Ngā ture a Kirchhoff – ngā raruraru me ngā otinga
1. He aha te ngaohiko pito o te pākahiko i te ara iahiko i raro nei?
otinga
emf = te kaha hikohiko = te rerekētanga pūmanawa i waenga i ngā pito ina kore o nāianei te rere ki tētahi ara iahiko o waho.
Ko te ngaohiko o te pito (V) = te rerekētanga pūmanawa i waenga i ngā pito ina rere te iahiko mai i te pākahiko.
Ki te kore he iahiko e tangohia mai i te pākahiko, ka rite te ngaohiko o te pito ki te emf.
Mōhiotia:
Ātete 1 (R 1 ) = 2 Ω
Ātete 2 (R 2 ) = 4 Ω
Ātete 3 (R 3 ) = 4 Ω
emf 1 (E 1 ) = 20 Volt
emf 2 (E 2 ) = 15 Volt
E hiahiatia ana: Te ngaohiko pito (V)
Rongoā 1:
Te ngaohiko pūrua:
V = E 1 – E 2 = 20 – 15 = 5 Volts
Rongoā 2:
Tātaihia ngā rerenga iahiko i roto i te ara iahiko (I)
Tuatahi , whiriwhiria te ahunga o ia ia. Ka taea te whiriwhiri i te ahunga i runga i te āhua noa: ki te mea kei te taha kē te ia, ka puta he tohu tango i roto i te otinga.
Kātahi, ka tīmata i tētahi wāhi o te ara iahiko, ka whakaarohia e tātou te haereere huri noa i tētahi porowhita, me te tāpiri i ngā emf me ngā kupu IR ina tae atu tātou ki a rātou.
Tuarua , ina haere tātou i roto i tētahi pūtake i te ahunga mai i te – ki te +, ka kiia te emf he pai; ina haere tātou mai i te + ki te -, ka kiia te emf he kino.
Tuatoru , ina haere tātou i roto i tētahi ātete i te ahunga kotahi me te iahiko e whakaarohia ana, ka kino te kupu IR nā te mea ka haere te iahiko i te ahunga o te pūmanawa e heke ana. Ina haere tātou i roto i tētahi ātete i te ahunga rerekē ki te iahiko e whakaarohia ana, ka pai te kupu IR nā te mea e tohu ana tēnei i te pikinga o te pūmanawa.
Ka whiriwhiria te ahunga o te iahiko kia rite ki te ahunga o te iahiko ki te ahunga o te iahiko matau:
E 1 – IR 1 – IR 2 – IR 3 – E 2 = 0
20 – I(2) – I(4) – I(4) – 15 = 0
20 – 15 – I (2) – I (4) – I (4) = 0
5 – 10 I = 0
5 = 10 ahau
I = 5/10
I = 0.5 Āmpere
Ko te iahiko e rere ana i roto i te ara iahiko he 0.5 Ampere. Ko te iahiko e tohu ana he pai te tohu ko te ahunga o te iahiko he rite ki te ahunga o te karaka.
Tātaihia te ātete ōrite (R):
Ka honoa raupapatia te ātete 1 ( R1 ) , te ātete 2 ( R2 ) me te ātete 3 (R3 ) . Ko te ātete ōrite:
R = R 1 + R 2 + R 3 = 2 Ω + 4 Ω + 4 Ω = 10 Ω
Te ngaohiko pito i roto i te ātete R (V)
V = IR = (0.5)(10) = 5 Ngāohiko
[irp]
2. I roto i te ara iahiko e whakaaturia ana i te pikitia i raro nei, kimihia te mana i marara i roto i te ātete 3-Ω.
Rongoā:
Mōhiotia:
Ātete 1 (R1) = 2 Ω 
Ātete 2 (R 2 ) = 3 Ω
Ātete 3 (R 3 ) = 4 Ω
emf 1 (E 1 ) = 8 Volt
emf 2 ( E 2 ) = 10 Volt
E hiahiatia ana: Te mana i marara i roto i te ātete 3-Ω
Rongoā:
Ko te mana i marara i roto i te ātete 3-Ω :
P = VI
P = mana , V = te ngaohiko puta noa i te ātete 3-Ω , I = te iahiko e rere ana i roto i te ātete 3-Ω
Tātaihia te iahiko hiko (I) e pā ana i roto i te ātete 3-Ω
Ka whiriwhiria te ahunga o te iahiko kia rite ki te ahunga o te iahiko ki te ahunga o te iahiko matau:
E 1 – IR 1 – IR 2 – IR 3 + E 2 = 0
8 – I(2) – I(3) – I(4) + 10 = 0
18 – 9 I = 0
18 = 9 ahau
I = 18/9
I = 2 Āmpere
Ko te iahiko e rere ana i roto i te ara iahiko he 2 Ampere. Ko te iahiko e tohu ana he pai te tohu ko te ahunga o te iahiko he rite ki te ahunga o te karaka.
Ka honoa ngā ara iahiko i roto i ngā raupapa kia puta ai te iahiko e rere ana i roto i te ara iahiko = ka haere te iahiko mā roto i te ātete 3- Ω = 2 Ampere.
Tātaihia te ngaohiko (V) puta noa i te ātete 3-Ω
V = IR 2 = (2 A)(3 Ω) = 6 Volts
Ko te mana i marara i roto i te ātete 3-Ω:
P = VI = (6 Volt)(2 Ampere) = 12 Volt Ampere = 12 Watt
[irp]
3. I runga i te ara iahiko e whakaaturia ana i te pikitia i raro nei, he aha te rerekētanga pūmanawa i waenga i ngā pūwāhi A me B.
Mōhiotia:
Tuhinga 1 (R1) = 2 Ω 
Ātete 2 (R 2 ) = 3 Ω
Ātete 3 (R 3 ) = 4 Ω
emf 1 (E 1 ) = 8 Volt
emf 2 (E 2 ) = 10 Volt
E hiahiatia ana: Te rerekētanga pūmanawa (V) i waenga i ngā pūwāhi A me B
Rongoā:
Tātaihia te iahiko hiko (I) e rere ana i roto i te ātete 3- Ω
Ka whiriwhiria te ahunga o te iahiko kia rite ki te ahunga o te iahiko ki te ahunga o te iahiko matau:
– E 1 – IR 1 – IR 2 – E 2 – IR 3 = 0
– 8 – Ahau (2) – Ahau (3) – 10 – Ahau (4) = 0
– 18 – 9 I = 0
– 18 = 9
I = -18 / 9
I = – 2 Āmpere
Ko te iahiko e rere ana i roto i te ara iahiko he 2 Ampere. Ko te iahiko kua tohua ki te tohu kino ko te ahunga o te iahiko e anga whakamuri ana ki te karaka.
Ka honoa ngā ara iahiko i roto i ngā raupapa kia puta ai te iahiko e rere ana i roto i te ara iahiko = ka haere te iahiko mā roto i te ātete 3- Ω = 2 Ampere.
Tātaihia te rerekētanga pūmanawa (V) puta noa i te ātete 3- Ω :
V = IR 2 = (2 A)(3 Ω) = 6 Volts
[irp]
4. I runga i te ara iahiko e whakaaturia ana i te pikitia i raro nei, he aha te rerekētanga pūmanawa puta noa i te ātete R 3.
Mōhiotia:
Tuhinga 1 (R1) = 2 Ω 
Ātete 2 (R 2 ) = 4 Ω
Ātete 3 (R 3 ) = 3 Ω
emf 1 (E 1 ) = 6 Volt
emf 2 (E 2 ) = 9 Volt
E hiahiatia ana: Te rerekētanga pūmanawa puta noa i te ātete R 3
Rongoā:
Tātaihia te iahiko hiko (I) e pā ana i roto i te ātete R 3
Ka whiriwhiria te ahunga o te iahiko kia rite ki te ahunga o te iahiko ki te ahunga o te iahiko matau:
E 1 – IR 1 – E 2 – IR 2 – IR 3 = 0
6 – 2I – 9 – 4I – 3I = 0
6 – 9 – 2I – 4I – 3I = 0
-3 – 9I = 0
-3 = 9I
I = -3/9
I = -1/3
Ko te iahiko e rere ana i roto i te ara iahiko he 1/3 Ampere. Ko te iahiko kua tohua ki te tohu kino ko te ahunga o te iahiko e anga whakamuri ana ki te karaka.
Ka honoa ngā ara iahiko i roto i te raupapa kia puta ai te iahiko e rere ana i roto i te ara iahiko = ka haere te iahiko mā roto i te ātete R 3 = 1/3 Ampere.
Tātaihia te rerekētanga pūmanawa (V) puta noa i te ātete R 3
V = IR 3 = (1/3)(3) = 1 Ngāohiko
[irp]
5. Ko te hiko pūmanawa i waenganui i ngā pūwāhi C me D = 4 Volts, kimihia a R!
Mōhiotia:
Tuhinga 1 (R1) = 2 Ω 
Ātete 2 (R 2 ) = 2 Ω
Ātete 3 (R 3 ) = R
emf 1 (E 1 ) = 8 Volt
emf 2 (E 2 ) = 4 Volt
Ko te rerekētanga pūmanawa i waenga i a C me D (V CD ) = 4 Volts
E hiahiatia ana: R
Rongoā:
V CD = IR
4 = IR
R = 4 / I
… …………
Tātaihia te iahiko (I) e pā ana i te ātete R
Ka whiriwhiria te ahunga o te iahiko kia rite ki te ahunga o te iahiko ki te ahunga o te iahiko matau:
– E 1 – 2I + E 2 – 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
I = -8 / 4
I = -2 Āmpere
Ko te iahiko e rere ana i roto i te ara iahiko he 2 Ampere. Ko te iahiko kua tohua ki te tohu kino ko te ahunga o te iahiko e anga whakamuri ana ki te karaka.
Ka honoa ngā ara iahiko ā-raupapa kia puta ai te iahiko e rere ana i roto i te ara iahiko = ka haere te iahiko mā roto i te ātete R = 2 Ampere.
R:
R = 4 / I = 4 / 2 = 2 Ōhm
