Muenzaniso weDambudziko reKukurukura nezveDunhu reKutenderera
Kurira kwesimba (Resonance) chiitiko umo sisitimu inotenderera nehukuru hwakanyanya pafrequency yakatarwa. Mumamiriro ezvinhu emagetsi, kurira kwesimba kunoitika kana kupindira kwesimba remagetsi kwasvika padanho repasi kana kuti repamusoro, zvichiita kuti magetsi kana voltage iri mudunhu ikwire zvakanyanya. Chiitiko ichi chakakosha zvikuru mukugadzira nekuongorora madunhu emagetsi, kunyanya mukushandiswa kwakadai semaredhiyo, mafirita, uye maoscillator.
Nheyo dzeKubatana muMasekete eMagetsi
Kupindirana kwema "resonance" muma "electrical circuits" kunowanzo kurukurwa mu "RLC circuit", iyo ine resistor (R), inductor (L), uye capacitor (C). Kune mhando mbiri dze "resonance" dzinowanzo kurukurwa:
1. Kubatana kweMutsetse: Kunoitika kana inductor ne capacitor zvakabatana mumutsara ne resistor. Kubatana kunoitika kana inductive reactance (XL) yakaenzana ne capacitive reactance (XC).
2. Parallel Resonance: Inoitika kana inductor ne capacitor zvakabatana zvakafanana. Resonance inoitika kana circuit impedance pane imwe frequency yasvika pahuwandu hwayo hwepamusoro.
Mafambiro e resonant (\( f_0 \)) emhando dzese dzemasekete akafanana uye anopiwa na:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Mibvunzo yemuenzaniso nekukurukurirana kweResonance yeRLC Series Circuits
Mubvunzo 1:
Tichipa seri kweRLC circuit ine resistor (R) ye10 ohms, inductor (L) ye10 mH, uye capacitor (C) ye1 μF. Sarudza:
1. Kuwanda kweresonant yedunhu.
2. Kuvharirwa kwedunhu pahuwandu hwe resonant.
3. Kuyerera kwemagetsi mudunhu kana voltage yemagetsi iri 10 V rms pafrequency ye resonant.
Kukurukurirana:
1. Kuwanda kweresonant yedunhu:
Mafambiro e resonant (\( f_0 \)) mu seti yeRLC yakatevedzana anopiwa ne:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Dimana:
– L = 10 mH = 10 x 10⁻³ H
– C = 1 μF = 1 x 10⁻⁶ F
Saka:
\[ f_0 = \frac{1}{2\pi\sqrt{(10 \kawa 10^{-3})(1 \kawa 10^{-6})}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10 \kawa 10^{-9}}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10^{-8}}} \]
\[ f_0 = \frac{1}{2\pi \times 10^{-4}} \]
\[ f_0 = \frac{10^4}{2\pi} \]
\[ f_0 ≈ 1591.55 \mashoko{ Hz} \]
2. Kupindirana kwedunhu pahuwandu hwe resonant:
Pa frequency ye resonant, inductive reactance (XL) yakaenzana ne capacitive reactance (XC), zvekuti:
\[ X_L = X_C \]
\[ 2\pi f_0 L = \frac{1}{2\pi f_0 C} \]
Sezvo inductive ne capacitive reactance zvichibvisana, circuit impedance ndiyo resistor (R) chete:
\[ Z = R = 10 \chinyorwa{ ohm} \]
3. Kuyerera kwemagetsi mudunhu:
Iyo current (\( I \)) iri mudunhu inogona kuverengerwa uchishandisa mutemo weOhm:
\[ I = \frac{V}{Z} \]
Di mana:
– V = 10 V rms
– Z = 10 ohms (pahuwandu hwe resonant)
Saka:
\[ I = \frac{10}{10} \]
\[ I = 1 \chinyorwa{ A} \]
Saka, magetsi ari kuyerera mudunhu iri i1 A.
Mibvunzo yeMienzaniso neKukurukurirana kweResonance yeParallel RLC Circuits
Mubvunzo 2:
Tichipa circuit yeRLC yakafanana ine resistor (R) ye10 ohms, inductor (L) ye5 mH, uye capacitor (C) ye2 μF. Sarudza:
1. Kuwanda kweresonant yedunhu.
2. Kuvharirwa kwedunhu pahuwandu hwe resonant.
3. Voltage inobva kumagetsi kana huwandu hwemagetsi ari kuyerera mudunhu iri 2 A pafrequency ye resonant.
Kukurukurirana:
1. Kuwanda kweresonant yedunhu:
Mafambiro e resonant (\( f_0 \)) muchikamu cheRLC chakafanana anopiwawo na:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Dimana:
– L = 5 mH = 5 x 10⁻³ H
– C = 2 μF = 2 x 10⁻⁶ F
Saka:
\[ f_0 = \frac{1}{2\pi\sqrt{(5 \kawa 10^{-3})(2 \kawa 10^{-6})}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10 \kawa 10^{-9}}} \]
\[ f_0 = \frac{1}{2\pi\sqrt{10^{-8}}} \]
\[ f_0 = \frac{1}{2\pi \times 10^{-4}} \]
\[ f_0 = \frac{10^4}{2\pi} \]
\[ f_0 ≈ 1591.55 \mashoko{ Hz} \]
2. Kupindirana kwedunhu pahuwandu hwe resonant:
Pa frequency ye resonant, huwandu hwe admittance (Y) ye inductor ne capacitor i zero. Saka, impedance (Z) ye parallel RLC circuit inongoenderana ne resistor (R). Saka, pa frequency ye resonant, impedance ye parallel RLC circuit yakaenzana ne resistor.
Saka:
\[ R = 10 \chinyorwa{ ohm} \]
3. Manyuko emagetsi:
Huwandu hwemagetsi (\( I \)) huri kuyerera mudunhu i2 A. Zvinorehwa nemutemo weOhm ndezvekuti voltage inobva kumagetsi (V) inopiwa ne:
\[ V = I \nguva Z \]
Di mana:
– Ini = 2 A
– Z = 10 ohms
Saka:
\[ V = 2 \kawa 10 \]
\[ V = 20 \chinyorwa{ V} \]
Saka, voltage yemagetsi inokwira kusvika 20 V.
Mhedziso
Kupindirana kwema "resonance" mu "electrical circuits" chinhu chakakosha chinogona kushandiswa mumhando dzakasiyana dzema "electrical" ne "electronic engineering". Kunzwisisa maverengerwo ema "resonance frequency" uye mhedzisiro yayo pa "current" ne "voltage" kwakakosha pakugadzira nekuongorora ma "circuit". Chinyorwa chino chinopa pfungwa huru dze "resonance" mu "RLC circuits" uye chinokurukura matambudziko ane chekuita nazvo kuti chipe ruzivo rwakajeka pamusoro penyaya iyi.
