Muenzaniso weMibvunzo yeKukurukurirana yeParizvino
Pendauluan
Kuchinjana kwemagetsi (AC) imhando yemagetsi anochinja divi nguva nenguva. Kusiyana nemagetsi akananga (DC), ayo anoyerera akananga kumwe chete, magetsi anochinjana achienda nekumhanya kwakasiyana uye divi. AC inoshandiswa zvakanyanya mukugoverwa kwemagetsi nekuda kwekubatsira kwayo mukutumirwa kure uye kugona kushandura voltage yayo zviri nyore uchishandisa ma transformer. Chinyorwa chino chichapa mienzaniso yakati wandei yezvinetso nehurukuro dzine chekuita nekuchinjana kwemagetsi kuti unzwisise zvakanyanya nyaya iyi.
Muenzaniso Mubvunzo 1: Kuwanda uye Nguva yeKuchinjana Kwemagetsi
Mubvunzo:
Mwenje unochinjana une frequency ye50 Hz. Verenga nguva yemagetsi.
Kukurukurirana:
Kuwanda (f) uye nguva (T) kwealternating current zvine hukama hunotevera:
\[ T = \frac{1}{f} \]
Nekawandei (f) ye50 Hz:
\[ T = \frac{1}{50} \]
\[ T = 0,02 \mashoko{ masekondi} \]
Saka, nguva yekuchinjana kwemagetsi imasekondi 0,02.
Muenzaniso Mubvunzo 2: Kushushikana Kwakanyanya uye Kushushikana Kunobudirira
Mubvunzo:
Kuchinjana kwemagetsi kune voltage yepamusoro (Vmax) ye311 V. Verenga voltage inoshanda (Veff) yemagetsi aya.
Kukurukurirana:
Voltage inoshanda (Veff) ye alternating current ndiyo avhareji ye voltage yayo yepamusoro uye inogona kuverengerwa uchishandisa fomura:
\[ V_{\text{eff}} = \frac{V_{\text{max}}}{\sqrt{2}} \]
Kana Vmax ichizivikanwa kuti 311 V, saka:
\[ V_{\text{eff}} = \frac{311 \zvinyorwa{V}}{\sqrt{2}} \]
\[ V_{\text{eff}} = \frac{311 \zvinyorwa{V}}{1,414} \]
\[ V_{\text{eff}} \approx 220 \text{ V} \]
Saka, voltage inoshanda ye alternating current ndeye 220 V.
Muenzaniso Mubvunzo 3: Simba reMagetsi muDunhu Rinodzivirira
Mubvunzo:
Mudunhu rinodzivirira chete, simba remagetsi rinoyerera (Ieff) i5 A uye simba remagetsi rinoyerera (Veff) i220 V. Verenga simba remagetsi rinotorwa nedunhu.
Kukurukurirana:
Simba remagetsi (P) rinotorwa nedunhu rinorwisa chete rinogona kuverengerwa uchishandisa fomura:
\[ P = V_{\text{eff}} \times I_{\text{eff}} \]
NeVeff ye220 V uye Ieff ye5 A, ipapo:
\[ P = 220 \chinyorwa{ V} \nguva 5 \chinyorwa{ A} \]
\[ P = 1100 \chinyorwa{ W} \]
Saka, simba remagetsi rinotorwa nedunhu i1100 watts.
Muenzaniso Dambudziko rechina: Kusapindirana muLR Series Circuit
Mubvunzo:
Dunhu rine resistor (R) ye10 ohms uye inductor (L) ine inductance ye0,1 H yakabatana muzvikamu zvakatevedzana. Kana alternating current ine frequency ye50 Hz ikapfuura nepakati pedunhu, verenga huwandu hwese hwe impedance yedunhu.
Kukurukurirana:
Huwandu hwe impedance (Z) mu LR circuit yakatevedzana hunogona kuverengerwa uchishandisa fomura:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
Di mana:
\[ X_L = \omega L \]
uye \(\omega\) ndiyo angular frequency inopiwa na:
\[ \omega = 2\pi f \]
Ne f ye50 Hz:
\[ \omega = 2\pi \kawa 50 \]
\[ \omega = 100\pi \text{ radians/second} \]
Kupinza (L) kwe 0,1 H:
\[ X_L = 100\pi \kawa 0,1 \]
\[ X_L = 10\pi \text{ ohm} \]
Saka, huwandu hwese hwe impedance (Z) ndehwekuti:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
\[ Z = \sqrt{10^2 + (10\pi)^2} \]
\[ Z = \sqrt{100 + (100\pi^2)} \]
\[ Z = \sqrt{100 + 986.96} \]
\[ Z \inenge \sqrt{1086.96} \]
\[ Z \inenge 32.97 \chinyorwa{ ohm} \]
Saka, huwandu hwese hweimpedance yedunhu hunosvika 32,97 ohms.
Muenzaniso Dambudziko 5: Power Factor muSeries RLC Circuits
Mubvunzo:
Zvichipiwa seri kweRLC circuit ine kukosha kweR = 20 ohms, L = 50 mH, uye C = 100 μF yakabatana neAC voltage source ine frequency ye60 Hz. Verenga simba remagetsi mucircuit.
Kukurukurirana:
Simba remudunhu reRLC rinosarudzwa ne
\[ \cos(\phi) = \frac{R}{Z} \]
Danho rekutanga nderekuverenga huwandu hwese hwe impedance (Z) yedunhu:
\[ \omega = 2\pi f \]
Kupi
\[ f = 60 \mashoko{ Hz} \]
\[ \omega = 2\pi \kawa 60 \]
\[ \omega = 120\pi \text{ rad/s} \]
Wobva waverenga inductive (XL) uye capacitive (XC) reactance:
\[ X_L = \omega L \]
\[ X_L = 120\pi \kawa 0,05 \]
\[ X_L = 6\pi \text{ ohm} \]
\[ X_C = \frac{1}{\omega C} \]
\[ X_C = \frac{1}{120\pi \times 100 \times 10^{-6}} \]
\[ X_C = \frac{1}{0,012\pi} \]
\[ X_C \inenge 26,525 \chinyorwa{ ohm} \]
Musiyano uripo pakati pe inductive ne capacitive reactance \(X_L – X_C\):
\[ X = X_L – X_C \]
\[ X = 6\pi – 26,525 \]
\[ X \inenge -7,903 \chinyorwa{ ohm} \]
Wobva waverenga huwandu hwese hwe impedance (Z):
\[ Z = \sqrt{R^2 + X^2} \]
\[ Z = \sqrt{20^2 + (-7,903)^2} \]
\[ Z = \sqrt{400 + 62,41} \]
\[ Z \inenge \sqrt{462,41} \]
\[ Z \inenge 21,51 \chinyorwa{ ohm} \]
Zvadaro chinhu chesimba (cos(φ)):
\[ \cos(\phi) = \frac{R}{Z} \]
\[ \cos(\phi) = \frac{20}{21,51} \]
\[ \cos(\phi) \inenge 0,93 \]
Saka, simba riri mudunhu iri rinenge 0,93.
Mhedziso
Kuchinjana kwemagetsi (alternating current) kune hunhu hwakasiyana hunoisiyanisa ne direct current, senge frequency, period, uye effective value. Mukuongorora kweAC circuit, tinofunga nezve resistive, inductive, uye capacitive components. Uyezve, kuverenga impedance uye power factor kwakakosha pakugadzira nekuongorora mashandiro ecircuit. Nekunzwisisa mienzaniso iri pamusoro, tinogona kunzwisisa zviri nyore pfungwa dzekutanga dzekuchinjana kwemagetsi uye mashandisirwo ayo mu electrical engineering.
