5 mau laʻana o ke kānāwai ʻelua o Kirchhoff
E aʻo pū i nā mea e pili ana i ke Kānāwai o Kirchhoff a me ke kūkākūkā ʻana i nā nīnau e pili ana i ke Kānāwai o Kirchhoff.
1. Aia kahi kaapuni uila i ʻehā mau resistors, kēlā me kēia R 1 = 6 Ohm, R 2 = 6 Ohm, R 3 = 9 Ohm a me R 4 = 3 Ohm i hoʻopili ʻia me E 1 = 6 Volt, E 2 = 12 Volt e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. ʻO ke au uila e kahe ana….
A. 1/5 A
B. 2/5 A
C. 3/5 A
D. 4/5 A
E. 1 A
Pahana
Ua ʻike ʻia:
Palekana 1 (R1) = 6 Ω
Palekana 2 (R2) = 6 Ω
Palekana 3 (R3) = 9 Ω
Palekana 4 (R4) = 3 Ω
Kumu o ka emf 1 (E1) = 6 Volt
Kumu o ka emf 2 (E2) = 12 Volt
Ua nīnau ʻia: ʻO ke au e kahe ana i loko o ke kaapuni (I)
Pane:
Palekana 1 (R1) a me ke kū'ē 2 (R2) i hoʻopili ʻia ma ke ʻano like. ʻO ke kū'ē pani:
1 / R12 = 1/R1 +1/R2 = 1/6 + 1/6 = 2/6
R12 = 6/2 = 3 Ω
Nā ʻanuʻu e hoʻoponopono ai i kēia pilikia:
ʻO ka mea mua , koho i ke kuhikuhi āu e makemake ai. Hiki iā ʻoe ke koho i ka ʻaoʻao hema a i ʻole ka ʻaoʻao ʻākau.
ʻO ka lua , ke hele ke au ma o ke kū'ē a i ʻole ke kū'ē (R), aia ka emi ʻana o ka hiki ke hana i mea maikaʻi ʻole ai ʻo V = IR.
ʻO ke kolu , inā neʻe ke au mai ka hiki haʻahaʻa a i ke kiʻekiʻe (- a i +) a laila ua hōʻailona ʻia ke kumu emf (E) he maikaʻi no ka mea aia kahi hoʻopiha ikehu i loko o ke kumu emf. Inā neʻe ke au mai ke kiʻekiʻe a i ka hiki haʻahaʻa (+ a i -) a laila ua hōʻailona ʻia ke kumu emf (E) he maikaʻi ʻole no ka mea aia kahi hoʻokuʻu ikehu i loko o ke kumu emf.
I ka hoʻoponopono ʻana i kēia pilikia, koho ʻia ke kuhikuhi o ke au e pili ana i ka ʻaoʻao o ka uaki.
- IR12 – ʻE1 – IR3 – IR4 + E.2 = 0
– 3I – 6 – 9I – 3I + 12 = 0
– 3I – 9I – 3I = 6 – 12
– 15I = – 6
ʻO wau = -6 /-15
ʻO I = 2/5 Ampere
2. E nānā i ke kiʻi hoʻonohonoho resistor ma lalo! ʻO ka nui o ke au ma o R 3 he…
Pahana
Ua ʻike ʻia:
R 1 = 4 Ω
R 2 = 4 Ω
R 3 = 8 Ω
Nīnau ʻia: I 3
Pane:
ʻO ke kuhikuhi o ke au uila i loko o ke kaapuni uila ma luna ua like ia me ke kuhikuhi o nā lima uaki, mai ka hiki ke kiʻekiʻe a i ka hiki ke haʻahaʻa.
ʻO ka mea mua , e helu i ke kū'ē pani (R). Ma hope o kēlā, e helu i ke au e hoʻohana ana i ke kānāwai o Ohm : I = V / R
Pale kū'ē pani:
E helu i ke kū'ē pani ma ke kaapuni ma luna.
Pale R1 a me ke kū'ē R2 hoʻonohonoho ʻia ma ke ʻano like. ʻO ke kū'ē pani:
1 / R12 = 1/R1 +1/R2 = 1/4 + 1/4 = 2/4
R12 = 4/2 = 2 Ω
Pale R12 a me ke kū'ē R3 hoʻonohonoho ʻia ma ke ʻano moʻo. ʻO ke kū'ē pani:
R = R12 + R3 = 2 + 8 = 10 Ω
Ke kahe nei ke au mai loko mai o ka pila :
ʻO I = V / R = 40 / 10 = 4 Amperes
Ke Kānāwai Mua o Kirchhoff ʻōlelo ʻia ua like ka nui o ke au uila e komo ana i kahi lālā me ka nui o ke au uila e haʻalele ana i kēlā lālā. Ma muli o ke kānāwai mua o Kirchhoff, ua hoʻoholo ʻia inā ʻo ke au uila e puka mai ana mai ka pila he 4 Amperes, a laila like ke au uila e hele ana ma o ab me 4 Amperes, pēlā nō ke au uila e hele ana ma o bc he 4 Amperes.
3. E nānā i ke kaapuni uila ma ke kiʻi ma lalo. E helu iā I1 , I2 a me I3.
Pahana
Neʻe ke au uila mai ka mana kiʻekiʻe a i ka mana haʻahaʻa; neʻe ke au uila mai ke kikowaena maikaʻi a i ke kikowaena maikaʻi ʻole. No laila, ua koho ʻia nā kuhikuhi o nā au I 1 a me I 2 e like me ka mea i hōʻike ʻia ma ke kiʻi, ʻoiai ke kuhikuhi o ke au I 3 ua koho wale ʻia.
ʻO ka mea mua , e hoʻopili i ke kānāwai mua o Kirchhoff ma kahi lālā.
I 3 = I 1 + I 2 ………. kaulike 1
ʻO ka lua , e hoʻopili i ke kānāwai ʻelua o Kirchhoff i ka loop 1 (loop hema)
32 – 4 I 1 – 10 I 3 = 0
8 – I 1 – 2,5 I 3 = 0
………. hoʻohālikelike 2
ʻO ke kolu , e hoʻopili i ke kānāwai ʻelua o Kirchhoff i ka loop 2 (loop ʻākau)
15 – 5 I 2 – 10 I 3 = 0
3 – I 2 – 2 I 3 = 0
………. hoʻohālikelike 3
E hoʻololi i nā kaulike 2 a me 3 i loko o ka kaulike 1:
ʻO ke ʻano o ka hōʻailona maikaʻi ʻole, ʻo ke kuhikuhi o I 2 e kūʻē ana i ke kuhikuhi i koho ʻia ma luna.
4. Aia kahi kaapuni uila i ʻehā mau resistors, kēlā me kēia me R1 = 12 Ohm, R2 = 12 Ohm, R3 = 3 Ohm a me R4 = 6 Ohm i hoʻopili ʻia me E1 = 6 Volts, E2 = 12 Volts e like me ka mea i hōʻike ʻia ma ke kiʻi aʻe. ʻO ke au uila e kahe ana….
A. 1/5 A
B. 2/5 A
C. 3/5 A
D. 4/5 A
E. 1 A
Pahana
Ua ʻike ʻia:
Palekana 1 (R1) = 12 Ω
Palekana 2 (R2) = 12 Ω
Palekana 3 (R3) = 3 Ω
Palekana 4 (R4) = 6 Ω
Kumu o ka emf 1 (E1) = 6 Volt
Kumu o ka emf 2 (E2) = 12 Volt
Makemake ʻia: Ka ikaika o ke au e kahe ana i loko o ke kaapuni (I)
Pane:
Pili kēia pilikia i ke kānāwai o Kirchhooff. Nā ʻanuʻu a me pehea e hoʻoponopono ai i kēia pilikia:
ʻO ka mea mua, koho i kāu kuhikuhi makemake o kēia manawa. Hiki iā ʻoe ke koho i ka ʻaoʻao hema a i ʻole ka ʻaoʻao ʻākau.
ʻO ka lua, ke hele ke au ma o ke kū'ē a i ʻole ke kū'ē (R) aia ka emi ʻana o ka hiki ke hana i mea maikaʻi ʻole ai ʻo V = IR.
ʻO ke kolu, inā neʻe ke au mai ka hiki haʻahaʻa a i ke kiʻekiʻe (- a i +) a laila ua hōʻailona ʻia ke kumu emf (E) he maikaʻi no ka mea aia kahi hoʻopiha ikehu i loko o ke kumu emf. Inā neʻe ke au mai ke kiʻekiʻe a i ka hiki haʻahaʻa (+ a i -) a laila ua hōʻailona ʻia ke kumu emf (E) he maikaʻi ʻole no ka mea aia kahi hoʻokuʻu ikehu i loko o ke kumu emf.
Palekana 1 (R1) a me ke kū'ē 2 (R2) i hoʻopili ʻia ma ke ʻano like. ʻO ke kū'ē pani:
1 / R12 = 1/R1 +1/R2 = 1/12 + 1/12 = 2/12
R12 = 12/2 = 6 Ω
I ka hoʻoponopono ʻana i kēia pilikia, koho ʻia ke kuhikuhi o ke au e pili ana i ka ʻaoʻao o ka uaki.
– IR12 – ʻE1 – IR3 – IR4 + E.2 = 0
– 6 I – 6 – 3I – 6I + 12 = 0
– 6I – 3I – 6I = 6 -12
– 15I = – 6
ʻO wau = -6/-15
ʻO I = 2/5 Ampere
ʻO ke au uila e kahe ana i loko o ke kaapuni he 2/5 Ampere. Hōʻike kahi au uila maikaʻi ua like ke kuhikuhi o ke au uila me ka mea i manaʻo ʻia, ma ka ʻaoʻao o ka uaki.
ʻO ka pane pololei ʻo B.
5. E nānā i ke kaapuni uila ma lalo nei! ʻO ka nui o ke au uila (I) e kahe ana i loko o ke kaapuni he….
A. 0,1 A
B. 0,2 A
C. 0,5 A
D. 1,0 A
E. 5,0 A
Pahana
Ua ʻike ʻia:
Palekana 1 (R1) = 10 Ω
Palekana 2 (R2) = 6 Ω
Palekana 3 (R3) = 5 Ω
Palekana 4 (R4) = 20 Ω
Kumu o ka emf 1 (E1) = 8 Volt
Kumu o ka emf 2 (E2) = 12 Volt
Makemake ʻia: Ka ikaika o ke au e kahe ana i loko o ke kaapuni (I)
Pane:
Palekana 3 (R3) a me ke kū'ē 4 (R4) i hoʻopili ʻia ma ke ʻano like. ʻO ke kū'ē pani:
1 / R34 = 1/R3 +1/R4 = 1/5 + 1/20 = 4/20 + 1/20 = 5/20
R34 = 20/5 = 4 Ω
I ka hoʻoponopono ʻana i kēia pilikia, koho ʻia ke kuhikuhi o ke au e pili ana i ka ʻaoʻao o ka uaki.
– IR1 – IR2 – ʻE1 – IR34 + E.2 = 0
– 10I – 6I – 8 – 4I + 12 = 0
– 10I – 6I – 4I = 8 – 12
– 20I = – 4
ʻO wau = -4/-20
ʻO I = 1/5 Ampere
ʻO I = 0,2 Amperes
ʻO ke au uila e kahe ana i loko o ke kaapuni he 1/5 Ampere. Hōʻike kahi au uila maikaʻi ua like ke kuhikuhi o ke au uila me ka mea i manaʻo ʻia, ma ka ʻaoʻao o ka uaki.
ʻO ka pane pololei ʻo B.
