Fa'ata'ita'iga o Fesili Talanoaga o le Inductor
O le inductor o se vaega e le gaoioi e masani ona faʻaaogaina i matagaluega eletise e teu ai le malosi i le tulaga o se fanua maneta. E ui o mataupu faavae autu o se inductor e fai si faigofie, o le malamalama ma le fuafuaina o lana amioga i le tele o faʻaoga faatino e mafai ona faigata. O lenei tusiga e faʻamoemoe e talanoaina ni faʻataʻitaʻiga o faʻafitauli ma talanoaga e uiga i inductors e faʻamanino ai le manatu ma lona faʻaoga i le inisinia eletise.
Manatu Fa'avae o Inductors
O se inductor, e masani lava o se uaea po'o se u'amea, e iai le gafatia e tete'e atu ai i suiga o le eletise e ui atu i ai. E mafua lea i le mataupu faavae a Faraday o le electromagnetic induction. A suia le eletise i totonu o se inductor, e suia fo'i le fanua maneta e gaosia e lena eletise, lea e maua ai se emf fa'aosofia (malosiaga eletise) e tete'e atu i le suiga o le eletise.
O le fua fa'atatau masani e masani ona fa'aaogaina e fa'amatala ai se inductor i se matagaluega eletise o le:
\[ V = L \frac{di}{dt} \]
di mana:
– \( V \) o le voltage i luga o le inductor (volts),
– \( L \) o le inductance o le inductor (henry),
– \(\frac{di}{dt} \) o le suiga o le tafe i le aluga o taimi (amperes i le sekone).
Seʻi o tatou vaʻai pe faʻapefea ona faʻaaogaina inductors i nisi o faʻataʻitaʻiga o faʻafitauli.
Faataitaiga 1: Voltage i luga o se Inductor
Fesili:
O se inductor e iai le inductance e 2 H e fa'asalalauina atu i se eletise e suia i le fua faatatau o le 3 A/s. O le a le voltage i luga o le inductor?
Talanoaga:
Faaaoga le fua fa'avae o le inductor:
\[ V = L \frac{di}{dt} \]
Ua iloa:
– \( L = 2 \) H
– \(\frac{di}{dt} = 3 \) A/s
\[ V = 2 \times 3 \]
\[ V = 6 \]
O lea la, o le voltage i luga o le inductor e 6 V.
Faʻataʻitaʻiga Fesili 2: Malosiaga o loʻo teuina i totonu o se Inductor
Fesili:
O le a le tele o le malosiaga e teuina i totonu o se inductor 4 H pe afai o le tafe eletise e ui atu i ai e 5 A?
Talanoaga:
E mafai ona fuafuaina le malosi o loʻo teuina i totonu o se inductor e faʻaaoga ai le fua faʻatatau:
\[ E = \frac{1}{2} LI^2 \]
di mana:
– \( E \) o le malosi (joules),
– \( L \) o le inductance (henry),
– \( I \) o le tafega o le eletise (amperes).
Ua iloa:
– \( L = 4 \) H
– \( I = 5 \) A
\[ E = \frac{1}{2} \times 4 \times 5^2 \]
\[ E = 2 \times 25 \]
\[ E = 50 \]
O lea la, o le malosiaga o loʻo teuina i totonu o le inductor e 50 joules.
Fa'ata'ita'iga Fa'afitauli 3: Matagaluega Fa'asologa RL
Fesili:
O se matagaluega fa'asologa RL e aofia ai se resistor 10 Ω ma se inductor 2 H. Afai e fa'aogaina se puna voltage 20 V, o le a le tafe tumau o lo'o tafe i le matagaluega?
Talanoaga:
Mo se matagaluega RL fa'asolosolo, e mafai ona fuafuaina le tafe tumau e fa'aaoga ai le tulafono a Ohm aua i le tulaga tumau, e amio le inductor e pei o se uaea fa'atautaia masani (zero impedance).
\[ V = IR \]
Ua iloa:
– \( V = 20 \) V
– \( R = 10 \) Ω
\[ I = \frac{V}{R} \]
\[ I = \frac{20}{10} \]
\[ I = 2 \]
O lea la, o le tafe tumau o le eletise o loʻo tafe i le matagaluega e 2 A.
Faataitaiga 4: Frequency Resonant o se Series RLC Circuit
Fesili:
O se matagaluega RLC fa'asologa e iai se resistor e 5 Ω, se inductor e 150 mH, ma se capacitor e 100 μF. O le a le resonant frequency o le matagaluega?
Talanoaga:
E mafai ona fuafuaina le resonant frequency \( f_0 \) o se faasologa o le RLC circuit e faʻaaoga ai le fua faʻatatau:
\[ f_0 = \frac{1}{2 \pi \sqrt{LC}} \]
di mana:
– \( L \) o le inductance (henry),
– \( C \) o le capacitance (farads).
Ua iloa:
– \( L = 150 \) mH = 0.15 H
– \( C = 100 \) μF = 100 × 10^-6 F
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \times 100 \times 10^{-6}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \times 10^{-4}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \times 10^{-4}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.000015}} \]
\[ f_0 = \frac{1}{2 \pi \times 0.00387} \]
\[ f_0 = \frac{1}{0.0243} \]
\[ f_0 \pe tusa ma le 41.15 \]
O lea la, o le televave o le resonant o le matagaluega RLC fa'asologa e tusa ma le 41.15 Hz.
Fa'ata'ita'iga Fesili 5: Fa'aliliuga i Mata'ituina RL
Fesili:
O se matagaluega RL e aofia ai se resistor e 8 Ω ma se inductor e 100 mH. A fa'aogaina se voltage la'asaga e 24 V, o le a le umi e alu ai se'ia o'o atu le eletise i le 63.2% o lona tau mulimuli?
Talanoaga:
O le taimi e manaʻomia e oʻo atu ai i le 63.2% o le tau mulimuli i se matagaluega RL o le taimi tumau \( \tau \), lea:
\[ \tau = \frac{L}{R} \]
Ua iloa:
– \( L = 100 \) mH = 0.1 H
– \( R = 8 \) Ω
\[ \tau = \frac{0.1}{8} \]
\[ \tau = 0.0125 \, s \]
O lea la, o le taimi e manaʻomia mo le tafe o le eletise e oʻo atu ai i le 63.2% o lona tau mulimuli e 0.0125 sekone.
I'uga
E ala i faʻataʻitaʻiga o loʻo i luga, ua tatou talanoaina ai vaega eseese e fesoʻotaʻi ma inductors, e aofia ai le voltage i luga o se inductor, le malosiaga o loʻo teuina, lana amioga i matagaluega RL, ma le resonant frequency i matagaluega RLC. O se malamalamaga maeʻaeʻa i nei manatu ma faʻatusatusaga e taua tele mo soʻo se tasi o loʻo tuliloaina se galuega i le inisinia eletise poʻo le eletise. E taua tele le matafaioi a inductors i le tele o faʻaoga, e aofia ai filters, matagaluega oscillator, ma power converters. I le malamalama i le auala latou te galulue ai ma le auala e fuafua ai a latou parameters, e mafai ona tatou mamanuina matagaluega e sili atu ona lelei ma aoga.
