Tusaale Su'aalaha Doodaha Wareegga RLC
Wareegga RLC waa nooc ka mid ah wareegga korantada oo ka kooban iska caabin (R), inductor (L), iyo capacitor (C) oo ku xiran taxane ama is barbar socda. Wareegyada RLC waxaa si weyn loogu isticmaalaa codsiyo elektaroonik ah oo kala duwan, oo ay ku jiraan shaandheeyayaasha hirarka, oscillators, isku-darka calaamadaha, iyo waxyaabo kaloo badan. Fahmidda sida loo falanqeeyo loona xalliyo dhibaatooyinka wareegyadan waa xirfad muhiim u ah ardayda injineernimada korontada iyo xirfadlayaasha goobta.
Maqaalkan, waxaan kaga hadli doonnaa dhowr tusaale oo dhibaatooyin ah iyo xalalkooda la xiriira falanqaynta wareegga RLC. Dhibaatooyinkan waxaa loogu talagalay inay kaa caawiyaan inaad fahamto mabaadi'da aasaasiga ah iyo codsiyada wareegyada RLC.
Tusaale ahaan Dhibaatada 1aad: Wareegga Taxanaha RLC
Su'aal:
Marka la eego wareeg taxane ah oo ka kooban iska caabin leh iska caabin \( R = 10 \, \Omega \), inductor leh inductance \( L = 0.1 \, H \), iyo capacitor leh capacitance \( C = 100 \, \mu F \). Wareeggan waxaa la siiyaa danab sinusoidal \( V(t) = 100 \sin(1000 t) \V). Go'aami:
1. Falcelinta Inductive \( X_L \) iyo falgalka capacitive \( X_C \).
2. Isku-darka guud ee wareegga.
3. Hadda ugu badan \( I_{max} \).
4. Danabka ugu badan ee qayb kasta.
Dood:
1. Falcelinta Inductive \( X_L \) iyo Falcelinta Capacitive \( X_C \)
Falcelinta Inductive \( X_L \) waxaa lagu xisaabiyaa qaacidada:
\[ X_L = \omega L \]
oo leh \( \omega = 1000 \, rad/s \) iyo \( L = 0.1 \, H \),
\[ X_L = 1000 \jeer 0.1 = 100 \, \Omega \]
Falcelinta capacitive \( X_C \) waxaa lagu xisaabiyaa qaacidada:
\[ X_C = \frac{1}{\omega C} \]
oo leh \( C = 100 \, \mu F = 100 \jeer 10^{-6} \, F \),
\[
2. Isku-darka Guud ee Wareegga
Wadarta guud ee is-hortaagga \( Z \) ee wareegga RLC ee taxanaha ah waa:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
Ku beddel qiimayaasha:
\[ Z = \sqrt{10^2 + (100 – 10)^2} = \sqrt{10^2 + 90^2} = \sqrt{100 + 8100} = \sqrt{8200} = 90.55 \, \Omega \]
3. Hadda ugu Badan \( I_{max} \)
Heerka ugu sarreeya ee hadda waxaa lagu xisaabin karaa iyadoo la adeegsanayo sharciga Ohm:
\[ I_{max} = \frac{V_{max}}{Z} \]
oo leh \( V_{max} = 100 \, V \) iyo \( Z = 90.55 \, \Omega \):
\[ I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. Danabka ugu Badan ee Qayb Kasta
Danab ku jira iska caabbinta:
\[ V_R = I_{ugu badnaan} \times R = 1.104 \times 10 = 11.04 \, V \]
Danab ku jira inductor-ka:
\[ V_L = I_{ugu badnaan} \times X_L = 1.104 \times 100 = 110.4 \, V \]
Danab ku jira kaansatoorka:
\[V_C = I_{ugu badnaan} \times X_C = 1.104 \times 10 = 11.04 \, V \]
Su'aal Tusaale 2: Wareegga RLC ee Isbarbar socda
Su'aal:
Marka la eego wareeg barbar socda oo ka kooban iska caabin leh iska caabin \( R = 50 \, \Omega \), inductor leh inductance \( L = 0.5 \, H \), iyo kapasitor leh capacitance \( C = 10 \, \mu F \). Isha danabku waa sinusoidal oo leh danab \( V(t) = 200 \cos(2000 t) \, V \). Go'aami:
1. Falcelinta Inductive \( X_L \) iyo falgalka capacitive \( X_C \).
2. Gelitaanka guud ee wareegga.
3. Hadda ugu badan \( I_{max} \).
Dood:
1. Falcelinta Inductive \( X_L \) iyo Falcelinta Capacitive \( X_C \)
Falcelinta Inductive \( X_L \) waxaa lagu xisaabiyaa qaacidada:
\[ X_L = \omega L \]
oo leh \( \omega = 2000 \, rad/s \) iyo \( L = 0.5 \, H \),
\[ X_L = 2000 \jeer 0.5 = 1000 \, \Omega \]
Falcelinta capacitive \( X_C \) waxaa lagu xisaabiyaa qaacidada:
\[ X_C = \frac{1}{\omega C} \]
oo leh \( C = 10 \, \mu F = 10 \jeer 10^{-6} \, F \),
\[
2. Wadarta Guud ee Wareegga
Admittance \( Y \) waa is-dhaafsiga impedance. Wareeg RLC oo is barbar socda:
\[ Y = \sqrt{G^2 + (B_L – B_C)^2} \]
halkaas oo \( G = \frac{1}{R} \),
\[ G = \frac{1}{50} = 0.02 \, S \]
Suuxdinta soo-jiidashada \( B_L \):
\[ B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Sugidda awoodda \( B_C \):
\[ B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S \]
Ku beddel dhammaan qiimayaasha qaacidada:
\[ Y = \sqrt{0.02^2 + (0.001 – 0.02)^2} = \sqrt{0.0004 + 0.000361} = \sqrt{0.000761} = 0.0276 \, S \]
Isku-darka guud ee is-hortaagga \( Z \) waa is-dhaafsiga ogolaanshaha:
\[ Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, \Omega \]
3. Hadda ugu Badan \( I_{max} \)
\[ I_{max} = \frac{V_{max}}{Z} \]
oo leh \( V_{max} = 200 \, V \) iyo \( Z = 36.23 \, \Omega \):
\[ I_{max} = \frac{200}{36.23} \qiyaastii 5.52 \, A \]
Gabagabo
Fahmidda sida loo xisaabiyo falcelinta, gelitaanka, impedance, iyo hadda wareegga RLC waa muhiim u ah codsiyada injineernimada korontada. Iyadoo la adeegsanayo ku celcelin joogto ah oo loo marayo tusaalooyin kala duwan sida kuwa aan ka wada hadalnay, fahamkaaga falanqaynta wareegga RLC ayaa sii qoto dheeraan doona. Layliga joogtada ah wuxuu sidoo kale horumarin doonaa xirfadahaaga xallinta dhibaatooyinka iyo naqshadeynta mustaqbalka ee wareegyada korantada ee adag.
