Fa'ata'ita'iga o Fesili Talanoaga a le Matagaluega o le RLC
O le matagaluega RLC o se ituaiga matagaluega eletise e aofia ai se resistor (R), inductor (L), ma le capacitor (C) ua feso'ota'i fa'asolosolo pe fa'alava. O matagaluega RLC e fa'aaogaina lautele i le tele o fa'aoga fa'aeletoronika, e aofia ai ma wave filters, oscillators, signal combinations, ma isi mea. O le malamalama i le auala e iloilo ai ma foia ai fa'afitauli i nei matagaluega o se tomai taua mo tamaiti a'oga inisinia eletise ma tagata tomai fa'apitoa i le matata.
I totonu o lenei tusiga, o le a matou talanoaina ni faʻataʻitaʻiga o faʻafitauli ma a latou fofo e fesoʻotaʻi ma le auʻiliʻiliga o matagaluega RLC. O nei faʻafitauli ua mamanuina e fesoasoani ia te oe e malamalama ai i mataupu faavae ma faʻaoga autu o matagaluega RLC.
Fa'ata'ita'iga Fa'afitauli 1: Mata'itusi Fa'asologa RLC
Fesili:
Tuuina atu se matagaluega fa'asolosolo e aofia ai se resistor ma le tete'e \( R = 10 \, \Omega \), o se inductor ma le inductance \( L = 0.1 \, H \), ma se capacitor ma le capacitance \( C = 100 \, \mu F \). O lenei matagaluega ua tu'uina atu i ai se voltage sinusoidal \( V(t) = 100 \sin(1000 t) \V). Fuafua:
1. Fa'aosofiaga fa'aosofiaga \(X_L \) ma le fa'aosofiaga fa'aosofiaga \(X_C \).
2. Aofa'i atoa o le impedance o le matagaluega.
3. Tafega maualuga \( I_{max} \).
4. Malosiaga maualuga i vaega taʻitasi.
Talanoaga:
1. Fa'agaoioiga Fa'aosofiaga \( X_L \) ma le Fa'agaoioiga Fa'amafa'atasi \( X_C \)
O le fa'atupu fa'alavelave fa'aosofiaga \( X_L \) e fuafuaina e ala i le fua fa'atatau:
\[ X_L = \omega L \]
faatasi ai ma le \( \omega = 1000 \, rad/s \) ma le \( L = 0.1 \, H \),
\[ X_L = 1000 \times 0.1 = 100 \, \Omega \]
O le capacitive reactance \( X_C \) e fuafuaina e ala i le fua fa'atatau:
\[ X_C = \frac{1}{\omega C} \]
fa'atasi ai ma le \( C = 100 \, \mu F = 100 \times 10^{-6} \, F \),
\[
2. Aofa'i o le Impedance o le Matagaluega
O le aofaʻi atoa o le impedance \( Z \) mo se matagaluega faʻasolosolo RLC e:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
Suitulaga ia tau:
\[ Z = \sqrt{10^2 + (100 – 10)^2} = \sqrt{10^2 + 90^2} = \sqrt{100 + 8100} = \sqrt{8200} = 90.55 \, \Omega \]
3. Taimi Maualuga \( I_{max} \)
E mafai ona fuafuaina le maualuga o le eletise e faʻaaoga ai le tulafono a Ohm:
\[ I_{max} = \frac{V_{max}}{Z} \]
fa'atasi ai ma le \( V_{max} = 100 \, V \) ma le \( Z = 90.55 \, \Omega \):
\[ I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. Voltage Maualuga i Vaega Taʻitasi
Voltage i luga o le resistor:
\[ V_R = I_{max} \times R = 1.104 \times 10 = 11.04 \, V \]
Voltage i luga o le inductor:
\[ V_L = I_{max} \times X_L = 1.104 \times 100 = 110.4 \, V \]
Voltage i luga o le capacitor:
\[ V_C = I_{max} \times X_C = 1.104 \times 10 = 11.04 \, V \]
Fa'ata'ita'iga Fesili 2: Mata'itusi RLC Fa'alava
Fesili:
Tuuina atu se matagaluega tutusa e aofia ai se resistor ma le tete'e \( R = 50 \, \Omega \), o se inductor ma le inductance \( L = 0.5 \, H \), ma se capacitor ma le capacitance \( C = 10 \, \mu F \). O le puna o le voltage e sinusoidal ma le voltage \( V(t) = 200 \cos(2000 t) \, V \). Fuafua:
1. Fa'aosofiaga fa'aosofiaga \(X_L \) ma le fa'aosofiaga fa'aosofiaga \(X_C \).
2. Aofa'i o le avanoa e ulufale ai i le matagaluega.
3. Tafega maualuga \( I_{max} \).
Talanoaga:
1. Fa'agaoioiga Fa'aosofiaga \( X_L \) ma le Fa'agaoioiga Fa'amafa'atasi \( X_C \)
O le fa'atupu fa'alavelave fa'aosofiaga \( X_L \) e fuafuaina e ala i le fua fa'atatau:
\[ X_L = \omega L \]
faatasi ai ma le \( \omega = 2000 \, rad/s \) ma le \( L = 0.5 \, H \),
\[ X_L = 2000 \times 0.5 = 1000 \, \Omega \]
O le capacitive reactance \( X_C \) e fuafuaina e ala i le fua fa'atatau:
\[ X_C = \frac{1}{\omega C} \]
fa'atasi ai ma le \( C = 10 \, \mu F = 10 \times 10^{-6} \, F \),
\[
2. Taliaina Atoa o le Matagaluega
O le Admittance \( Y \) o le fa'atusatusaga lea o le impedance. Mo se matagaluega RLC fa'atasi:
\[ Y = \sqrt{G^2 + (B_L – B_C)^2} \]
lea \( G = \frac{1}{R} \),
\[ G = \frac{1}{50} = 0.02 \, S \]
Fa'asolo ina fa'aosofia \( B_L \):
\[ B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Fa'aletonu o le gafatia \( B_C \):
\[ B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S \]
Suia uma tau i totonu o le fua fa'atatau:
\[ Y = \sqrt{0.02^2 + (0.001 – 0.02)^2} = \sqrt{0.0004 + 0.000361} = \sqrt{0.000761} = 0.0276 \, S \]
O le aofaʻi atoa o le impedance \( Z \) o le fesuiaʻiga lea o le admittance:
\[ Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, \Omega \]
3. Taimi Maualuga \( I_{max} \)
\[ I_{max} = \frac{V_{max}}{Z} \]
fa'atasi ai ma le \( V_{max} = 200 \, V \) ma le \( Z = 36.23 \, \Omega \):
\[ I_{max} = \frac{200}{36.23} \approx 5.52 \, A \]
I'uga
O le malamalama i le auala e fuafua ai le reactance, admittance, impedance, ma le current i totonu o se RLC circuit e taua tele mo faʻaoga i le inisinia eletise. Faatasi ai ma le faataitai faifai pea e ala i faataitaiga eseese e pei o na ua tatou talanoaina, o le a faalolotoina ai lou malamalama i le auiliiliga o le RLC circuit. O le faataitai faifai pea o le a faaleleia atili ai foi ou tomai i le foia o faafitauli ma le mamanuina o matagaluega eletise faigata i le lumanai.
