Mafunso Osiyanasiyana Okambirana Pakalipano
Pendauluan
Mphamvu yosinthira magetsi (AC) ndi mtundu wa mphamvu yamagetsi yomwe imasintha njira nthawi ndi nthawi. Mosiyana ndi mphamvu yolunjika (DC), yomwe imayenda mbali imodzi, mphamvu yosinthasintha imayenda pa liwiro ndi njira zosiyanasiyana. AC imagwiritsidwa ntchito kwambiri pakugawa mphamvu yamagetsi chifukwa cha ubwino wake pakutumiza magetsi mtunda wautali komanso kuthekera kosintha mphamvu yake mosavuta pogwiritsa ntchito ma transformer. Nkhaniyi ipereka zitsanzo zingapo za mavuto ndi zokambirana zokhudzana ndi mphamvu yosinthira magetsi kuti mumvetse bwino nkhaniyi.
Chitsanzo Funso 1: Kuchuluka ndi Nthawi ya Mphamvu Yosinthana
Funso:
Mphamvu yosinthira imakhala ndi ma frequency a 50 Hz. Werengani nthawi ya mphamvu.
Kukambirana:
Mafupipafupi (f) ndi nthawi (T) ya alternating current ali ndi ubale wotsatira:
\[ T = \frac{1}{f} \]
Ndi ma frequency (f) a 50 Hz:
\[ T = \frac{1}{50} \]
\[ T = 0,02 \malemba{masekondi} \]
Kotero, nthawi ya alternating current ndi masekondi 0,02.
Chitsanzo cha Funso 2: Kupsinjika Kwambiri ndi Kupsinjika Kogwira Mtima
Funso:
Mphamvu yosinthira mphamvu imakhala ndi mphamvu yayikulu (Vmax) ya 311 V. Werengani mphamvu yogwira ntchito (Veff) ya mphamvu iyi.
Kukambirana:
Voltage yogwira ntchito (Veff) ya alternating current ndi sikweya yapakati ya voltage yake yayikulu ndipo imatha kuwerengedwa pogwiritsa ntchito fomula iyi:
\[ V_{\text{eff}} = \frac{V_{\text{max}}}{\sqrt{2}} \]
Ngati Vmax imadziwika kuti ndi 311 V, ndiye kuti:
\[ V_{\text{eff}} = \frac{311 \mawu{V}}{\sqrt{2}} \]
\[ V_{\text{eff}} = \frac{311 \mawu{V}}{1,414} \]
\[ V_{\text{eff}} \pafupifupi 220 \text{ V} \]
Chifukwa chake, mphamvu yogwira ntchito ya alternating current ndi 220 V.
Chitsanzo Funso 3: Mphamvu Zamagetsi mu Dera Losasinthika
Funso:
Mu dera lokhalokha loletsa mphamvu, mphamvu yogwira ntchito (Ieff) imayenda ndi 5 A ndipo mphamvu yogwira ntchito (Veff) ndi 220 V. Werengani mphamvu yamagetsi yomwe imatengedwa ndi dera.
Kukambirana:
Mphamvu yamagetsi (P) yomwe imatengedwa ndi dera losasinthika yokha ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[ P = V_{\text{eff}} \times I_{\text{eff}} \]
Ndi Veff ya 220 V ndi Ieff ya 5 A, ndiye:
\[ P = 220 \malemba{ V} \nthawi 5 \malemba{ A} \]
\[ P = 1100 \malemba{ W} \]
Chifukwa chake, mphamvu yamagetsi yomwe imatengedwa ndi dera ndi 1100 watts.
Chitsanzo Vuto 4: Kusakhazikika mu LR Series Circuit
Funso:
Dera limakhala ndi resistor (R) ya 10 ohms ndi inductor (L) yokhala ndi inductance ya 0,1 H yolumikizidwa motsatizana. Ngati mphamvu yosinthira yokhala ndi pafupipafupi ya 50 Hz ikuyenda mudera, werengani impedance yonse ya dera.
Kukambirana:
Chiwerengero chonse cha impedance (Z) mu LR circuit yotsatizana chikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
Kumene:
\[ X_L = \omega L \]
ndipo \(\omega\) ndi ma frequency a angular omwe amaperekedwa ndi:
\[ \omega = 2\pi f \]
Ndi f ya 50 Hz:
\[ \omega = 2\pi \nthawi 50 \]
\[ \omega = 100\pi \text{ radians/second} \]
Kutuluka kwa mpweya (L) kwa 0,1 H:
\[ X_L = 100\pi \nthawi 0,1 \]
\[ X_L = 10\pi \text{ ohm} \]
Kotero, impedance yonse (Z) ndi:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
\[ Z = \sqrt{10^2 + (10\pi)^2} \]
\[ Z = \sqrt{100 + (100\pi^2)} \]
\[ Z = \sqrt{100 + 986.96} \]
\[ Z \pafupifupi \sqrt{1086.96} \]
\[ Z \pafupifupi 32.97 \malemba{ ohm} \]
Chifukwa chake, kulephera konse kwa dera ndi pafupifupi 32,97 ohms.
Chitsanzo Vuto 5: Power Factor mu Series RLC Circuits
Funso:
Popeza pali dera la RLC lotsatizana lomwe lili ndi ma R = 20 ohms, L = 50 mH, ndi C = 100 μF lolumikizidwa ku gwero la AC voltage lomwe lili ndi pafupipafupi ya 60 Hz. Werengani mphamvu yamagetsi mu dera.
Kukambirana:
Mphamvu yamagetsi mu RLC circuit imatsimikiziridwa ndi
\[ \cos(\phi) = \frac{R}{Z} \]
Gawo loyamba ndikuwerengera impedance yonse (Z) ya dera:
\[ \omega = 2\pi f \]
Kumene
\[ f = 60 \malemba{ Hz} \]
\[ \omega = 2\pi \nthawi 60 \]
\[ \omega = 120\pi \text{ rad/s} \]
Kenako werengani reactance ya inductive (XL) ndi capacitive (XC):
\[ X_L = \omega L \]
\[ X_L = 120\pi \nthawi 0,05 \]
\[ X_L = 6\pi \text{ ohm} \]
\[ X_C = \frac{1}{\omega C} \]
\[ X_C = \frac{1}{120\pi \times 100 \times 10^{-6}} \]
\[ X_C = \frac{1}{0,012\pi} \]
\[ X_C \pafupifupi 26,525 \malemba{ ohm} \]
Kusiyana pakati pa reactance ya inductive ndi capacitive \(X_L – X_C\):
\[ X = X_L – X_C \]
\[ X = 6\pi – 26,525 \]
\[ X \pafupifupi -7,903 \malemba{ ohm} \]
Kenako werengani chiwongolero chonse cha impedance (Z):
\[ Z = \sqrt{R^2 + X^2} \]
\[ Z = \sqrt{20^2 + (-7,903)^2} \]
\[ Z = \sqrt{400 + 62,41} \]
\[ Z \pafupifupi \sqrt{462,41} \]
\[ Z \pafupifupi 21,51 \malemba{ ohm} \]
Kenako mphamvu chinthu (cos(φ)):
\[ \cos(\phi) = \frac{R}{Z} \]
\[ \cos(\phi) = \frac{20}{21,51} \]
\[ \cos(\phi) \pafupifupi 0,93 \]
Kotero, mphamvu yamagetsi mu dera ndi pafupifupi 0,93.
Mapeto
Mphamvu yosinthira magetsi ili ndi makhalidwe enaake omwe amasiyanitsa mphamvu yolunjika ndi mphamvu yolunjika, monga ma frequency, period, ndi effective value. Mu kusanthula kwa AC circuit, timaganizira za resistive, inductive, ndi capacitive components. Kuphatikiza apo, kuwerengera impedance ndi power factor ndikofunikira kwambiri popanga ndi kusanthula magwiridwe antchito a circuit. Pomvetsetsa zitsanzo zomwe zili pamwambapa, titha kumvetsetsa mosavuta mfundo zoyambira za mphamvu yosinthira magetsi ndi momwe imagwiritsidwira ntchito mu uinjiniya wamagetsi.
