Mohlala oa Lipotso tsa Puisano ea Potoloho ea RLC
Potoloho ea RLC ke mofuta oa potoloho ea motlakase e nang le resistor (R), inductor (L), le capacitor (C) tse hokahantsoeng ka letoto kapa ka tsela e tšoanang. Lipotoloho tsa RLC li sebelisoa haholo lits'ebetsong tse fapaneng tsa elektroniki, ho kenyeletsoa le li-filter tsa maqhubu, li-oscillator, metsoako ea matšoao, le tse ling. Ho utloisisa mokhoa oa ho sekaseka le ho rarolla mathata lipotolohong tsena ke tsebo ea bohlokoa bakeng sa baithuti ba boenjiniere ba motlakase le litsebi lefapheng lena.
Sehloohong sena, re tla buisana ka mehlala e 'maloa ea mathata le litharollo tsa ona tse amanang le tlhahlobo ea potoloho ea RLC. Mathata ana a etselitsoe ho u thusa ho utloisisa melao-motheo ea motheo le ts'ebeliso ea lipotoloho tsa RLC.
Mohlala Bothata ba 1: Potoloho ea Letoto la RLC
Potso:
Ho fanoe ka potoloho ea letoto e nang le resistor e nang le khanyetso \( R = 10 \, \Omega \), inductor e nang le inductance \( L = 0.1 \, H \), le capacitor e nang le capacitance \( C = 100 \, \mu F \). Potoloho ena e fuoa voltage ea sinusoidal \( V(t) = 100 \sin(1000 t) \V). Fumana:
1. Karabelo e inductive \( X_L \) le karabelo e capacitive \( X_C \).
2. Phetoho e felletseng ea potoloho.
3. Nako e phahameng ka ho fetisisa \( I_{max} \).
4. Motlakase o moholo ka ho fetisisa karolong ka 'ngoe.
Puisano:
1. Reactance e Inductive \( X_L \) le Reactance e Kgolo \( X_C \)
Reactance e susumetsang \( X_L \) e balwa ka foromo:
\[ X_L = \omega L \]
ka \( \omega = 1000 \, rad/s \) le \( L = 0.1 \, H \),
\[ X_L = 1000 \makgetlo 0.1 = 100 \, \Omega \]
Karabelo ea capacitive \( X_C \) e baloa ka foromo:
\[ X_C = \frac{1}{\omega C} \]
ka \( C = 100 \, \mu F = 100 \makgetlo a 10^{-6} \, F \),
\[
2. Kakaretso ea Impedance ea Potoloho
Kakaretso ea impedance \( Z \) bakeng sa potoloho ea RLC ea letoto ke:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
Kenya boleng sebakeng sa bona:
\[ Z = \sqrt{10^2 + (100 – 10)^2} = \sqrt{10^2 + 90^2} = \sqrt{100 + 8100} = \sqrt{8200} = 90.55 \, \Omega \]
3. Nako e Phahameng ea Hona Joale \( I_{max} \)
Palo e phahameng ka ho fetisisa ea hona joale e ka baloa ho sebelisoa molao oa Ohm:
\[ I_{max} = \frac{V_{max}}{Z} \]
ka \( V_{max} = 100 \, V \) le \( Z = 90.55 \, \Omega \):
\[ I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. Motlakase o Phahameng Karolong ka 'Ngoe
Motlakase ho resistor:
\[ V_R = I_{max} \makhetlo R = 1.104 \makhetlo 10 = 11.04 \, V \]
Motlakase ho inductor:
\[ V_L = I_{max} \makhetlo X_L = 1.104 \makhetlo 100 = 110.4 \, V \]
Motlakase ho capacitor:
\[ V_C = I_{max} \makhetlo X_C = 1.104 \makhetlo 10 = 11.04 \, V \]
Mohlala oa Potso ea 2: Potoloho ea RLC e Tšoanang
Potso:
Ha ho fanoe ka potoloho e bapileng e nang le resistor e nang le khanyetso \( R = 50 \, \Omega \), inductor e nang le inductance \( L = 0.5 \, H \), le capacitor e nang le capacitance \( C = 10 \, \mu F \). Mohloli oa motlakase ke sinusoidal e nang le voltage \( V(t) = 200 \cos(2000 t) \, V \). Fumana:
1. Karabelo e inductive \( X_L \) le karabelo e capacitive \( X_C \).
2. Kakaretso ea ho kena ha potoloho.
3. Nako e phahameng ka ho fetisisa \( I_{max} \).
Puisano:
1. Reactance e Inductive \( X_L \) le Reactance e Kgolo \( X_C \)
Reactance e susumetsang \( X_L \) e balwa ka foromo:
\[ X_L = \omega L \]
ka \( \omega = 2000 \, rad/s \) le \( L = 0.5 \, H \),
\[ X_L = 2000 \makgetlo 0.5 = 1000 \, \Omega \]
Karabelo ea capacitive \( X_C \) e baloa ka foromo:
\[ X_C = \frac{1}{\omega C} \]
ka \( C = 10 \, \mu F = 10 \makgetlo a 10^{-6} \, F \),
\[
2. Kakaretso ea ho Kena ha Potoloho
Ho amoheloa \( Y \) ke phetolo ya impedance. Bakeng sa potoloho ya RLC e bapileng:
\[ Y = \sqrt{G^2 + (B_L – B_C)^2} \]
moo \( G = \frac{1}{R} \),
\[ G = \frac{1}{50} = 0.02 \, S \]
Ho susumetsoa ke ho susumetsa \( B_L \):
\[ B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Ho tshwarwa ke bokgoni \( B_C \):
\[ B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S \]
Kenya boleng bohle ka mokhoa ona:
\[ Y = \ sqrt{0.02^2 + (0.001 – 0.02)^2} = \ sqrt{0.0004 + 0.000361} = \ sqrt{0.000761} = 0.0276 \, S \]
Phetoho e felletseng \(Z \) ke phetolo ea kamohelo:
\[ Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, \Omega \]
3. Nako e Phahameng ea Hona Joale \( I_{max} \)
\[ I_{max} = \frac{V_{max}}{Z} \]
ka \( V_{max} = 200 \, V \) le \( Z = 36.23 \, \Omega \):
\[ I_{max} = \frac{200}{36.23} \hoo e ka bang 5.52 \, A \]
Qetello
Ho utloisisa mokhoa oa ho bala karabelo, kamohelo, impedance, le hona joale potolohong ea RLC ho bohlokoa bakeng sa lits'ebetso tsa boenjiniere ba motlakase. Ka mokhoa o tsitsitseng ka mehlala e fapaneng e kang eo re buileng ka eona, kutloisiso ea hau ea tlhahlobo ea potoloho ea RLC e tla teba. Mokhoa o tsoelang pele oa ho ikoetlisa o tla boela o ntlafatse tsebo ea hau ea ho rarolla mathata le moralo oa nakong e tlang oa lipotoloho tse rarahaneng tsa motlakase.
