Tusaale Dhibaato Ka Hadlaysa Falcelinta Wareegga
Resonance waa dhacdo uu nidaamku ku wareego baaxadda ugu badan ee soo noqnoqoshada gaarka ah. Marka laga hadlayo wareegyada korontada, resonance-ku wuxuu dhacaa marka impedance-ka wareegga uu gaaro qiimaha ugu yar ama ugu badan, taasoo keenta in hadda ama danabka wareegga uu gaaro heer sare. Dhacdadani aad ayey muhiim ugu tahay naqshadeynta iyo falanqaynta wareegyada korontada, gaar ahaan codsiyada sida raadiyaha, shaandheeyayaasha, iyo oscillators.
Mabaadi'da Aasaasiga ah ee Cod-bixinta Wareegyada Korontada
Resonance-ka wareegyada korantada waxaa badanaa laga hadlaa macnaha wareegga RLC, kaas oo ka kooban resistor (R), inductor (L), iyo capacitor (C). Waxaa jira laba nooc oo resonance ah oo si caadi ah looga hadlo:
1. Taxanaha Resonance: Waxay dhacdaa marka inductor iyo capacitor ay si taxane ah ugu xiran yihiin iska caabin. Resonance waxay dhacdaa marka reactance-ka inductive (XL) uu la mid noqdo reactance-ka capacitive (XC).
2. Isbarbardhigga Isbarbardhigga: Waxay dhacdaa marka inductor iyo kapastor ay isku xiran yihiin isbarbardhigga. Isbarbardhigga wuxuu dhacaa marka is-hortaagga wareegga ee soo noqnoqoshada qaarkood uu gaaro qiimahiisa ugu sarreeya.
Soo noqnoqoshada soo noqnoqoshada (\( f_0 \)) ee labada nooc ee wareegyada waa isku mid waxaana bixiya:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Su'aalo Tusaale ah iyo Doodo ku saabsan Resonance of RLC Series Circuits
Su'aal 1aad:
Marka la eego wareegga RLC ee taxanaha ah oo leh iska caabin (R) oo ah 10 ohms, inductor (L) oo ah 10 mH, iyo capacitor (C) oo ah 1 μF. Go'aami:
1. Soo noqnoqoshada dhawaaqa ee wareegga.
2. Isku-xidhka wareegga oo leh soo noqnoqoshada resonant.
3. Hadda socodka wareegga haddii danabku yahay 10 V rms marka loo eego inta jeer ee resonant-ka.
Dood:
1. Soo noqnoqoshada dhawaaqa ee wareegga:
Soo noqnoqoshada soo noqnoqoshada (\( f_0 \)) ee wareegga RLC ee taxanaha ah waxaa bixiya:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Halkee:
– L = 10mH = 10 x 10⁻³ H
– C = 1 μF = 1 x 10⁻⁶ F
Markaa:
\[ f_0 = \frac{1}{2\pi\sqrt{(10 \jeer 10^{-3})(1 \jeer 10^{-6})}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10 \times 10^{-9}}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10^{-8}}} \]
\[ f_0 = \frac{1}{2\pi \times 10^{-4}} \]
\[ f_0 = \frac{10^4}{2\pi} \]
\[ f_0 ≈ 1591.55 \qoraal{ Hz} \]
2. Isku-celinta wareegga ee soo noqnoqoshada resonant:
Marka la eego soo noqnoqoshada resonant-ka, falgalka inductive-ka (XL) wuxuu la mid yahay falgalka capacitive-ka (XC), sidaa darteed:
\[ X_L = X_C \]
\[ 2\pi f_0 L = \frac{1}{2\pi f_0 C} \]
Maadaama falgalka inductive iyo capacitive uu midba midka kale joojiyo, is-hortaagga wareegga waa iska caabinta (R) oo keliya:
\[ Z = R = 10 \qoraal{ ohm} \]
3. Hadda socda wareegga:
Hadda (\( I \)) ee wareegga waxaa lagu xisaabin karaa iyadoo la adeegsanayo sharciga Ohm:
\[ I = \frac{V}{Z} \]
Halkee:
– V = 10 V rms
– Z = 10 ohms (marka la eego soo noqnoqoshada dhawaaqa)
Markaa:
\[ I = \frac{10}{10} \]
\[ I = 1 \qoraal{ A} \]
Markaa, qulqulka hadda ee wareegga waa 1 A.
Su'aalo Tusaale ah iyo Doodo ku saabsan Resonance of Parallel RLC Circuits
Su'aal 2aad:
Iyada oo la siinayo wareeg RLC oo is barbar socda oo leh iska caabin (R) oo ah 10 ohms, inductor (L) oo ah 5 mH, iyo capacitor (C) oo ah 2 μF. Go'aami:
1. Soo noqnoqoshada dhawaaqa ee wareegga.
2. Isku-xidhka wareegga oo leh soo noqnoqoshada resonant.
3. Danabka isha haddii wadarta guud ee qulqulka wareegga uu yahay 2 A marka la eego inta jeer ee resonant-ka.
Dood:
1. Soo noqnoqoshada dhawaaqa ee wareegga:
Soo noqnoqoshada resonant-ka (\( f_0 \)) ee wareegga RLC ee isbarbar socda waxaa sidoo kale bixiya:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Halkee:
– L = 5mH = 5 x 10⁻³ H
– C = 2 μF = 2 x 10⁻⁶ F
Markaa:
\[ f_0 = \frac{1}{2\pi\sqrt{(5 \jeer 10^{-3})(2 \jeer 10^{-6})}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10 \times 10^{-9}}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10^{-8}}} \]
\[ f_0 = \frac{1}{2\pi \times 10^{-4}} \]
\[ f_0 = \frac{10^4}{2\pi} \]
\[ f_0 ≈ 1591.55 \qoraal{ Hz} \]
2. Isku-celinta wareegga ee soo noqnoqoshada resonant:
Marka la eego soo noqnoqoshada soo noqnoqoshada, wadarta gelitaanka (Y) ee inductor-ka iyo capacitor-ka waa eber. Sidaa darteed, is-hortaagga (Z) ee wareegga RLC ee is-barbar socda wuxuu ku xiran yahay oo keliya iska caabbinta (R). Sidaa darteed, soo noqnoqoshada soo noqnoqoshada, is-hortaagga wareegga RLC ee is-barbar socda wuxuu la mid yahay iska caabbinta.
Markaa:
\[ R = 10 \qoraal{ ohm} \]
3. Danabka isha:
Wadarta guud ee hadda (\( I \)) ee ku socota wareegga waa 2 A. Macnaha sharciga Ohm waa in danabka isha (V) lagu bixiyo:
\[ V = I \ jeer Z \]
Halkee:
– I = 2 A
– Z = 10 ohms
Markaa:
\[ V = 2 \ jeer 10 \]
\[ V = 20 \qoraal{ V} \]
Sidaas darteed, danab isha waa 20 V.
Gabagabo
Resonance-ka wareegyada korontada waa dhacdo muhiim ah oo loo isticmaali karo noocyo kala duwan oo ah codsiyada injineernimada korontada iyo elektarooniga ah. Fahmidda sida loo xisaabiyo soo noqnoqoshada resonant-ka iyo saameynteeda ku aaddan hadda iyo danabka waa aasaaska naqshadeynta iyo falanqaynta wareegga. Maqaalkani wuxuu soo bandhigayaa fikradaha aasaasiga ah ee resonance-ka wareegyada RLC wuxuuna ka hadlayaa dhibaatooyinka la xiriira si loo bixiyo dulmar cad oo ku saabsan mowduucan.
