Tauira o ngā Pātai Kōrero mō te Ara Whakapūhui
Pendahuluan
He kaupapa nui ngā ara iahiko hiko i roto i te ako i te ahupūngao me te hangarau hiko. Ko ngā ara iahiko whakakotahi, e kiia ana he ara iahiko whakakotahi, he huinga o ngā ara iahiko raupapa me ngā ara iahiko whakarara. He mea nui te mārama ki ngā ara iahiko whakakotahi mō te hunga e whai mahi ana i roto i te hangarau hiko me te hikohiko. Ka kapi i tēnei tuhinga ngā ariā taketake o ngā ara iahiko whakakotahi, ka whakarato tauira, ka whakarato kōrero hei āwhina i a koe ki te mārama hohonu ake ki te rauemi.
Ngā Ariā Taketake o ngā Porowhita Whakapūhui
He maha ngā wāhanga matua o tētahi ara iahiko hiko pērā i te ātete (R), te ine hiko (L), me te kaha hiko (C). Ko te ara iahiko whakakotahi he huinga o ngā ara iahiko e rua, neke atu rānei, he rerekē ngā momo, he raupapa, he whakarara rānei.
Porowhita Raupapa
I roto i te ara iahiko raupapa, ka honoa ngā wāhanga hiko i roto i te ara kotahi me te kōwhiringa rere iahiko kotahi anake. He ōrite te iahiko e puta ana i ia wāhanga, engari ka tohaina te ngaohiko i waenga i ngā wāhanga.
Porowhita Whakarara
I roto i te ara iahiko whakarara, ka honoa ngā wāhanga kia whai peka motuhake ia wāhanga mō te rere o te iahiko. He ōrite te ngaohiko puta noa i ia wāhanga, engari ka wehea te iahiko ki waenga i ngā wāhanga.
Raupapa Whakakotahi
Ka whakakotahihia ēnei ariā e rua e ngā ara iahiko whakakotahi mā te whakakotahi i ngā wāhanga i roto i ngā whirihoranga raupapa me ngā whirihoranga whakarara. Hei mārama ki te mahi a ngā ara iahiko whakakotahi me mōhio koe ki ngā ture hiko taketake pēnei i te Ture a Ohm me ngā Ture a Kirchhoff.
Ngā Pātai Tauira me te Kōrero
Pātai 1: Ara iahiko Māmā
I roto i tētahi ara iahiko pūhui māmā, e toru ngā ātete: R1 = 2Ω, R2 = 4Ω, me R3 = 6Ω. Ka honoa ngā ātete R1 me R2 i roto i te raupapa, kātahi ka honoa whakarara ki a R3. Mena ko te ngaohiko katoa e pā ana ki te ara iahiko he 12V, tatauhia:
1. Ātete katoa
2. Tapeke o te au
3. Ngaohiko i runga i ia ātete
Kōrero:
1. Ātete Katoa (R_total):
– Tuatahi, tatauhia te ātete honohono o R1 me R2 e honoa raupapa ana.
\[
R_{ser} = R1 + R2 = 2Ω + 4Ω = 6Ω
\]
– Kātahi, tatauhia te ātete honohono o R_ser me R3 e honoa whakarara ana.
\[
\frac{1}{R_{tapeke}} = \frac{1}{R_{ser}} + \frac{1}{R3} = \frac{1}{6Ω} + \frac{1}{6Ω} =\frac{1+1}{6Ω}= \frac{2}{6Ω} = \frac{1}{3Ω}
\]
\[
R_{katoa} = 3Ω
\]
2. Tapeke o te Ia Wā (I_total):
Mā te whakamahi i te Ture a Ohm (\(V = IR\)):
\[
I_{tapeke} = \frac{V}{R_{tapeke}} = \frac{12V}{3Ω} = 4A
\]
3. Ngaohiko i runga i ia Ātete:
– Ka wehea te ngaohiko i runga i te R1 me te R2 (raupapa) i runga i ō rātou uara ātete:
\[
V_{R_{ser}} = I_{tapeke} \times R_{ser} = 4A \times 6Ω = 24V
\]
– Heoi, nā te mea he ātete katoa anō hoki kei roto i tēnei ara iahiko, me tirotiro anō te tātai mēnā he tika.
– Ka wehea te ngaohiko katoa o te 12V kia whakarara i waenganui i a (R1+R2) me R3.
\[
V_{R3} = I_{tapeke} \times R3 = 4A \times 6Ω = 24V
\]
– Ka taea te arotake i te hapa i runga ake nei, arā, ko te tikanga pea he whakamārama i ngā āhuatanga ngaohiko whakarara e hiahia ana ki ngā uara ōrite.
Tauira Raru 2: Ngā Ara Iahiko Uaua
I roto i tētahi ara iahiko matatini, e rima ngā ātete: R1 = 2Ω, R2 = 3Ω, R3 = 5Ω, R4 = 10Ω, me R5 = 2Ω. Ka honoa raupapatia a R1 me R2, kātahi ka honoa whakararatia ki a R3. Kātahi ka honoa raupapatia tēnei huinga ātete ki te huinga whakarara o R4 me R5. Mena he 24V te ngaohiko katoa, whakatauhia:
1. Ātete katoa
2. Tapeke o te au
3. Ngaohiko i runga i ia ātete
Kōrero:
1. Ātete Katoa (R_total):
– Te whakakotahitanga o R1 me R2 (raupapa):
\[
R_{12} = R1 + R2 = 2Ω + 3Ω = 5Ω
\]
– Hononga whakarara ki te R3:
\[
\frac{1}{R_{123}} = \frac{1}{R_{12}} + \frac{1}{R3} = \frac{1}{5Ω} + \frac{1}{5Ω} = \frac{2}{5Ω} = \frac{1}{2.5Ω}
\]
\[
R_{123} = 2.5Ω
\]
– Te huinga whakarara o R4 me R5:
\[
\frac{1}{R_{45}} = \frac{1}{R4} + \frac{1}{R5} = \frac{1}{10Ω} + \frac{1}{2Ω} = \frac{1+5}{10Ω}= \frac{6}{10Ω}= \frac{3}{5Ω}
\]
\[
R_{45} = \frac{5}{3Ω} = 1.67Ω
\]
– Te whakakotahitanga katoa me ngā whakatau mai i ngā kaupapa whakarōpū R123 me R45:
\[
R_{12345} = R_{123} + R_{45} = 2.5Ω + 1.67Ω = 4.17Ω
\]
2. Tapeke o te Iahiko:
\[
I_{tapeke} = \frac{V_{tapeke}}{R_{tapeke}} = \frac{24V}{4.17Ω} = 5.76A
\]
3. Ngaohiko i runga i ia Ātete:
– Mō te whakarara tuatahi, ā, e hangai ana ki te mea māmā:
\[
V_{123} = I_{tapeke} \times R_{123} = 5.76A \times 2.5Ω = 14.4V
\]
\[
V_{45} = I_{tapeke} \times R_{45} = 5.76A \times 1.67Ω = 9.6V
\]
– Te tātari i ngā wāhanga o te kaupapa rori rerekē me te tohatoha o ngā uara o nāianei mā te ātete katoa hei whakamātautau i ngā uara semper.
Whakamutunga
Ko te mārama ki ngā ara iahiko pūhui me mārama ki ngā ariā taketake pēnei i ngā ara iahiko raupapa me ngā ara iahiko whakarara, tae atu ki ngā ture matua o te hiko. Mā te mōhio ki ngā tikanga whakaoti rapanga pēnei ka hohonu ake tō māramatanga ki ngā ara iahiko pūhui, he mea tino nui tēnei i roto i te ao o te miihini hiko me te hikohiko. Nō reira, ko te mahi tonu me te kōrero taipitopito ka tino whai hua hei mōhio ki tēnei rauemi.
