Chitsanzo cha Mavuto Okambirana za Ma Equation Alternating Current
Pendauluan
Mphamvu yosinthira magetsi (AC) ndi mtundu wa mphamvu yamagetsi yomwe imatha kusintha njira nthawi ndi nthawi. Mosiyana ndi mphamvu yolunjika (DC), yomwe imayenda mbali imodzi, AC ili ndi mawonekedwe a sinusoidal waveform ndipo ndi yofunika kwambiri pa ntchito zosiyanasiyana za tsiku ndi tsiku, kuyambira panyumba mpaka kumafakitale. Kudziwa momwe mungagwiritsire ntchito ma equation alternating current ndikofunikira kuti mumvetsetse mbali zingapo zofunika zamagetsi ndi magetsi. Nkhaniyi ikambirana zitsanzo zingapo za mavuto ndi mayankho kuti timvetse bwino lingaliro la ma equation alternating current.
Chiwerengero Cha Nthawi Yosinthira
Mphamvu yosinthira nthawi zambiri imawonetsedwa ndi equation ya sinusoidal:
\[ i(t) = I_m \sin(\omega t + \phi) \]
Kumene:
– \( i(t) \) ndi mphamvu ya instantaneous monga momwe zimakhalira nthawi.
– \( I_m \) ndi mtengo wapamwamba (wapamwamba) wa mphamvu yamagetsi.
– \( \omega \) ndi liwiro la angular, ndi mayunitsi a ma radians pa sekondi.
– \(t \) ndi nthawi.
– \( \phi \) ndi gawo loyamba la mphamvu yamagetsi.
Chitsanzo Funso 1: Kudziwa Zomwe Zikuchitika Pa Nthawi Yina
Funso:
Popeza pali equation ya alternating current \( i(t) = 10 \sin(100\pi t + \pi/3) \). Dziwani kukula kwa current panthawi \( t = 0.01 \) masekondi.
Kukambirana:
Ndizodziwika kuti:
\[ Ine_m = 10 \, \malemba{A} \]
\[ \omega = 100\pi \, \text{rad/s} \]
\[ \phi = \pi/3 \]
\[t = 0.01 \, \malemba{masekondi} \]
Sinthani mfundo izi mu equation yapano:
\[ i(0.01) = 10 \sin(100\pi \times 0.01 + \pi/3) \]
\[ i(0.01) = 10 \tchimo(\pi + \pi/3) \]
\[ i(0.01) = 10 \tchimo(4\pi/3) \]
Ndinazindikira kuti:
\[ \tchimo(4\pi/3) = -\tchimo(\pi/3) \]
\[ \tchimo(\pi/3) = \sqrt{3}/2 \]
Kotero:
\[ \tchimo(4\pi/3) = -\sqrt{3}/2 \]
\[ i(0.01) = 10 \nthawi -\sqrt{3}/2 \]
\[ i(0.01) = -5\sqrt{3} \]
\[ i(0.01) \pafupifupi -8.66 \, \malemba{A} \]
Kotero, kukula kwa nthawi yamagetsi \(t = 0.01 \) masekondi ndi pafupifupi \(-8.66 \, \text{A} \).
Chitsanzo Funso 2: Kudziwa Kuthamanga kwa Angular ndi Kuchuluka kwa Mafupipafupi
Funso:
Kuti mupeze mphamvu yosinthira yomwe imafotokozedwa ndi equation \( i(t) = 5 \cos(200\pi t – \pi/4) \), dziwani liwiro la angular (ω) ndi pafupipafupi (f) ya mphamvuyo.
Kukambirana:
Zoperekedwa:
\[ i(t) = 5 \cos(200\pi t – \pi/4) \]
Liwiro la angular (\( \omega \)) ndi coefficient ya \( t \) mu mkangano wa cosine, womwe ndi \( 200 \pi \).
\[ \omega = 200\pi \, \text{rad/s} \]
Kuchuluka kwa (f) kungapezeke pogwiritsa ntchito ubale:
\[ \omega = 2\pi f \]
\[ f = \frac{\omega}{2\pi} \]
M'malo mwa velocity ya angular:
\[ f = \frac{200\pi}{2\pi} \]
\[ f = 100 \, \malemba{Hz} \]
Kotero, liwiro la angular la current ndi \( 200\pi \, \text{rad/s} \) ndipo mafupipafupi a current ndi \( 100 \, \text{Hz} \).
Chitsanzo Funso 3: Kudziwa Mtengo wa RMS
Funso:
Pa mphamvu yosinthira yomwe yaperekedwa ndi \( i(t) = 7 \sin(50t) \), dziwani mtengo wa RMS (root mean square).
Kukambirana:
Ndizodziwika kuti:
\[ i(t) = 7 \sin(50t) \]
Mtengo wa RMS wa sinusoidal current ndi:
\[ I_{\text{RMS}} = \frac{I_m}{\sqrt{2}} \]
kumene \( I_m \) ndi mtengo wamakono wapamwamba.
Mtengo wapamwamba wa current \( I_m \) ndi 7 A.
Kotero:
\[ I_{\text{RMS}} = \frac{7}{\sqrt{2}} \]
\[ I_{\text{RMS}} = \frac{7 \sqrt{2}}{2} \]
\[ I_{\text{RMS}} \pafupifupi 4.95 \, \text{A} \]
Kotero, mtengo wa RMS wa mphamvu imeneyo ndi pafupifupi 4.95 A.
Chitsanzo Funso 4: Kuwerengera Mphamvu Yapakati
Funso:
Chitoliro chamagetsi chimakhala ndi resistor ya 10 ohm ndipo chimakhala ndi alternating current \( i(t) = 6 \sin(120\pi t) \). Werengani mphamvu yapakati yomwe resistor imamwa.
Kukambirana:
Popeza mphamvu yamagetsi:
\[ i(t) = 6 \sin(120\pi t) \]
Mtengo wamakono wapamwamba (\( I_m \)) ndi 6 A.
Mtengo wa RMS wa mphamvu yamagetsi ndi:
\[ I_{\text{RMS}} = \frac{I_m}{\sqrt{2}} \]
\[ I_{\text{RMS}} = \frac{6}{\sqrt{2}} \]
\[ I_{\text{RMS}} = 3\sqrt{2} \]
Chotsutsa (\( R \)) = 10 ohms.
Mphamvu yapakati (\(P \)) mu resistor ikhoza kuwerengedwa ndi:
\[ P = I_{\text{RMS}}^2 \times R \]
\[ P = (3\sqrt{2})^2 \nthawi 10 \]
\[ P = 18 \nthawi 10 \]
\[ P = 180 \, \malemba{W} \]
Chifukwa chake, mphamvu yapakati yomwe resistor imadya ndi 180 W.
Kutseka
Munkhaniyi, takambirana zitsanzo zingapo za mavuto ndipo takambirana za ma equation a alternating current. Kudziwa momwe mungawerengere current pa unit time, angular velocity, frequency, RMS value, ndi avereji ya mphamvu ndikofunikira kwambiri kuti timvetsetse alternating current ndi momwe imagwiritsidwira ntchito tsiku ndi tsiku. Kumvetsetsa mfundo izi kumatithandiza kupanga ndi kusanthula ma circuits osiyanasiyana amagetsi omwe amagwiritsa ntchito alternating current.
