Muenzaniso weMibvunzo yeRLC Circuit Discussion
Dunhu reRLC rudzi rwedunhu remagetsi rine resistor (R), inductor (L), uye capacitor (C) zvakabatana zvakatevedzana kana zvakafanana. Dunhu reRLC rinoshandiswa zvakanyanya mumhando dzakasiyana dzemagetsi, kusanganisira mumafirita emafungu, maoscillator, musanganiswa wemasaini, nezvimwewo. Kunzwisisa maitiro ekuongorora nekugadzirisa matambudziko mudunhu iri hunyanzvi hwakakosha kune vadzidzi veinjiniya yemagetsi nenyanzvi mubasa iri.
Muchinyorwa chino, tichakurukura mimwe mienzaniso yezvinetso uye mhinduro dzazvo dzine chekuita nekuongorora kweRLC circuit. Matambudziko aya akagadzirirwa kukubatsira kunzwisisa misimboti yekutanga uye mashandisirwo eRLC circuit.
Muenzaniso Dambudziko 1: RLC Series Circuit
Mubvunzo:
Tichipa seri kwedunhu rine resistor ine resistance \( R = 10 \, \Omega \), inductor ine inductance \( L = 0.1 \, H \), uye capacitor ine capacitance \( C = 100 \, \mu F \). Dunhu iri rinopiwa sinusoidal voltage \( V(t) = 100 \sin(1000 t) \V). Sarudza:
1. Kugadzirisa zvinhu \( X_L \) uye kugadzirisa zvinhu \( X_C \).
2. Kuvharirwa kwese kwedunhu.
3. Kuwanda kwemagetsi \( I_{max} \).
4. Voltage yepamusoro pane chimwe nechimwe chikamu.
Kukurukurirana:
1. Kupindura Kwemukati \( X_L \) uye Kupindura Kwemukati \( X_C \)
Inductive reactance \( X_L \) inoverengwa nefomura:
\[ X_L = \omega L \]
ne \( \omega = 1000 \, rad/s \) uye \( L = 0.1 \, H \),
\[ X_L = 1000 \kawa 0.1 = 100 \, \Omega \]
Kugadziriswa kwe capacitive \( X_C \) kunoverengerwa nefomura:
\[ X_C = \frac{1}{\omega C} \]
ne \( C = 100 \, \mu F = 100 \kawa 10^{-6} \, F \),
\[
2. Kusapindirana Kwese kweDunhu
Huwandu hwese hwe impedance \( Z \) hweseji yeRLC yakatevedzana ndeiyi:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
Tsiva tsika:
\[ Z = \sqrt{10^2 + (100 – 10)^2} = \sqrt{10^2 + 90^2} = \sqrt{100 + 8100} = \sqrt{8200} = 90.55 \, \Omega \]
3. Nguva Yakanyanya Kushandiswa \( I_{max} \)
Iyo yakanyanya simba inogona kuverengerwa uchishandisa mutemo weOhm:
\[ I_{max} = \frac{V_{max}}{Z} \]
ne \( V_{max} = 100 \, V \) uye \( Z = 90.55 \, \Omega \):
\[ I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. Voltage Yakanyanya paChikamu Chega Chega
Voltage pa resistor:
\[ V_R = I_{max} \nguva R = 1.104 \nguva 10 = 11.04 \, V \]
Voltage pa inductor:
\[ V_L = I_{max} \nguva X_L = 1.104 \nguva 100 = 110.4 \, V \]
Voltage pa capacitor:
\[ V_C = I_{max} \nguva X_C = 1.104 \nguva 10 = 11.04 \, V \]
Muenzaniso Mubvunzo 2: Parallel RLC Circuit
Mubvunzo:
Zvichipiwa dunhu rakafanana rine resistor ine resistance \( R = 50 \, \Omega \), inductor ine inductance \( L = 0.5 \, H \), uye capacitor ine capacitance \( C = 10 \, \mu F \). Soko revoltage i sinusoidal ine voltage \( V(t) = 200 \cos(2000 t) \, V \). Sarudza:
1. Kugadzirisa zvinhu \( X_L \) uye kugadzirisa zvinhu \( X_C \).
2. Kupinda kwese kwedunhu.
3. Kuwanda kwemagetsi \( I_{max} \).
Kukurukurirana:
1. Kupindura Kwemukati \( X_L \) uye Kupindura Kwemukati \( X_C \)
Inductive reactance \( X_L \) inoverengwa nefomura:
\[ X_L = \omega L \]
ne \( \omega = 2000 \, rad/s \) uye \( L = 0.5 \, H \),
\[ X_L = 2000 \kawa 0.5 = 1000 \, \Omega \]
Kugadziriswa kwe capacitive \( X_C \) kunoverengerwa nefomura:
\[ X_C = \frac{1}{\omega C} \]
ne \( C = 10 \, \mu F = 10 \kawa 10^{-6} \, F \),
\[
2. Kugamuchirwa Kwese kweDunhu
Kupinda \( Y \) ndiko kudzokororwa kwe impedance. Kune circuit yeRLC yakafanana:
\[ Y = \sqrt{G^2 + (B_L – B_C)^2} \]
apo \( G = \frac{1}{R} \),
\[ G = \frac{1}{50} = 0.02 \, S \]
Kufungidzira kweInductive \( B_L \):
\[ B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Kufungidzira kwesimba \( B_C \):
\[ B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S \]
Isa zvese zvinodiwa mufomura:
\[ Y = \sqrt{0.02^2 + (0.001 – 0.02)^2} = \sqrt{0.0004 + 0.000361} = \sqrt{0.000761} = 0.0276 \, S \]
Kuvharirwa kwese \(Z \) ndiko kudzokororwa kwekubvumidzwa:
\[ Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, \Omega \]
3. Nguva Yakanyanya Kushandiswa \( I_{max} \)
\[ I_{max} = \frac{V_{max}}{Z} \]
ne \( V_{max} = 200 \, V \) uye \( Z = 36.23 \, \Omega \):
\[ I_{max} = \frac{200}{36.23} \inenge 5.52 \, A \]
Mhedziso
Kunzwisisa maitiro ekuverenga reactance, admittance, impedance, uye current muRLC circuit kwakakosha pamashandisirwo muengineering yemagetsi. Nekudzidzira kwakasimba kuburikidza nemienzaniso yakasiyana-siyana yakaita seyatakurukura, kunzwisisa kwako kweRLC circuit analysis kuchawedzera. Kudzidzira nguva dzose kuchavandudzawo hunyanzvi hwako hwekugadzirisa matambudziko uye dhizaini yeramangwana yemagetsi akaomarara.
