuhi o ka ʻaoʻao uaki:
– ʻE1 – 2I + E2 – 2I – IR = 0
– 8 – 2I + 4 – 2I – I (4/I) = 0
– 8 – 2I + 4 – 2I – 4 = 0
– 8 + 4 – 4 – 2I – 2I = 0
– 8 – 4I = 0
– 8 = 4I
ʻO wau = -8 / 4
ʻO I = -2 Amperes
ʻO ke au uila e kahe ana i loko o ke kaapuni 2 Ampere. Ua kau inoa ʻia ke au uila maikaʻi ' ʻo ia hoʻi ke kuhikuhi o ke au uila loankuhikuhi ʻana ma ka ʻaoʻao uaki.
Hoʻopili ʻia nā kaapuni ma ke ʻano he moʻo i hiki ai i ke au uila e kahe ana i loko o ke kaapuni = ke kahe nei ke au uila ma o ka R pale pale = 2 ʻAmepere.
R:
R = 4 / I = 4 / 2 = 2 Ohm
