Chitsanzo cha Mafunso Okambirana a RLC Circuit
Chigawo cha RLC ndi mtundu wa chizunguliro chamagetsi chomwe chili ndi resistor (R), inductor (L), ndi capacitor (C) yolumikizidwa motsatizana kapena motsatizana. Chizunguliro cha RLC chimagwiritsidwa ntchito kwambiri m'magwiritsidwe osiyanasiyana amagetsi, kuphatikiza mu zosefera zamafunde, ma oscillator, kuphatikiza ma signal, ndi zina zambiri. Kumvetsetsa momwe mungasankhire ndikuthetsa mavuto m'magawo awa ndi luso lofunikira kwa ophunzira aukadaulo wamagetsi ndi akatswiri pantchitoyi.
Munkhaniyi, tikambirana zitsanzo zingapo za mavuto ndi mayankho awo okhudzana ndi kusanthula kwa ma RLC circuit. Mavutowa adapangidwa kuti akuthandizeni kumvetsetsa mfundo zoyambira ndi momwe ma RLC circuit amagwiritsidwira ntchito.
Chitsanzo Vuto 1: RLC Series Circuit
Funso:
Popeza pali dera lotsatizana lomwe lili ndi resistor yokhala ndi resistance \( R = 10 \, \Omega \), inductor yokhala ndi inductance \( L = 0.1 \, H \), ndi capacitor yokhala ndi capacitance \( C = 100 \, \mu F \). Dera ili limapatsidwa sinusoidal voltage \( V(t) = 100 \sin(1000 t) \V). Dziwani:
1. Kuyankha koyambitsa \( X_L \) ndi kuyankha kogwira ntchito \( X_C \).
2. Kulephera konse kwa dera.
3. Mphamvu yayikulu \( I_{max} \).
4. Mphamvu yamagetsi yokwanira pa gawo lililonse.
Kukambirana:
1. Kuyankha Mwachangu \( X_L \) ndi Kuyankha Mwachangu \( X_C \)
Kuyankha koyambitsa \( X_L \) kumawerengedwa ndi fomula iyi:
\[ X_L = \omega L \]
ndi \( \omega = 1000 \, rad/s \) ndi \( L = 0.1 \, H \),
\[ X_L = 1000 \nthawi 0.1 = 100 \, \Omega \]
Capacitive reactance \( X_C \) imawerengedwa ndi fomula iyi:
\[ X_C = \frac{1}{\omega C} \]
ndi \( C = 100 \, \mu F = 100 \nthawi 10^{-6} \, F \),
\[
2. Kulephera Konse kwa Dera
Chiwerengero chonse cha impedance \( Z \) cha circuit ya RLC ndi:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
M'malo mwa mfundo izi:
\[ Z = \sqrt{10^2 + (100 – 10)^2} = \sqrt{10^2 + 90^2} = \sqrt{100 + 8100} = \sqrt{8200} = 90.55 \, \Omega \]
3. Mphamvu Yokwanira \( I_{max} \)
Mphamvu yayikulu kwambiri imatha kuwerengedwa pogwiritsa ntchito lamulo la Ohm:
\[ I_{max} = \frac{V_{max}}{Z} \]
ndi \( V_{max} = 100 \, V \) ndi \( Z = 90.55 \, \Omega \):
\[ I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. Voltage Yokwanira pa Chigawo Chilichonse
Voltage pa resistor:
\[ V_R = I_{max} \nthawi R = 1.104 \nthawi 10 = 11.04 \, V \]
Voltage pa inductor:
\[ V_L = I_{max} \nthawi X_L = 1.104 \nthawi 100 = 110.4 \, V \]
Voltage pa capacitor:
\[ V_C = I_{max} \nthawi X_C = 1.104 \nthawi 10 = 11.04 \, V \]
Chitsanzo Funso 2: Parallel RLC Circuit
Funso:
Popeza pali dera lofanana lomwe lili ndi resistor yokhala ndi resistance \( R = 50 \, \Omega \), inductor yokhala ndi inductance \( L = 0.5 \, H \), ndi capacitor yokhala ndi capacitance \( C = 10 \, \mu F \). Gwero la voltage ndi sinusoidal yokhala ndi voltage \( V(t) = 200 \cos(2000 t) \, V \). Dziwani:
1. Kuyankha koyambitsa \( X_L \) ndi kuyankha kogwira ntchito \( X_C \).
2. Kulowa konse kwa dera.
3. Mphamvu yayikulu \( I_{max} \).
Kukambirana:
1. Kuyankha Mwachangu \( X_L \) ndi Kuyankha Mwachangu \( X_C \)
Kuyankha koyambitsa \( X_L \) kumawerengedwa ndi fomula iyi:
\[ X_L = \omega L \]
ndi \( \omega = 2000 \, rad/s \) ndi \( L = 0.5 \, H \),
\[ X_L = 2000 \nthawi 0.5 = 1000 \, \Omega \]
Capacitive reactance \( X_C \) imawerengedwa ndi fomula iyi:
\[ X_C = \frac{1}{\omega C} \]
ndi \( C = 10 \, \mu F = 10 \nthawi 10^{-6} \, F \),
\[
2. Kuloledwa Konse kwa Dera
Kulowa \( Y \) ndi kubwerezabwereza kwa impedance. Pa dera lofanana la RLC:
\[ Y = \sqrt{G^2 + (B_L – B_C)^2} \]
kumene \( G = \frac{1}{R} \),
\[ G = \frac{1}{50} = 0.02 \, S \]
Kuzindikira koyambitsa \( B_L \):
\[ B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Kusakhazikika kwa capacitive \( B_C \):
\[ B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S \]
Sinthani mfundo zonse mu fomula iyi:
\[ Y = \sqrt{0.02^2 + (0.001 – 0.02)^2} = \sqrt{0.0004 + 0.000361} = \sqrt{0.000761} = 0.0276 \, S \]
Impedance yonse \(Z \) ndi kubwerezabwereza kwa kulowa:
\[ Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, \Omega \]
3. Mphamvu Yokwanira \( I_{max} \)
\[ I_{max} = \frac{V_{max}}{Z} \]
ndi \( V_{max} = 200 \, V \) ndi \( Z = 36.23 \, \Omega \):
\[ I_{max} = \frac{200}{36.23} \pafupifupi 5.52 \, A \]
Mapeto
Kumvetsetsa momwe mungawerengere reactance, admittance, impedance, ndi current mu RLC circuit ndikofunikira kwambiri pakugwiritsa ntchito mu uinjiniya wamagetsi. Ndi machitidwe okhazikika kudzera mu zitsanzo zosiyanasiyana monga zomwe takambiranazi, kumvetsetsa kwanu kwa RLC circuit kuzama. Kuchita mosalekeza kudzakuthandizanso kukonza luso lanu lothetsa mavuto komanso kapangidwe ka mtsogolo ka ma circuit ovuta amagetsi.
