Ihe atụ nke Ajụjụ Mkparịta ụka RLC Circuit
Sekit RLC bụ ụdị sekit eletriki nke nwere resistor (R), inductor (L), na capacitor (C) ejikọtara na usoro ma ọ bụ parallel. A na-eji sekit RLC eme ihe nke ukwuu n'ọtụtụ ngwa eletrọniki, gụnyere na nzacha ebili mmiri, oscillators, njikọta mgbaàmà, na ndị ọzọ. Ịghọta otu esi enyocha ma dozie nsogbu dị na sekit ndị a bụ nkà dị mkpa maka ụmụ akwụkwọ injinia eletriki na ndị ọkachamara n'ọhịa ahụ.
N'isiokwu a, anyị ga-atụle ọtụtụ nsogbu atụ na azịza ha metụtara nyocha sekit RLC. E mere nsogbu ndị a iji nyere gị aka ịghọta ụkpụrụ na ojiji nke sekit RLC.
Ihe atụ Nsogbu nke 1: Sekit Usoro RLC
Ajụjụ:
E nyere sekit usoro nke nwere resistor nwere nguzogide \( R = 10 \, \Omega \), inductor nwere inductance \( L = 0.1 \, H \), na capacitor nwere capacitance \( C = 100 \, \mu F \). A na-enye sekit a voltaji sinusoidal \( V(t) = 100 \sin(1000 t) \V). Chọpụta:
1. Mmeghachi omume inductive \( X_L \) na mmeghachi omume capacitive \( X_C \).
2. Mbelata zuru oke nke sekit ahụ.
3. Oke ọkụ eletrik \( I_{max} \).
4. Oke voltaji na ihe ọ bụla.
Azịza:
1. Mmeghachi omume Inductive \( X_L \) na Mmeghachi omume Capacitive \( X_C \)
A na-agbakọ mmeghachi omume inductive \( X_L \) site na usoro a:
\[ X_L = \omega L \]
na \( \omega = 1000 \, rad/s \) na \( L = 0.1 \, H \),
\[ X_L = 1000 \ugboro 0.1 = 100 \, \Omega \]
A na-agbakọ mmeghachi omume capacitive \( X_C \) site na usoro a:
\[ X_C = \frac{1}{\omega C} \]
na \( C = 100 \, \mu F = 100 \ugboro 10^{-6} \, F \),
\[
2. Mbelata zuru oke nke sekit ahụ
Mkpokọta impedance \( Z \) maka usoro sekit RLC bụ:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
Dochie ụkpụrụ ndị a:
\[ Z = \sqrt{10^2 + (100 – 10)^2} = \sqrt{10^2 + 90^2} = \sqrt{100 + 8100} = \sqrt{8200} = 90.55 \, \Omega \]
3. Oke Ọsọ \( I_{max} \)
Enwere ike ịgbakọ oke ugbu a site na iji iwu Ohm:
\[ I_{max} = \frac{V_{max}}{Z} \]
na \( V_{max} = 100 \, V \) na \( Z = 90.55 \, \Omega \):
\[ I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. Voltaji kachasị elu na ihe ọ bụla
Voltaji na resistor:
\[V_R = I_{max} \times R = 1.104 \times 10 = 11.04 \, V \]
Voltaji na inductor:
\[V_L = I_{max} \ugboro X_L = 1.104 \ugboro 100 = 110.4 \, V \]
Voltaji na capacitor:
\[V_C = I_{max} \ugboro X_C = 1.104 \ugboro 10 = 11.04 \, V \]
Ajụjụ Ihe Nlereanya nke 2: Sekit RLC Parallel
Ajụjụ:
E nyere sekit yiri nke ahụ nke nwere resistor nwere nguzogide \( R = 50 \, \Omega \), inductor nwere inductance \( L = 0.5 \, H \), na capacitor nwere capacitance \( C = 10 \, \mu F \). Isi iyi voltaji ahụ bụ sinusoidal nwere voltaji \( V(t) = 200 \cos(2000 t) \, V \). Chọpụta:
1. Mmeghachi omume inductive \( X_L \) na mmeghachi omume capacitive \( X_C \).
2. Ọnụọgụ mmadụ niile na-abata na sekit ahụ.
3. Oke ọkụ eletrik \( I_{max} \).
Azịza:
1. Mmeghachi omume Inductive \( X_L \) na Mmeghachi omume Capacitive \( X_C \)
A na-agbakọ mmeghachi omume inductive \( X_L \) site na usoro a:
\[ X_L = \omega L \]
na \( \omega = 2000 \, rad/s \) na \( L = 0.5 \, H \),
\[ X_L = 2000 \ugboro 0.5 = 1000 \, \Omega \]
A na-agbakọ mmeghachi omume capacitive \( X_C \) site na usoro a:
\[ X_C = \frac{1}{\omega C} \]
na \( C = 10 \, \mu F = 10 \ugboro 10^{-6} \, F \),
\[
2. Nnweta zuru oke nke sekit ahụ
Admittance \( Y \) bụ ihe na-eme ka impedance ghara ịdị mma. Maka sekit RLC yiri ya:
\[ Y = \sqrt{G^2 + (B_L – B_C)^2} \]
ebe \(G = \frac{1}{R} \),
\[ G = \frac{1}{50} = 0.02 \, S \]
Mgbochi inductive \( B_L \):
\[ B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Ike mgbochi ike \( B_C \):
\[ B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S \]
Tinye ụkpụrụ niile n'ime usoro ahụ:
\[ Y = \sqrt{0.02^2 + (0.001 – 0.02)^2} = \sqrt{0.0004 + 0.000361} = \sqrt{0.000761} = 0.0276 \, S \]
Mkpuchi zuru oke \(Z \) bụ otu ụzọ isi bata:
\[ Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, \Omega \]
3. Oke Ọsọ \( I_{max} \)
\[ I_{max} = \frac{V_{max}}{Z} \]
na \( V_{max} = 200 \, V \) na \( Z = 36.23 \, \Omega \):
\[ I_{max} = \frac{200}{36.23} \ihe dị ka 5.52 \, A \]
Mmechi
Ịghọta otu esi agbakọ mmeghachi omume, nnabata, impedance, na ugbu a na sekit RLC dị oke mkpa maka ojiji na injinia eletriki. Site na omume na-aga n'ihu site na ihe atụ dị iche iche dịka ndị anyị tụlere, nghọta gị gbasara nyocha sekit RLC ga-eme ka ọ dịkwuo omimi. Omume na-aga n'ihu ga-emekwa ka nkà idozi nsogbu gị na nhazi sekit eletriki dị mgbagwoju anya ka mma n'ọdịnihu.
