Tauira o ngā Pātai e Matapaki ana i ngā Ara Hiko
He kaupapa nui ngā ara iahiko hiko i roto i te ahupūngao me te hangarau hiko. He mea nui te mārama ki te mahi a ngā ara iahiko me te tatau i ngā uara mō te hunga e hiahia ana ki te hangarau hiko, ki te mahi rānei me ngā taputapu hiko. Ka kapi tēnei tuhinga i ētahi tauira o ngā raruraru ara iahiko hiko me ō rātou whakamārama hei tohutoro mā ngā ākonga me ngā tohunga e hiahia ana ki te whakawhānui ake i ō rātou mātauranga.
He Kupu Whakataki ki ngā Ara Hiko
I te nuinga o te wā, he maha ngā wāhanga taketake o tētahi ara iahiko hiko pērā i ngā ātete, ngā pūnga hiko, ngā ine hiko, me ngā pūtake hiko, ngā pūtake hiko rānei. Ka honoa ēnei wāhanga i roto i ngā whirihoranga motuhake hei mahi i ngā mahi motuhake, pērā i te tātari i ngā tohu, te whakanui, te whakaiti rānei i te hiko. I roto i te tātari ara iahiko, ka whakamahia pinepinetia ngā ture a Ohm me Kirchhoff hei tatau i te iahiko me te hiko i roto i tētahi ara iahiko.
Tauira Raru 1: Ara Iahiko Raupapa Māmā
Pātai:
Homai he ara iahiko raupapa e toru ngā ātete \( R1 = 2 \Omega \), \( R2 = 3 \Omega \), me \( R3 = 5 \Omega \) e hono ana ki tētahi pūtake ngaohiko \( V = 10 V \). Tātaihia te iahiko e rere ana i roto i te ara iahiko me te ngaohiko puta noa i ia ātete.
Kōrero:
1. Kimihia te Ātete Katoa:
I roto i te ara iahiko raupapa, ko te ātete katoa ko te tapeke o ngā ātete takitahi katoa.
\[
R_{\text{katoa}} = R1 + R2 + R3 = 2 \Omega + 3 \Omega + 5 \Omega = 10 \Omega
\]
2. Kimihia te Ia Rere:
E ai ki te ture a Ohm, ka taea te tatau i te iahiko penei:
\[
I = \frac{V}{R_{\text{total}}} = \frac{10 V}{10 \Omega} = 1 A
\]
3. Kimihia te Ngaohiko i runga i ia Ātete:
Ka tatauhia te ngaohiko puta noa i ia ātete penei:
\[
V_{R1} = I \times R1 = 1 A \times 2 \Omega = 2 V
\]
\[
V_{R2} = I \times R2 = 1 A \times 3 \Omega = 3 V
\]
\[
V_{R3} = I \times R3 = 1 A \times 5 \Omega = 5 V
\]
Nō reira, ko te iahiko e rere ana i roto i te ara iahiko ko 1 A, ā, ko te ngaohiko puta noa i ia ātete ko 2 V, 3 V, me te 5 V, ia.
Tauira Pātai 2: Porowhita Whakarara Māmā
Pātai:
Homai he ara iahiko whakarara e toru ngā ātete \( R1 = 6 \Omega \), \( R2 = 3 \Omega \), me \( R3 = 2 \Omega \) e hono ana ki tētahi pūtake ngaohiko \( V = 12 V \). Tātaihia te iahiko e puta ana i ia ātete.
Kōrero:
1. Ia Ātete i roto i ia Ātete:
I roto i te ara iahiko whakarara, he ōrite te ngaohiko puta noa i ia ātete ki te ngaohiko pūtake. Nō reira, ka tatauhia te iahiko puta noa i ia ātete mā te whakamahi i te ture a Ohm.
\[
I_{R1} = \frac{V}{R1} = \frac{12 V}{6 \Omega} = 2 A
\]
\[
I_{R2} = \frac{V}{R2} = \frac{12 V}{3 \Omega} = 4 A
\]
\[
I_{R3} = \frac{V}{R3} = \frac{12 V}{2 \Omega} = 6 A
\]
Nō reira, ko te iahiko e puta ana i ia ātete he 2 A, 4 A, me te 6 A.
Tauira Pātai 3: Te Huinga o ngā Porowhita Raupapa me ngā Porowhita Whakarara
Pātai:
Homai he ara iahiko whakakotahi kei roto ko \( R1 = 4 \Omega \), \( R2 = 2 \Omega \), me \( R3 = 3 \Omega \). Ka honoa whakarara a \( R2 \) me \( R3 \), kātahi ka honoa raupapa ki \( R1 \) me te pūtake ngaohiko \( V = 15 V \). Tātaihia te iahiko me te ngaohiko puta noa i ia ātete.
Kōrero:
1. Kimihia te ātete ōrite o \( R2 \) me \( R3 \):
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{R2} + \frac{1}{R3} = \frac{1}{2 \Omega} + \frac{1}{3 \Omega} = \frac{3 + 2}{6} = \frac{5}{6 \Omega}
\]
\[
R_{\text{whakarara}} = \frac{6}{5} \Omega = 1,2 \Omega
\]
2. Ātete Katoa:
\[
R_{\text{tapeke}} = R1 + R_{\text{whakarara}} = 4 \Omega + 1,2 \Omega = 5,2 \Omega
\]
3. Tapeke o te Iahiko:
\[
I_{\text{tapeke}} = \frac{V}{R_{\text{tapeke}}} = \frac{15 V}{5,2 \Omega} \approx 2,88 A
\]
4. Ngaohiko i \( R1 \):
\[
V_{R1} = I_{\text{tapeke}} \times R1 = 2,88 A \times 4 \Omega \approx 11,52 V
\]
5. Ngaohiko i \( R2 \) me \( R3 \):
Nā te mea kei te whakarara a \( R2 \) me \( R3 \), he ōrite ngā ngaohiko:
\[
V_{\text{whakarara}} = V – V_{R1} = 15 V – 11,52 V \approx 3,48 V
\]
6. Kimihia te au i roto i te \( R2 \) me te \( R3 \):
\[
I_{R2} = \frac{V_{\text{parallel}}}{R2} = \frac{3,48 V}{2 \Omega} \approx 1,74 A
\]
\[
I_{R3} = \frac{V_{\text{parallel}}}{R3} = \frac{3,48 V}{3 \Omega} \approx 1,16 A
\]
Nō reira, ko te iahiko e rere ana i roto i te ara iahiko he tata ki te 2,88 A. Ko te ngaohiko puta noa i \( R1 \) he tata ki te 11,52 V, ā, ko ngā ngaohiko puta noa i \( R2 \) me \( R3 \) he tata ki te 3,48 V. Ko te iahiko puta noa i \( R2 \) he 1,74 A, ā, puta noa i \( R3 \) he 1,16 A.
Whakamutunga
Ka matapakihia e tēnei tuhinga ētahi tauira o ngā rapanga ara iahiko māmā me ngā rapanga ara iahiko whakakotahi, me ngā mahi hei whakaoti i aua rapanga. Mā te mārama ki ngā ariā taketake me te whakamahi i ngā ture a Ohm me Kirchhoff ka māmā ake te whakaoti rapanga ara iahiko. Mā te mahi tonu me ngā momo rapanga ka pai ake tō māramatanga me tō kaha ki te tātari i ngā ara iahiko hiko. Mō te hunga e rapu ana i te māramatanga hohonu ake, me ruku hohonu ake ki ngā rauemi mō ngā ara iahiko AC, ngā tātari, me te tātari rohe auau.
