Isibonelo Semibuzo Yengxoxo Yomgqugquzeli
I-inductor iyisakhi esingasebenzi esivame ukusetshenziswa kumasekethe kagesi ukugcina amandla ngesimo sensimu yamagnetic. Nakuba izimiso eziyisisekelo ze-inductor zilula kakhulu, ukuqonda nokubala ukuziphatha kwayo ezindleleni ezahlukahlukene ezisebenzayo kungaba yinselele. Lesi sihloko sihlose ukuxoxa ngezinkinga eziningana zezibonelo kanye nezingxoxo mayelana nama-inductor ukuze kucaciswe umqondo kanye nokusetshenziswa kwawo kubunjiniyela kagesi.
Umqondo Oyisisekelo Wabathuthukisi
I-inductor, ngokuvamile ikhoyili noma ikhoyili yocingo, inamandla okumelana nezinguquko kugesi kagesi odlula kuyo. Lokhu kungenxa yesimiso sikaFaraday sokungeniswa kwe-electromagnetic. Lapho ugesi kagesi ushintsha ku-inductor, insimu yamagnetic ekhiqizwa yilowo mshini nayo iyashintsha, okuholela ekukhiqizeni i-emf ebangelwayo (amandla kagesi) ephikisana noshintsho kugesi.
Ifomula eyisisekelo evame ukusetshenziswa ukuchaza i-inductor kusekethe kagesi yile:
\[ V = L \frac{di}{dt} \]
Kuphi:
– \( V \) yi-voltage edlula i-inductor (ama-volts),
– \( L \) ukujikijelwa kwe-inductor (henry),
– \(\frac{di}{dt} \) ushintsho lwamanje ngokuhamba kwesikhathi (ama-ampere ngomzuzwana).
Manje ake sibone ukuthi ama-inductor asetshenziswa kanjani kwezinye izinkinga zesibonelo.
Isibonelo 1: I-Voltage Kuyo Yonke I-Inductor
Umbuzo:
I-inductor ene-inductance engu-2 H idlula ekushintsheni kwamanje ngesivinini esingu-3 A/s. Iyini i-voltage kuyo yonke i-inductor?
Ingxoxo:
Sebenzisa ifomula eyisisekelo ye-inductor:
\[ V = L \frac{di}{dt} \]
Kuyaziwa:
– \( L = 2 \) H
– \(\frac{di}{dt} = 3 \) A/s
\[ V = 2 \izikhathi 3 \]
\[ V = 6 \]
Ngakho-ke, i-voltage kuyo yonke i-inductor ingu-6 V.
Isibonelo Umbuzo 2: Amandla Agcinwe Ku-Inductor
Umbuzo:
Mangaki amandla agcinwa ku-inductor engu-4 H uma ugesi odlula kuyo ungu-5 A?
Ingxoxo:
Amandla agcinwe ku-inductor angabalwa kusetshenziswa ifomula:
\[ E = \frac{1}{2} LI^2 \]
Kuphi:
– \( E \) amandla (ama-joules),
– \( L \) yi-inductance (henry),
– \( I \) yi-current (ama-ampere).
Kuyaziwa:
– \( L = 4 \) H
– \( I = 5 \) A
\[ E = \frac{1}{2} \izikhathi 4 \izikhathi 5^2 \]
\[ E = 2 \izikhathi ezingu-25 \]
\[ E = 50 \]
Ngakho-ke, amandla agcinwe ku-inductor angama-joules angu-50.
Isibonelo Inkinga 3: Isekethe Yochungechunge lwe-RL
Umbuzo:
Isekethe yochungechunge lwe-RL iqukethe i-resistor engu-10 Ω kanye ne-inductor engu-2 H. Uma kusetshenziswa umthombo we-voltage engu-20 V, uyini ugesi ozinzile ogeleza kusekethe?
Ingxoxo:
Kumjikelezo we-RL ochungechunge, ugesi ozinzile ungabalwa kusetshenziswa umthetho we-Ohm ngoba esimweni esizinzile i-inductor iziphatha njengentambo ejwayelekile yokuqhuba (i-zero impedance).
\[ V = IR \]
Kuyaziwa:
– \( V = 20 \) V
– \( R = 10 \) Ω
\[ I = \frac{V}{R} \]
\[ I = \frac{20}{10} \]
\[ I = 2 \]
Ngakho-ke, ugesi ozinzile ogeleza kusekethe ngu-2 A.
Isibonelo 4: Imvamisa Yokuzwakala Kochungechunge Lwesekethe Ye-RLC
Umbuzo:
Isekethe ye-RLC ewuchungechunge ine-resistor engu-5 Ω, i-inductor engu-150 mH, kanye ne-capacitor engu-100 μF. Iyini imvamisa ye-resonant yesekethe?
Ingxoxo:
Imvamisa ye-resonant \( f_0 \) yesekethe ye-RLC yochungechunge ingabalwa kusetshenziswa ifomula:
\[ f_0 = \frac{1}{2 \pi \sqrt{LC}} \]
Kuphi:
– \( L \) yi-inductance (henry),
– \( C \) yi-capacitance (farads).
Kuyaziwa:
– \( L = 150 \) mH = 0.15 H
– \( C = 100 \) μF = 100 × 10^-6 F
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \times 100 \times 10^{-6}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \times 10^{-4}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \times 10^{-4}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.000015}} \]
\[ f_0 = \frac{1}{2 \pi \times 0.00387} \]
\[ f_0 = \frac{1}{0.0243} \]
\[ f_0 \cishe 41.15 \]
Ngakho-ke, imvamisa yokuzwakala kwesekethe ye-RLC yochungechunge icishe ibe ngu-41.15 Hz.
Isibonelo Umbuzo 5: Izikhathi Ezifushane Kumasekethe e-RL
Umbuzo:
Isekethe ye-RL iqukethe i-resistor engu-8 Ω kanye ne-inductor engu-100 mH. Uma kusetshenziswa i-voltage yesinyathelo engu-24 V, kuthatha isikhathi esingakanani ukuthi ugesi ufinyelele ku-63.2% wenani lawo lokugcina?
Ingxoxo:
Isikhathi esidingekayo ukuze kufinyelelwe ku-63.2% wenani lokugcina kusekethe ye-RL yisikhathi esingaguquki \( \tau \), lapho:
\[ \tau = \frac{L}{R} \]
Kuyaziwa:
– \( L = 100 \) mH = 0.1 H
– \( R = 8 \) Ω
\[ \tau = \frac{0.1}{8} \]
\[ \tau = 0.0125 \, s \]
Ngakho-ke, isikhathi esidingekayo ukuze ugesi ufinyelele ku-63.2% wenani lawo lokugcina yimizuzwana engu-0.0125.
Isiphetho
Ngezibonelo ezingenhla, sixoxe ngezici ezahlukahlukene ezihlobene nama-inductor, okuhlanganisa i-voltage kuyo yonke i-inductor, amandla agciniwe, ukuziphatha kwawo kumasekethe e-RL, kanye nemvamisa yokuzwakala kwamasekethe e-RLC. Ukuqonda kahle le mibono kanye nokubala kubalulekile kunoma ngubani ophishekela umsebenzi wobunjiniyela kagesi noma be-elekthronikhi. Ama-inductor adlala indima ebalulekile ezinhlelweni eziningi, okuhlanganisa izihlungi, amasekethe e-oscillator, kanye nama-power converter. Ngokuqonda ukuthi asebenza kanjani nokuthi singabala kanjani amapharamitha awo, singaklama amasekethe asebenza kahle futhi asebenzayo.
