Nā Nīnau Kūkākūkā o ke Au Hou
Pendahuluan
ʻO ke au uila ʻē aʻe (AC) kahi ʻano au uila e hoʻololi pinepine i ke kuhikuhi. ʻAʻole e like me ke au pololei (DC), e kahe ana i hoʻokahi kuhikuhi, ke kahe nei ke au uila ʻē aʻe i nā wikiwiki a me nā kuhikuhi like ʻole. Hoʻohana nui ʻia ʻo AC i ka hoʻolaha mana uila ma muli o kona mau pono i ka hoʻoili mamao loa a me ka hiki ke hoʻololi maʻalahi i kona voltage me ka hoʻohana ʻana i nā transformers. E hāʻawi kēia ʻatikala i kekahi mau pilikia hoʻohālike a me nā kūkākūkā e pili ana i ke au uila ʻē aʻe e hoʻoikaika i kou ʻike i kēia kumuhana.
Laʻana Nīnau 1: Alapine (frequency) a me ka wā o ke au hoʻololi
Nīnau:
He 50 Hz ke alapine (frequency) o ke au uila ʻē aʻe. E helu i ka wā o ke au.
Kūkākūkā:
ʻO ke alapine (f) a me ka wā (T) o ke au hoʻololi e like me kēia ka pilina:
\[ T = \frac{1}{f} \]
Me ke alapine (f) o 50 Hz:
\[ T = \frac{1}{50} \]
\[ T = 0,02 \kikokikona{ kekona} \]
No laila, ʻo ka wā o ke au hoʻololi he 0,02 kekona.
Laʻana Nīnau 2: Ka Hopohopo Nui a me ke Hopohopo Kūpono
Nīnau:
ʻO 311 V ka volta kiʻekiʻe loa o ke au uila (Vmax). E helu i ka volta kūpono (Veff) o kēia au.
Kūkākūkā:
ʻO ke ana uila kūpono (Veff) o ke au uila ʻē aʻe ka awelika huinahā o kona ana uila kiʻekiʻe loa a hiki ke helu ʻia me ka hoʻohana ʻana i ke ʻano hana:
\[ V_{\text{eff}} = \frac{V_{\text{max}}}{\sqrt{2}} \]
Inā ʻike ʻia ʻo Vmax he 311 V, a laila:
\[ V_{\text{eff}} = \frac{311 \text{ V}}{\sqrt{2}} \]
\[ V_{\text{eff}} = \frac{311 \text{ V}}{1,414} \]
\[ V_{\text{eff}} \approx 220 \text{ V} \]
No laila, ʻo ka volta kūpono o ke au uila he 220 V.
Laʻana Nīnau 3: Mana Uila ma kahi Kaapuni Resistive
Nīnau:
I loko o kahi kaapuni resistive maʻemaʻe, ʻo ke au kūpono (Ieff) e kahe ana he 5 A a ʻo ka volta kūpono (Veff) he 220 V. E helu i ka mana uila i omo ʻia e ke kaapuni.
Kūkākūkā:
Hiki ke helu ʻia ka mana uila (P) i omo ʻia e kahi kaapuni resistive maʻemaʻe me ka hoʻohana ʻana i ke ʻano hana:
\[ P = V_{\text{eff}} \times I_{\text{eff}} \]
Me ka Veff o 220 V a me Ieff o 5 A, a laila:
\[ P = 220 \text{ V} \times 5 \text{ A} \]
\[ P = 1100 \kikokikona{ W} \]
No laila, ʻo ka mana uila i omo ʻia e ke kaapuni he 1100 watts.
Laʻana Pilikia 4: Impedance ma kahi Kaapuni Moʻo LR
Nīnau:
Aia i loko o kahi kaapuni kahi resistor (R) o 10 ohms a me kahi inductor (L) me ka inductance o 0,1 H i hoʻopili ʻia ma ke ʻano series. Inā kahe kahi au alternating me ke alapine o 50 Hz ma o ke kaapuni, e helu i ka huina impedance o ke kaapuni.
Kūkākūkā:
Hiki ke helu ʻia ka huina impedance (Z) i loko o kahi kaapuni LR series me ka hoʻohana ʻana i ke ʻano:
Z = \sqrt{R^2 + (X_L)^2}
Ma hea:
\[ X_L = \omega L \]
a ʻo \(\omega\) ke alapine angular i hāʻawi ʻia e:
\[ \omega = 2\pi f \]
Me f o 50 Hz:
\[ \omega = 2\pi \times 50 \]
\[ \omega = 100\pi \text{ radians/kekona} \]
Inductance (L) o 0,1 H:
\[ X_L = 100\pi \times 0,1 \]
\[ X_L = 10\pi \text{ ohm} \]
No laila, ʻo ka huina impedance (Z) penei:
Z = \sqrt{R^2 + (X_L)^2}
\[ Z = \sqrt{10^2 + (10\pi)^2} \]
\[ Z = \sqrt{100 + (100\pi^2)} \]
\[ Z = \sqrt{100 + 986.96} \]
\[ Z \approx \sqrt{1086.96} \]
\[ Z \approx 32.97 \text{ ohm} \]
No laila, ʻo ka huina impedance o ke kaapuni ma kahi o 32,97 ohms.
Laʻana Pilikia 5: Mana Factor i nā Kaapuni RLC Series
Nīnau:
Hāʻawi ʻia kahi kaapuni RLC moʻo me nā waiwai o R = 20 ohms, L = 50 mH, a me C = 100 μF i hoʻopili ʻia i kahi kumu uila AC me ke alapine (frequency) o 60 Hz. E helu i ka mana kumu i loko o ke kaapuni.
Kūkākūkā:
Hoʻoholo ʻia ka mana mana ma ke kaapuni RLC e
\[ \cos(\phi) = \frac{R}{Z} \]
ʻO ka hana mua, ʻo ia ka helu ʻana i ka huina impedance (Z) o ke kaapuni:
\[ \omega = 2\pi f \]
Ma hea
\[ f = 60 \text{ Hz} \]
\[ \omega = 2\pi \times 60 \]
\[ \omega = 120\pi \text{ rad/s} \]
A laila e helu i ka inductive (XL) a me ka capacitive (XC) reactance:
\[ X_L = \omega L \]
\[ X_L = 120\pi \times 0,05 \]
\[ X_L = 6\pi \text{ ohm} \]
\[ X_C = \frac{1}{\omega C} \]
\[ X_C = \frac{1}{120\pi \times 100 \times 10^{-6}} \]
\[ X_C = \frac{1}{0,012\pi} \]
\[ X_C \approx 26,525 \text{ ohm} \]
ʻOkoʻa ma waena o ka reactance inductive a me ka capacitive \(X_L – X_C\):
\[ X = X_L – X_C \]
\[ X = 6\pi – 26,525 \]
\[ X \approx -7,903 \text{ ohm} \]
A laila e helu i ka huina impedance (Z):
\[ Z = \sqrt{R^2 + X^2} \]
Z = 20^2 + (-7,903)^2}
\[ Z = \sqrt{400 + 62,41} \]
\[ Z \approx \sqrt{462,41} \]
\[ Z \approx 21,51 \text{ ohm} \]
A laila ka mana kumu (cos(φ)):
\[ \cos(\phi) = \frac{R}{Z} \]
\[ \cos(\phi) = \frac{20}{21,51} \]
\[ \cos(\phi) \approx 0,93 \]
No laila, ʻo ka mana mana i loko o ke kaapuni ma kahi o 0,93.
Ka hopena
Loaʻa i ke au hoʻololi nā ʻano kikoʻī e hoʻokaʻawale iā ia mai ke au pololei, e like me ke alapine (frequency), ka wā (period), a me ka waiwai kūpono. I ka loiloi kaapuni AC, noʻonoʻo mākou i nā ʻāpana resistive, inductive, a me capacitive. Eia kekahi, he mea nui ka helu ʻana i ka impedance a me ka mana no ka hoʻolālā ʻana a me ka nānā ʻana i ka hana kaapuni. Ma ka hoʻomaopopo ʻana i nā hiʻohiʻona ma luna, hiki iā mākou ke hoʻomaopopo maʻalahi i nā manaʻo kumu o ke au hoʻololi a me kāna mau noi i ka ʻenekinia uila.
