Tauira o ngā Pātai Kōrero mō ngā Momo Ātete
He ariā taketake te ātete i roto i te aukume hiko, ā, he wāhanga nui hoki o te ako ahupūngao, inā koa i roto i ngā ara iahiko hiko. Ka matapakihia e tēnei tuhinga ētahi tauira o ngā raruraru ātete, me ngā whakamārama me ngā otinga.
He aha te momo ārai?
Ko te ātete (\(\rho\)) he mehua o te āhuatanga o tētahi rauemi e whakatau ana i te nui o tana aukati i te rere o te iahiko hiko. Ka inehia te ātete i roto i ngā mita ohm (Ω·m). Ka teitei ake te ātete o tētahi rauemi, ka uaua ake te rere o te iahiko mā roto.
Ko te tātai taketake mō te tatau i te ātete (\(R\)) i roto i te ara iahiko me te roa (\(L\)) me te horahanga whakawhiti-wāhanga (\(A\)) ko:
\[ R = \rho \frac{L}{A} \]
Ngā Pātai Tauira me te Kōrero
Tauira Pātai 1:
E 2 mita te roa o tētahi waea parahi, ā, ko te horahanga whakawhiti o te 0,5 mm te roa. Ko te ātete motuhake o te parahi ko \(1.68 \times 10^{-8} \; \Omega \cdot m\). Tātaihia te ātete o te waea.
Kōrero:
1. Tahurihia te horahanga whakawhiti-wāhanga mai i te mm\(^2\) ki te m\(^2\):
\[ 0.5 \; \kuputuhi{mm}^2 = 0.5 \whakareatia 10^{-6} \; \kuputuhi{m}^2 \]
2. Whakamahia te tātai \( R = \rho \frac{L}{A} \):
\[ R = (1.68 \times 10^{-8}) \frac{2}{0.5 \times 10^{-6}} \]
\[ R = (1.68 \times 10^{-8}) \times (4 \times 10^{6}) \]
\[ R = 6.72 \times 10^{-2} \; \Omega\]
Nō reira, ko te ātete o te waea parahi he 0.0672 Ω.
Tauira Pātai 2:
Ko te ātete o tētahi waea konumohe he \(2.82 \times 10^{-8} \; \Omega \cdot m\). Mēnā he 10 mita te roa o te waea, ā, ko te ātete he 0.0564 Ω, he aha te horahanga whakawhiti-wāhanga o te waea?
Kōrero:
1. E mōhiotia ana:
– Ātete motuhake, \(\rho = 2.82 \times 10^{-8} \; \Omega \cdot m\)
– Roa, \( L = 10 \; \text{m} \)
– Ātete \( R = 0.0564 \; \Omega \)
2. Whakamahia te tātai \( R = \rho \frac{L}{A} \) hei kimi i te horahanga whakawhiti-wāhanga:
\[ R = \rho \frac{L}{A} \]
\[ 0.0564 = 2.82 \times 10^{-8} \frac{10}{A} \]
\[ 0.0564 = 2.82 \times 10^{-7} \frac{1}{A} \]
\[ A = \frac{2.82 \times 10^{-7}}{0.0564} \]
\[ A = 5 \times 10^{-6} \; \text{m}^2 \]
Nō reira, ko te horahanga whakawhiti-wāhanga o te waea konumohe ko \(5 \times 10^{-6} \; \text{m}^2\).
Tauira Pātai 3:
Mehemea ka honoa e tātou ētahi waea kawe hiko rerekē e rua i roto i te raupapa me te whakarara, he aha te pānga ki te ātete katoa, me pēhea te tatau? Me kī he waea parahi me he waea konumohe, he 5 mita te roa o ia waea, ā, he 1 mm te horahanga whakawhiti-wāhanga. Ko te ātete motuhake o te parahi ko \(1.68 \times 10^{-8} \; \Omega \cdot m\) ā, ko te konumohe ko \(2.82 \times 10^{-8} \; \Omega \cdot m\).
Kōrero:
1. Tātaihia te ātete o ia waea.
– Waea parahi:
\[ R_{\text{parahi}} = \rho \frac{L}{A} = (1.68 \times 10^{-8}) \frac{5}{1 \times 10^{-6}} \]
\[ R_{\text{parahi}} = 8.4 \times 10^{-2} \; \Omega \]
– Waea konumohe:
\[ R_{\text{konumohe}} = \rho \frac{L}{A} = (2.82 \times 10^{-8}) \frac{5}{1 \times 10^{-6}} \]
\[ R_{\text{konumohe}} = 1.41 \times 10^{-1} \; \Omega\]
2. Mēnā ka honoa raupapa:
\[ R_{\kuputuhi{katoa}} = R_{\kuputuhi{parahi}} + R_{\kuputuhi{konumohe}} \]
\[ R_{\text{tapeke}} = 8.4 \times 10^{-2} + 1.41 \times 10^{-1} \]
\[ R_{\kuputuhi{katoa}} = 0.224 \; \Omega\]
3. Mēnā ka honoa whakarara:
\[ \frac{1}{R_{\text{tapeke}}} = \frac{1}{R_{\text{parahi}}} + \frac{1}{R_{\text{konumohe}}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{8.4 \times 10^{-2}} + \frac{1}{1.41 \times 10^{-1}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{0.084} + \frac{1}{0.141} \]
\[ \frac{1}{R_{\text{total}}} = 11.905 + 7.092 \]
\[ \frac{1}{R_{\text{total}}} = 18.997 \]
\[ R_{\kuputuhi{katoa}} = \frac{1}{18.997} \]
\[ R_{\kuputuhi{katoa}} \tata ki te 0.0526 \; \Omega\]
Nō reira, ko te ātete katoa ina honoa raupapatia ngā waea e rua ko 0.224 Ω, ā, ina honoa whakarara ko 0.0526 Ω.
Whakamutunga
He mea nui te ātete o tētahi rauemi hei whakatau i te ātete katoa o tētahi kaiārahi hiko. Mā te mōhio ki te ātete, te roa, me te horahanga whakawhiti, ka taea e tātou te tatau i te ātete o tētahi rauemi mā te whakamahi i tētahi tātai māmā. E whakaatu ana ngā tauira i runga ake nei he mea nui te mārama me te tatau i te ātete i roto i te hoahoa me te tātari i ngā ara iahiko hiko. Mā te mahi, ka hohonu ake tō tātou mārama ki te ariā o te ātete, ā, ka whai hua ki ngā horopaki rerekē.
He mea nui te ātete me ōna tataunga e pā ana ki ngā tono mahi maha i roto i te hangarau me te ahupūngao. Nō reira, he mea nui te māramatanga pakari ki tēnei ariā mō te hunga katoa e uru ana ki ēnei mara.
