Tauira o ngā Pātai Kōrero mō te Hiko Auaha Tika
He āhuatanga rongonui te hiko au tika (DC) i roto i te hangarau me te ahupūngao. Ko te au tika te rere o ngā irahiko i te taha kotahi mā roto i tētahi kaiārahi, mai i te pito pai ki te pito kino i roto i tētahi ara iahiko. I roto i tēnei tuhinga, ka tūhuratia e mātou ētahi tauira raruraru me ā rātou matapakinga e pā ana ki te hiko au tika hei āwhina i te whakapai ake i tō mātou māramatanga ki tēnei kaupapa.
1. Porowhita Raupapa
Pātai 1:
E hoatu ana he ara iahiko raupapa kei roto ko ngā ātete e toru, ko ia ātete he 4Ω, he 6Ω, me te 10Ω, e honoa ana ki tētahi pūtake ngaohiko o te 20V. Tātaihia te iahiko e rere ana i roto i te ara iahiko.
Kōrero:
Tuatahi, me tatau tātou i te ātete katoa i roto i te ara iahiko raupapa. I roto i te ara iahiko raupapa, ko te ātete katoa (R_total) ko te tapeke o ia ātete takitahi.
\[ R_{\kuputuhi{katoa}} = R_1 + R_2 + R_3 \]
\[ R_{\text{total}} = 4Ω + 6Ω + 10Ω = 20Ω \]
Whai muri i tēnā, ka whakamahia e tātou te ture a Ohm hei tatau i te iahiko. E kī ana te ture a Ohm ko \( V = I \times R \). Nō reira, ka taea te tatau i te iahiko (I) mā te:
\[ I = \frac{V}{R_{\text{total}}} \]
\[ I = \frac{20V}{20Ω} = 1A \]
Nō reira, ko te iahiko e rere ana i roto i te ara iahiko he 1 āpere.
2. Porowhita Whakarara
Pātai 2:
E toru ngā ātete, ko ō rātou ātete he 3Ω, he 6Ω, me te 12Ω, kua honoa whakararatia, ā, kua honoa ki tētahi pūtake ngaohiko 12V. Tātaihia te ia e rere ana i roto i ia ātete.
Kōrero:
Mō tētahi ara iahiko whakarara, he ōrite te ngaohiko (V) puta noa i ia ātete ki te ngaohiko pūtake. Tuatahi, ka tatauhia e tātou ia iahiko mā te whakamahi i te ture a Ohm.
\[ I_1 = \frac{V}{R_1} = \frac{12V}{3Ω} = 4A \]
\[ I_2 = \frac{V}{R_2} = \frac{12V}{6Ω} = 2A \]
\[ I_3 = \frac{V}{R_3} = \frac{12V}{12Ω} = 1A \]
Ko te iahiko e rere ana i roto i ia ātete he 4A, 2A, me te 1A.
Hei tāpiritanga, ka taea e tātou te tatau i te iahiko katoa e rere ana mai i te pūtake mā te whakamahi i te ture iahiko a Kirchoff e kī ana ko te iahiko katoa e tomo ana ki tētahi pūwāhi he ōrite ki te iahiko e puta atu ana i reira:
\[ I_{\text{tapeke}} = I_1 + I_2 + I_3 = 4A + 2A + 1A = 7A \]
3. Te Huinga o ngā Porowhita Raupapa me ngā Porowhita Whakarara
Pātai 3:
E whā ngā ātete, ko ō rātou uara he 4Ω, he 6Ω, he 12Ω, me te 12Ω, kua whakaritea ki roto i tētahi ara iahiko whakakotahi, arā, ko te 4Ω me te 6Ω kua whakaritea kia raupapa, kātahi ka whakaritea te hua kia whakarara ki te 12Ω, ā, hei whakamutunga, ka whakaritea kia raupapa ki te tuatoru o ngā 12Ω. Mena ko te pūtake ngaohiko he 24V, tātaihia te iahiko katoa e rere ana i roto i te ara iahiko.
Kōrero:
Ko te taahiraa tuatahi ko te tatau i te ātete o te ara iahiko raupapa tuatahi.
\[ R_{\text{raupapa}} = 4Ω + 6Ω = 10Ω \]
Kātahi ka honoa ngā hua o runga ake nei ki te 12Ω i roto i te whakaritenga whakarara.
\[ \frac{1}{R_{\text{parallel}}} = \frac{1}{10Ω} + \frac{1}{12Ω} \]
\[ \frac{1}{R_{\text{parallel}}} = \frac{6}{60} + \frac{5}{60} = \frac{11}{60} \]
\[ R_{\text{parallel}} = \frac{60}{11}Ω \approx 5.45Ω \]
Nā, ka whakatakotoria tēnei hua ki roto i te raupapa me te 12Ω whakamutunga.
\[ R_{\text{tapeke}} = R_{\text{whakarara}} + 12Ω \]
\[ R_{\text{katoa}} = 5.45Ω + 12Ω = 17.45Ω \]
Hei whiwhi i te iahiko katoa, ka whakamahia e mātou te ture a Ohm:
\[ I_{\kuputuhi{tapeke}} = \frac{V}{R_{\kuputuhi{tapeke}}} \]
\[ I_{\text{katoa}} = \frac{24V}{17.45Ω} \approx 1.38A \]
4. Te Mana i roto i te Ara Iahiko
Pātai 4:
Ki te hoatu he ātete he 5Ω te uara, ā, he iahiko e rere ana i roto i te ātete he 2A, tatauhia te mana ka mararahia e te ātete.
Kōrero:
Ka taea te tatau i te mana (P) mā te whakamahi i te tātai:
\[ P = I^2 \times R \]
\[ P = (2A)^2 \whakanuia te 5Ω \]
\[ P = 4 \whakanuia te 5 = 20W \]
Nō reira, ko te mana e tohatohahia ana e te ātete he 20 watts.
5. Pūmanawa i ngā Pūwāhi i roto i te Porowhita
Pātai 5:
E rua ngā ātete o tētahi ara iahiko, 10Ω me te 20Ω, e honoa raupapa ana ki tētahi pūtake ngaohiko 30V. Tātaihia te pūmanawa kei te pūwāhi i waenganui i ngā ātete e rua.
Kōrero:
Tuatahi, ka tatauhia e mātou te iahiko e rere ana i roto i te ara iahiko.
\[ R_{\text{katoa}} = 10Ω + 20Ω = 30Ω \]
\[ I = \frac{30V}{30Ω} = 1A \]
Ka taea te kimi i te pūmanawa i te pūwāhi i waenganui i ngā ātete e rua mā te tatau i te maturuturunga ngaohiko puta noa i te ātete tuatahi.
\[ V_{10Ω} = I \times R_1 = 1A \times 10Ω = 10V \]
Nō reira, ko te pūmanawa i te pūwāhi i waenganui i ngā ātete e rua ko \( 30V – 10V = 20V \).
Whakamutunga
Kua matapakihia e tēnei tuhinga ētahi tauira raruraru me ā rātou otinga e pā ana ki ngā ara iahiko hiko au tika. Kei roto i ēnei ko ngā ara iahiko raupapa, whakarara, me ngā ara iahiko whakakotahi, tae atu ki te tatau i te mana me te pūmanawa i ngā pūwāhi rerekē. He mea nui te māramatanga pakari ki ēnei ariā taketake mō te hunga e ako ana i te hiko me te hikohiko. Mā te whakaharatau auau ki ngā momo raruraru ka tino āwhina i te mōhio ki tēnei rauemi.
