He tauira o te ture tuarua a Kirchhoff

5 Ngā Tauira o te Ture Tuarua a Kirchhoff

Akohia hoki ngā rauemi mō te Ture a Kirchhoff me te matapaki i ngā pātai e pā ana ki te Ture a Kirchhoff.

1. E whā ngā ātete o tētahi ara iahiko hiko, ko ia R ₁ = 6 Ohm, ko R ₂ = 6 Ohm, ko R ₃ = 9 Ohm, ā, ko R ₄ = 3 Ohm e hono ana ki a E ₁ = 6 Volt, E ₂ = 12 Volt e whakaaturia ana i te pikitia e whai ake nei. Ko te iahiko e rere ana ko….

A. 1/5 A
B. 2/5 A
C. 3/5 A
D. 4/5 A
E. 1 A

Kōrero

E mōhiotia ana:
Ātete 1 (R₁) = 6 Ω
Ātete 2 (R₂) = 6 Ω
Ātete 3 (R₃) = 9 Ω
Ātete 4 (R₄) = 3 Ω
Pūtake o te emf 1 (E₁) = 6 Ngāohiko
Pūtake o te emf 2 (E₂) = 12 Ngāohiko
I pātaihia: Te iahiko e rere ana i roto i te ara iahiko (I)
Whakautu:

Ātete 1 (R₁) me te ātete 2 (R₂) e honoa ana i te taha whakarara. Ko te ātete whakakapinga ko:
1 / R₁₂ = 1/R₁ + 1/R₂ = 1/6 + 1/6 = 2/6
R₁₂ = 6/2 = 3 Ω

Ngā mahi hei whakaoti i tēnei raruraru:

Tuatahi , whiriwhiria te ahunga e pai ana ki a koe. Ka taea e koe te whiriwhiri i te taha maui, i te taha matau rānei.

Tuarua , ina pā te iahiko mā roto i te ātete, i te ātete rānei (R), ka heke te pūmanawa, ā, he kino te V = IR.

Tuatoru , ki te neke te ia mai i te pūmanawa iti ki te pūmanawa teitei (- ki te +) ka tohua te pūtake emf (E) he pai nā te mea he whakakī pūngao kei roto i te pūtake emf. Ki te neke te ia mai i te pūmanawa teitei ki te pūmanawa iti (+ ki te -) ka tohua te pūtake emf (E) he kino nā te mea he tukunga pūngao kei roto i te pūtake emf.

Hei whakaoti i tēnei raruraru, ka whiriwhiria te ahunga o te ia kia huri ki te matau.

- IR₁₂ - E₁ – IR₃ – IR₄ Ā,₂ = 0
– 3I – 6 – 9I – 3I + 12 = 0
– 3I – 9I – 3I = 6 – 12
– 15I = – 6
I = -6 /-15
I = 2/5 Āpere

2. Tirohia te ahua o te whakaritenga ātete i raro nei! Ko te rahi o te iahiko e puta ana i te R ₃ ko…

Kōrero

E mōhiotia ana:

R ₁ = 4 Ω

R ₂ = 4 Ω

R ₃ = 8 Ω

I pātaihia: I ₃

Whakautu:

Ko te ahunga o te iahiko i roto i te ara iahiko i runga ake nei he rite tonu ki te ahunga o ngā ringa karaka, mai i te pūmanawa teitei ki te pūmanawa iti.

Tuatahi , tatauhia te ātete whakakapinga (R). Muri iho, tatauhia te iahiko mā te whakamahi i te ture a Ohm : I = V / R

Ātete whakakapinga:
Tātaihia te ātete whakakapinga i te ara iahiko i runga ake nei.
Ātete R₁ me te ātete R₂ whakaritea kia whakarara. Ko te ātete whakakapinga ko:
1 / R₁₂ = 1/R₁ + 1/R₂ = 1/4 + 1/4 = 2/4
R₁₂ = 4/2 = 2 Ω
Ātete R₁₂ me te ātete R₃ kua whakaritea kia raupapa. Ko te ātete whakakapinga ko:
R = R₁₂ + R₃ = 2 + 8 = 10 Ω
Te iahiko e rere ana i waho o te pākahiko :
I = V / R = 40 / 10 = 4 Āpere

Te Ture Tuatahi a Kirchhoff e kī ana ko te nui o te iahiko e tomo ana ki tētahi peka he rite ki te nui o te iahiko e puta ana i taua peka. I runga i te ture tuatahi a Kirchhoff, ka whakatauhia mēnā ko te iahiko e puta mai ana i te pākahiko he 4 Amperes, ko te iahiko e puta ana i roto i te ab he rite ki te 4 Amperes, waihoki ko te iahiko e puta ana i roto i te bc he 4 Amperes.

3. Tirohia te ara iahiko hiko i te ahua i raro nei. Tātaihia te _I1 , te _I2 me te _I3.

Kōrero

Ka neke te iahiko mai i te pūmanawa teitei ki te pūmanawa iti; ka neke te iahiko mai i te pito pai ki te pito kino. Nō reira, ko ngā ahunga o ngā iahiko I ₁ me I ₂ ka tīpakohia e ai ki te pikitia, ko te ahunga o te iahiko I ₃ ka tīpakohia i runga i te āhua noa.

Tuatahi , whakamahia te ture tuatahi a Kirchhoff ki te pūwāhi peka.

I ₃ = I ₁ + I ₂ ………. whārite 1

Tuarua , whakamahia te ture tuarua a Kirchhoff ki te koropiko 1 (koropiko maui)

32 – 4 I ₁ – 10 I ₃ = 0

8 – I ₁ – 2,5 I ₃ = 0

…… whārite 2

Tuatoru , whakamahia te ture tuarua a Kirchhoff ki te koropiko 2 (koropiko matau)

15 – 5 I ₂ – 10 I ₃ = 0

3 – I ₂ – 2 I ₃ = 0

…… whārite 3

Whakakapia ngā whārite 2 me te 3 ki te whārite 1:

Ko te tohu kino e tohu ana kei te ritenga kē te ahunga o I ₂ i te ahunga i whiriwhiria i runga ake nei.

4. E whā ngā ātete o tētahi ara iahiko hiko, he R kei ia ātete₁ = 12 Ōhm, R₂ = 12 Ōhm, R₃ = 3 Ōhm me R₄ = 6 Ohm e hono ana ki a E₁ = 6 Ngā Waohiko, E₂ = 12 Volts e whakaaturia ana i te ahua e whai ake nei. Ko te iahiko e rere ana ko….

A. 1/5 A
B. 2/5 A
C. 3/5 A
D. 4/5 A
E. 1 A

Kōrero
E mōhiotia ana:
Ātete 1 (R₁) = 12 Ω
Ātete 2 (R₂) = 12 Ω
Ātete 3 (R₃) = 3 Ω
Ātete 4 (R₄) = 6 Ω
Pūtake o te emf 1 (E₁) = 6 Ngāohiko
Pūtake o te emf 2 (E₂) = 12 Ngāohiko
E hiahiatia ana: Te kaha o te ia e rere ana i roto i te ara iahiko (I)
Whakautu:

E pā ana tēnei raruraru ki te ture a Kirchhooff. Ngā taahiraa me pēhea te whakaoti i tēnei raruraru:
Tuatahi, whiriwhiria te ahunga o nāianei e pai ana ki a koe. Ka taea e koe te whiriwhiri i te taha maui, i te taha matau rānei.
Tuarua, ina pā te iahiko mā roto i te ātete, i te ātete rānei (R) ka heke te pūmanawa, ā, he kino te V = IR.
Tuatoru, ki te neke te ia mai i te pūmanawa iti ki te pūmanawa teitei (- ki te +) ka tohua te pūtake emf (E) he pai nā te mea he whakakī pūngao kei roto i te pūtake emf. Ki te neke te ia mai i te pūmanawa teitei ki te pūmanawa iti (+ ki te -) ka tohua te pūtake emf (E) he kino nā te mea he tukunga pūngao kei roto i te pūtake emf.

Ātete 1 (R₁) me te ātete 2 (R₂) e honoa ana i te taha whakarara. Ko te ātete whakakapinga ko:
1 / R₁₂ = 1/R₁ + 1/R₂ = 1/12 + 1/12 = 2/12
R₁₂ = 12/2 = 6 Ω

Hei whakaoti i tēnei raruraru, ka whiriwhiria te ahunga o te ia kia huri ki te matau.
– IR₁₂ - E₁ – IR₃ – IR₄ Ā,₂ = 0
– 6 I – 6 – 3I – 6I + 12 = 0
– 6I – 3I – 6I = 6 -12
– 15I = – 6
I = -6/-15
I = 2/5 Āpere

Ko te iahiko e rere ana i roto i te ara iahiko he 2/5 Ampere. Ko te iahiko pai e tohu ana ko te ahunga o te iahiko e rite ana ki te mea e tumanakohia ana, ki te taha matau.
Ko te whakautu tika ko B.

5. Tirohia te ara iahiko e whai ake nei! Ko te rahi o te iahiko (I) e rere ana i roto i te ara iahiko ko….

A. 0,1 A
B. 0,2 A
C. 0,5 A
D. 1,0 A
E. 5,0 A

Kōrero
E mōhiotia ana:
Ātete 1 (R₁) = 10 Ω
Ātete 2 (R₂) = 6 Ω
Ātete 3 (R₃) = 5 Ω
Ātete 4 (R₄) = 20 Ω
Pūtake o te emf 1 (E₁) = 8 Ngāohiko
Pūtake o te emf 2 (E₂) = 12 Ngāohiko
E hiahiatia ana: Te kaha o te ia e rere ana i roto i te ara iahiko (I)
Whakautu:
Ātete 3 (R₃) me te ātete 4 (R₄) e honoa ana i te taha whakarara. Ko te ātete whakakapinga ko:
1 / R₃₄ = 1/R₃ + 1/R₄ = 1/5 + 1/20 = 4/20 + 1/20 = 5/20
R₃₄ = 20/5 = 4 Ω

Hei whakaoti i tēnei raruraru, ka whiriwhiria te ahunga o te ia kia huri ki te matau.
– IR₁ – IR₂ - E₁ – IR₃₄ Ā,₂ = 0
– 10I – 6I – 8 – 4I + 12 = 0
– 10I – 6I – 4I = 8 – 12
– 20I = – 4
I = -4/-20
I = 1/5 Āpere
I = 0,2 Āmpere
Ko te iahiko e rere ana i roto i te ara iahiko he 1/5 Ampere. Ko te iahiko pai e tohu ana ko te ahunga o te iahiko e rite ana ki te mea e tumanakohia ana, ki te taha matau.
Ko te whakautu tika ko B.