Tauira o tētahi Raru e Matapaki ana i te Āhuatanga Porowhita
Ko te haruru he āhuatanga e wiri ana te pūnaha me te kaha mōrahi i tētahi auau motuhake. I roto i te horopaki o ngā ara iahiko hiko, ka puta te haruru ina tae te aukati ara iahiko ki tētahi uara iti rawa, mōrahi rānei, ka puta te iahiko, te ngaohiko rānei i roto i te ara iahiko ki te tihi. He mea tino nui tēnei āhuatanga i roto i te hoahoa me te tātari i ngā ara iahiko hiko, inā koa i roto i ngā tono pēnei i ngā reo irirangi, ngā tātari, me ngā wiri.
Ngā Mātāpono Taketake o te Āhuatanga i roto i ngā Porowhita Hiko
Ko te haruru i roto i ngā ara iahiko hiko ka kōrerohia i roto i te horopaki o tētahi ara iahiko RLC, e titoa ana i tētahi ātete (R), he inductor (L), me tētahi capacitor (C). E rua ngā momo haruru e kōrerohia ana:
1. Te Āhuatanga Raupapa: Ka puta ina honoa raupapatia te inductor me te capacitor ki te ātete. Ka puta te āhuatanga ina ōrite te tauhohenga inductor (XL) ki te tauhohenga capacitive (XC).
2. Te Āhuatanga Whakarara: Ka puta ina honoa whakarara te inductor me te capacitor. Ka puta te āhuatanga ina tae te ātete ara iahiko i tētahi auau ki tōna uara mōrahi.
He rite tonu te auau orooro (\( f_0 \)) mō ngā momo ara iahiko e rua, ā, e homai ana e:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Ngā Tauira Pātai me te Kōrero mō te Āhuatanga o ngā Porowhita Raupapa RLC
Pātai 1:
Hoatu he ara iahiko raupapa RLC me te ātete (R) o te 10 ohms, he inductor (L) o te 10 mH, me te capacitor (C) o te 1 μF. Whakatauhia:
1. Auautanga haruru o te ara iahiko.
2. Āraitanga ara iahiko i te auau āwhati.
3. Te iahiko e rere ana i roto i te ara iahiko mēnā ko te ngaohiko pūtake he 10 V rms i te auau whakakorikori.
Kōrero:
1. Auautanga haruru o te ara iahiko:
Ko te auau āwhati (\( f_0 \)) i roto i te ara iahiko raupapa RLC ka hoatuhia e:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Dimana:
– L = 10 mH = 10 x 10⁻³ H
– C = 1 μF = 1 x 10⁻⁶ F
Nā reira:
\[ f_0 = \frac{1}{2\pi\sqrt{(10 \times 10^{-3})(1 \times 10^{-6})}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10 \times 10^{-9}}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10^{-8}}} \]
\[ f_0 = \frac{1}{2\pi \times 10^{-4}} \]
\[ f_0 = \frac{10^4}{2\pi} \]
\[ f_0 ≈ 1591.55 \kuputuhi{ Hz} \]
2. Āraitanga porowhita i te auau āwhati:
I te auau orooro, he ōrite te tauhohenga ā-whakaoho (XL) ki te tauhohenga ā-kaha (XC), nō reira:
\[ X_L = X_C \]
\[ 2\pi f_0 L = \frac{1}{2\pi f_0 C} \]
Nā te mea ka whakakorehia te tauhohenga inductive me te capacitive, ko te aukati ara iahiko ko te ātete anake (R):
\[ Z = R = 10 \text{ ohm} \]
3. Te iahiko e rere ana i roto i te ara iahiko:
Ka taea te tatau i te iahiko (\( I \)) i roto i te ara iahiko mā te whakamahi i te ture a Ohm:
\[ I = \frac{V}{Z} \]
Kei hea:
– V = 10 V rms
– Z = 10 ohms (i te auautanga haruru)
Nā reira:
\[ I = \frac{10}{10} \]
\[ I = 1 \text{ A} \]
Nō reira, ko te iahiko e rere ana i roto i te ara iahiko he 1 A.
Tauira Pātai me te Kōrero mō te Āhuatanga o ngā Porowhita RLC Whakarara
Pātai 2:
Homai he ara iahiko RLC whakarara me te ātete (R) o te 10 ohms, he inductor (L) o te 5 mH, me te capacitor (C) o te 2 μF. Whakatauhia:
1. Auautanga haruru o te ara iahiko.
2. Āraitanga ara iahiko i te auau āwhati.
3. Ngaohiko pūtake mēnā ko te iahiko katoa e rere ana i roto i te ara iahiko he 2 A i te auautanga orooro.
Kōrero:
1. Auautanga haruru o te ara iahiko:
Ko te auau orooro (\( f_0 \)) i roto i te ara iahiko RLC whakarara ka hoatuhia hoki e:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Dimana:
– L = 5 mH = 5 x 10⁻³ H
– C = 2 μF = 2 x 10⁻⁶ F
Nā reira:
\[ f_0 = \frac{1}{2\pi\sqrt{(5 \times 10^{-3})(2 \times 10^{-6})}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10 \times 10^{-9}}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10^{-8}}} \]
\[ f_0 = \frac{1}{2\pi \times 10^{-4}} \]
\[ f_0 = \frac{10^4}{2\pi} \]
\[ f_0 ≈ 1591.55 \kuputuhi{ Hz} \]
2. Āraitanga porowhita i te auau āwhati:
I te auau orooro, ko te urunga katoa (Y) o te inductor me te capacitor he kore. Nō reira, ko te aukati (Z) o te ara iahiko RLC whakarara e whakawhirinaki ana ki te ātete (R) anake. Nō reira, i te auau orooro, ko te aukati o te ara iahiko RLC whakarara he ōrite ki te ātete.
Nā reira:
\[ R = 10 \text{ ohm} \]
3. Pūtake hiko:
Ko te iahiko katoa (\( I \)) e rere ana i roto i te ara iahiko he 2 A. Ko te tikanga o te ture a Ohm ko te pūtake o te ngaohiko (V) ka hoatuhia e:
\[ V = I \whakareatia ki a Z \]
Kei hea:
– I = 2 A
– Z = 10 ōhm
Nā reira:
\[ V = 2 \whakareatia ki te 10 \]
\[ V = 20 \text{ V} \]
Nō reira, ko te ngaohiko pūtake he 20 V.
Whakamutunga
Ko te haruru i roto i ngā ara iahiko hiko he āhuatanga matua ka taea te whakamahi mō ngā momo tono hangarau hiko me te hiko. Ko te mārama ki te tatau i te auau haruru me ōna pānga ki te iahiko me te ngaohiko he mea nui ki te hoahoa me te tātari ara iahiko. Kei roto i tēnei tuhinga ngā ariā taketake o te haruru i roto i ngā ara iahiko RLC, ā, e matapakihia ana ngā raruraru e pā ana hei whakarato i tētahi tirohanga whānui mō tēnei kaupapa.
