Isibonelo Semibuzo Yengxoxo Yesifunda Se-RLC
Isekethe ye-RLC uhlobo lwesekethe kagesi oluqukethe i-resistor (R), i-inductor (L), kanye ne-capacitor (C) exhunywe ngochungechunge noma ngokulingana. Amasekethe e-RLC asetshenziswa kabanzi ezinhlotsheni ezahlukene ze-elekthronikhi, kufaka phakathi izihlungi zamagagasi, ama-oscillator, inhlanganisela yesignali, nokuningi. Ukuqonda ukuthi ungahlaziya kanjani futhi uxazulule izinkinga kulezi zifunda kuyikhono elibalulekile kubafundi bobunjiniyela kagesi kanye nochwepheshe kulo mkhakha.
Kulesi sihloko, sizoxoxa ngezinkinga eziningana zezibonelo kanye nezixazululo zazo ezihlobene nokuhlaziywa kwesekethe ye-RLC. Lezi zinkinga zenzelwe ukukusiza uqonde izimiso eziyisisekelo kanye nokusetshenziswa kwesekethe ye-RLC.
Isibonelo Inkinga 1: Isekethe Yochungechunge lwe-RLC
Umbuzo:
Uma unikezwe isekethe yochungechunge equkethe i-resistor enokumelana \( R = 10 \, \Omega \), i-inductor ene-inductance \( L = 0.1 \, H \), kanye ne-capacitor ene-capacitance \( C = 100 \, \mu F \). Le sekethe inikezwa i-voltage ye-sinusoidal \( V(t) = 100 \sin(1000 t) \V). Thola:
1. Ukusabela okukhuthazayo \( X_L \) kanye nokusabela okunamandla \( X_C \).
2. I-impedance ephelele yesekethe.
3. Umkhawulo wamanje \( I_{max} \).
4. I-voltage ephezulu kakhulu engxenyeni ngayinye.
Ingxoxo:
1. Ukusabela Okubangela Ukuguquka \( X_L \) kanye Nokusabela Okunamandla \( X_C \)
Ukusabela okukhuthazayo \( X_L \) kubalwa ngefomula:
\[ X_L = \omega L \]
nge \( \omega = 1000 \, rad/s \) kanye \( L = 0.1 \, H \),
\[ X_L = 1000 \izikhathi 0.1 = 100 \, \Omega \]
Ukusabela kwe-capacitive \( X_C \) kubalwa ngefomula:
\[ X_C = \frac{1}{\omega C} \]
nge \( C = 100 \, \mu F = 100 \izikhathi 10^{-6} \, F \),
\[
2. I-Impedance Ephelele Yesekethe
Ingqikithi ye-impedance \( Z \) yesekethe ye-RLC yochungechunge yile:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
Faka amanani esikhundleni sawo:
\[ Z = \sqrt{10^2 + (100 – 10)^2} = \sqrt{10^2 + 90^2} = \sqrt{100 + 8100} = \sqrt{8200} = 90.55 \, \Omega \]
3. Umkhawulo Wamanje \( I_{max} \)
Umthamo omkhulu ungabalwa kusetshenziswa umthetho ka-Ohm:
\[ I_{max} = \frac{V_{max}}{Z} \]
nge \( V_{max} = 100 \, V \) kanye \( Z = 90.55 \, \Omega \):
\[ I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. I-Voltage Ephakeme Kuyo Yonke Ingxenye
I-voltage ku-resistor:
\[ V_R = I_{max} \izikhathi R = 1.104 \izikhathi 10 = 11.04 \, V \]
I-voltage ku-inductor:
\[ V_L = I_{max} \izikhathi X_L = 1.104 \izikhathi 100 = 110.4 \, V \]
I-voltage ku-capacitor:
\[ V_C = I_{max} \izikhathi X_C = 1.104 \izikhathi 10 = 11.04 \, V \]
Isibonelo Umbuzo 2: Isekethe ye-RLC Ehambisanayo
Umbuzo:
Uma unikezwe isekethe efanayo equkethe i-resistor enokumelana \( R = 50 \, \Omega \), i-inductor ene-inductance \( L = 0.5 \, H \), kanye ne-capacitor ene-capacitance \( C = 10 \, \mu F \). Umthombo we-voltage uyi-sinusoidal ene-voltage \( V(t) = 200 \cos(2000 t) \, V \). Thola:
1. Ukusabela okukhuthazayo \( X_L \) kanye nokusabela okunamandla \( X_C \).
2. Ukungena okuphelele kwesekethe.
3. Umkhawulo wamanje \( I_{max} \).
Ingxoxo:
1. Ukusabela Okubangela Ukuguquka \( X_L \) kanye Nokusabela Okunamandla \( X_C \)
Ukusabela okukhuthazayo \( X_L \) kubalwa ngefomula:
\[ X_L = \omega L \]
nge \( \omega = 2000 \, rad/s \) kanye \( L = 0.5 \, H \),
\[ X_L = 2000 \izikhathi 0.5 = 1000 \, \Omega \]
Ukusabela kwe-capacitive \( X_C \) kubalwa ngefomula:
\[ X_C = \frac{1}{\omega C} \]
nge \( C = 10 \, \mu F = 10 \izikhathi 10^{-6} \, F \),
\[
2. Ukwamukelwa Okuphelele Kwesekethe
Ukwamukelwa \( Y \) kuyindlela yokubuyiselana ye-impedance. Kwisekethe ye-RLC ehambisanayo:
\[ Y = \sqrt{G^2 + (B_L – B_C)^2} \]
lapho \( G = \frac{1}{R} \),
\[ G = \frac{1}{50} = 0.02 \, S \]
Ukuqonda okukhuthazayo \( B_L \):
\[ B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Ukwehliswa kwamandla \( B_C \):
\[ B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S \]
Faka wonke amanani kufomula:
\[ Y = \sqrt{0.02^2 + (0.001 – 0.02)^2} = \sqrt{0.0004 + 0.000361} = \sqrt{0.000761} = 0.0276 \, S \]
I-total impedance \(Z \) iyi-reciprocal yokwamukelwa:
\[ Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, \Omega \]
3. Umkhawulo Wamanje \( I_{max} \)
\[ I_{max} = \frac{V_{max}}{Z} \]
nge \( V_{max} = 200 \, V \) kanye \( Z = 36.23 \, \Omega \):
\[ I_{max} = \frac{200}{36.23} \cishe 5.52 \, A \]
Isiphetho
Ukuqonda ukuthi ungabala kanjani ukusabela, ukungena, ukuvimba, kanye nogesi kusekethe ye-RLC kubalulekile ekusetshenzisweni kobunjiniyela kagesi. Ngokuzijwayeza njalo ngezibonelo ezahlukahlukene ezifana nalezo esixoxe ngazo, ukuqonda kwakho ukuhlaziywa kwesekethe ye-RLC kuzojula. Ukuzijwayeza okuqhubekayo kuzothuthukisa namakhono akho okuxazulula izinkinga kanye nokuklama kwesikhathi esizayo kwesekethe kagesi eziyinkimbinkimbi.
