Ngā Pātai Kōrero mō te Au Whakarerekē
Pendahuluan
Ko te au hurihuri (AC) he momo au hiko e huri haere ana i ia wā, i ia wā. Kāore i rite ki te au tika (DC), e rere ana i te kotahi te ahunga, ka rere te au hurihuri i ngā tere me ngā ahunga rerekē. He whānuitia te whakamahinga o te AC i roto i te tohatoha hiko nā ōna painga i roto i te tuku tawhiti me te kaha ki te huri ngāwari i tōna ngaohiko mā te whakamahi i ngā whakawhiti hiko. Ka whakaratohia e tēnei tuhinga ētahi tauira raruraru me ngā kōrero e pā ana ki te au hurihuri hei whakahōhonu ake i tō māramatanga ki tēnei kaupapa.
Tauira Pātai 1: Auautanga me te Wā o te Ia Hurihuri
Pātai:
Ko te auau o te iahiko tauutuutu he 50 Hz. Tātaihia te wā o te iahiko.
Kōrero:
Ko te auau (f) me te wā (T) o te aukume whakawhiti ko te whanaungatanga e whai ake nei:
\[ T = \frac{1}{f} \]
Me te auau (f) o te 50 Hz:
\[ T = \frac{1}{50} \]
\[ T = 0,02 \text{ hēkona} \]
Nō reira, ko te wā o te iahiko tauutuutu he 0,02 hēkona.
Tauira Pātai 2: Te Taumahatanga Nui me te Taumahatanga Whai Hua
Pātai:
Ko te ngaohiko mōrahi (Vmax) o te iahiko tauutuutu he 311 V. Tātaihia te ngaohiko whai hua (Veff) o tēnei iahiko.
Kōrero:
Ko te ngaohiko whai hua (Veff) o te au hurihuri ko te tapawhā toharite o tōna ngaohiko mōrahi, ā, ka taea te tatau mā te whakamahi i te tātai:
\[ V_{\text{eff}} = \frac{V_{\text{max}}}{\sqrt{2}} \]
Mena e mōhiotia ana ko te Vmax he 311 V, kāti:
\[ V_{\text{eff}} = \frac{311 \text{ V}}{\sqrt{2}} \]
\[ V_{\text{eff}} = \frac{311 \text{ V}}{1,414} \]
\[ V_{\text{eff}} \approx 220 \text{ V} \]
Nō reira, ko te ngaohiko whai hua o te iahiko whakawhiti ko 220 V.
Tauira Pātai 3: Te Mana Hiko i roto i te Ara Iahiko Ātete
Pātai:
I roto i tētahi ara iahiko ātete-tūturu, ko te iahiko whai hua (Ieff) e rere ana ko te 5 A, ā, ko te ngaohiko whai hua (Veff) ko te 220 V. Tātaihia te mana hiko e mimitihia ana e te ara iahiko.
Kōrero:
Ka taea te tatau i te mana hiko (P) e mimitihia ana e te ara iahiko ātete mā te whakamahi i te tātai:
\[ P = V_{\text{eff}} \times I_{\text{eff}} \]
Me te Veff o te 220 V me te Ieff o te 5 A, kātahi:
\[ P = 220 \kuputuhi{ V} \whakanuia te 5 \kuputuhi{ A} \]
\[ P = 1100 \kuputuhi{ W} \]
Nō reira, ko te mana hiko e mimitihia ana e te ara iahiko he 1100 watts.
Tauira Raru 4: Ārai i roto i te Ara Iahiko Raupapa LR
Pātai:
Kei roto i tētahi ara iahiko he ātete (R) he 10 ohms te rahi, me tētahi inductor (L) he inductor o te 0,1 H e honoa raupapa ana. Mēnā ka rere he aukume tauutuutu me te auau o te 50 Hz mā roto i te ara iahiko, tatauhia te aukati katoa o te ara iahiko.
Kōrero:
Ka taea te tatau i te aukati katoa (Z) i roto i te ara iahiko raupapa LR mā te whakamahi i te tātai:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
Kei hea:
\[ X_L = \omega L \]
ā, ko \(\omega\) te auau koki e homai ana e:
\[ \omega = 2\pi f \]
Me te f o te 50 Hz:
\[ \omega = 2\pi \whakareatia ki te 50 \]
\[ \omega = 100\pi \text{ ngā rātiana/hēkona} \]
Te Āheinga (L) o te 0,1 H:
\[ X_L = 100\pi \whakanuia ki te 0,1 \]
\[ X_L = 10\pi \text{ ohm} \]
Nō reira, ko te aukati katoa (Z) ko:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
\[ Z = \sqrt{10^2 + (10\pi)^2} \]
\[ Z = \sqrt{100 + (100\pi^2)} \]
\[ Z = \sqrt{100 + 986.96} \]
\[ Z \tata \sqrt{1086.96} \]
\[ Z \tata ki te 32.97 \kuputuhi{ ohm} \]
Nō reira, ko te tapeke aukati o te ara iahiko he tata ki te 32,97 ohms.
Tauira Raru 5: Tauwehe Mana i roto i ngā Porowhita RLC Raupapa
Pātai:
E hoatu ana he ara iahiko raupapa RLC me ngā uara o R = 20 ohms, L = 50 mH, me C = 100 μF kua honoa ki tētahi pūtake ngaohiko AC me te auau o 60 Hz. Tātaihia te tauwehenga mana i roto i te ara iahiko.
Kōrero:
Ka whakatauhia te tauwehenga mana i roto i te ara iahiko RLC e
\[ \cos(\phi) = \frac{R}{Z} \]
Ko te taahiraa tuatahi ko te tatau i te tapeke aukati (Z) o te ara iahiko:
\[ \omega = 2\pi f \]
Kei hea
\[ f = 60 \text{ Hz} \]
\[ \omega = 2\pi \whakareatia ki te 60 \]
\[ \omega = 120\pi \text{ rad/s} \]
Kātahi ka tatau i te tauhohenga inductive (XL) me te capacitive (XC):
\[ X_L = \omega L \]
\[ X_L = 120\pi \whakanuia ki te 0,05 \]
\[ X_L = 6\pi \text{ ohm} \]
\[ X_C = \frac{1}{\omega C} \]
\[ X_C = \frac{1}{120\pi \times 100 \times 10^{-6}} \]
\[ X_C = \frac{1}{0,012\pi} \]
\[ X_C \tata ki te 26,525 \kuputuhi{ ohm} \]
Te rerekētanga i waenga i te tauhohenga ā-whakaoho me te tauhohenga ā-pūmanawa \(X_L – X_C\):
\[ X = X_L – X_C \]
\[ X = 6\pi – 26,525 \]
\[ X \tata -7,903 \kuputuhi{ ohm} \]
Kātahi ka tatau i te aukati katoa (Z):
\[ Z = \sqrt{R^2 + X^2} \]
\[ Z = \sqrt{20^2 + (-7,903)^2} \]
\[ Z = \sqrt{400 + 62,41} \]
\[ Z \tata \sqrt{462,41} \]
\[ Z \tata ki te 21,51 \kuputuhi{ ohm} \]
Kātahi ka puta te tauwehenga mana (cos(φ)):
\[ \cos(\phi) = \frac{R}{Z} \]
\[ \cos(\phi) = \frac{20}{21,51} \]
\[ \cos(\phi) \tata ki te 0,93 \]
Nō reira, ko te tauwehenga mana i roto i te ara iahiko he tata ki te 0,93.
Whakamutunga
He āhuatanga motuhake tō te au hurihuri e wehewehe ana i a ia mai i te au tika, pērā i te auau, te wā, me te uara whai hua. I roto i te tātaritanga ara iahiko AC, ka whakaarohia e mātou ngā wāhanga ātete, ā-whakaoho, me te ā-kaha. Hei tāpiri, he mea nui te tatau i te aukati me te tauwehenga mana mō te hoahoa me te tātari i te mahi ara iahiko. Mā te mārama ki ngā tauira i runga ake nei, ka taea e tātou te mārama ake ki ngā ariā taketake o te au hurihuri me ōna tono i roto i te hangarau hiko.
