Tambayoyin Tattaunawa na Yanzu Masu Sauya
Pendahuluan
Alternating current (AC) wani nau'in wutar lantarki ne wanda ke canza alkibla lokaci-lokaci. Ba kamar direct current (DC) ba, wanda ke gudana a alkibla ɗaya, yana canza kwararar wutar lantarki a cikin gudu da kwatance daban-daban. Ana amfani da AC sosai a cikin rarraba wutar lantarki saboda fa'idodinsa a watsawa ta nesa da kuma ikon canza ƙarfin lantarki cikin sauƙi ta amfani da na'urorin canza wutar lantarki. Wannan labarin zai samar da misalai da dama na matsaloli da tattaunawa da suka shafi alternating current don zurfafa fahimtar ku game da wannan batu.
Misali Tambaya ta 1: Yawan da Lokacin Canjin Wutar Lantarki
Tambaya:
Wutar lantarki mai canzawa tana da mitar 50 Hz. Lissafa lokacin wutar lantarki.
Tattaunawa:
Mita (f) da period (T) na canjin wutar lantarki suna da alaƙa kamar haka:
\[ T = \frac{1}{f} \]
Tare da mita (f) na 50 Hz:
\[ T = \frac{1}{50} \]
\[ T = 0,02 \rubutu{ daƙiƙa} \]
Don haka, lokacin canjin wutar lantarki shine daƙiƙa 0,02.
Misali Tambaya ta 2: Damuwa Mafi Girma da Damuwa Mai Inganci
Tambaya:
Wutar lantarki mai canzawa tana da matsakaicin ƙarfin lantarki (Vmax) na 311 V. Lissafa ƙarfin lantarki mai inganci (Veff) na wannan wutar lantarki.
Tattaunawa:
Ingancin ƙarfin lantarki (Veff) na wutar lantarki mai canzawa shine matsakaicin murabba'in matsakaicin ƙarfinsa kuma ana iya ƙididdige shi ta amfani da dabarar:
\[ V_{\text{eff}} = \frac{V_{\text{max}}}{\sqrt{2}} \]
Idan an san cewa Vmax shine 311 V, to:
\[ V_{\text{eff}} = \ frac{311 \rubutu{V}}{\sqrt{2}} \]
\[ V_{\text{eff}} = \ frac{311 \rubutu{V}}{1,414} \]
\[ V_{\text{eff}} \approx 220 \text{ V} \]
Saboda haka, ƙarfin lantarki mai inganci na canjin wutar lantarki shine 220 V.
Misali Tambaya ta 3: Ƙarfin Wutar Lantarki a cikin Da'irar Juriya
Tambaya:
A cikin da'irar juriya kawai, kwararar wutar lantarki mai inganci (Ieff) ita ce 5 A kuma ƙarfin lantarki mai inganci (Veff) shine 220 V. Lissafa wutar lantarki da da'irar ke sha.
Tattaunawa:
Ana iya ƙididdige wutar lantarki (P) da da'irar juriya ta sha ta amfani da dabarar:
\[ P = V_{\text{eff}} \times I_{\text{eff}} \]
Da Veff na 220 V da Ieff na 5 A, to:
\[ P = 220 \rubutu{ V} \sau 5 \rubutu{ A} \]
\[ P = 1100 \rubutu{ W} \]
Don haka, wutar lantarki da da'irar ke sha shine watts 1100.
Misali Matsala ta 4: Rashin ƙarfi a cikin Da'irar Jerin LR
Tambaya:
Da'ira tana ƙunshe da resistor (R) na ohms 10 da inductor (L) tare da inductance na 0,1 H da aka haɗa a jere. Idan akwai wutar lantarki mai sauyawa mai mita 50 Hz da ke ratsa da'irar, a ƙididdige jimlar impedance na da'irar.
Tattaunawa:
Ana iya ƙididdige jimlar impedance (Z) a cikin da'irar LR ta hanyar amfani da dabarar:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
Ina:
\[ X_L = \omega L \]
kuma \(\omega\) shine mitar kusurwa da aka bayar ta:
\[ \omega = 2\pi f \]
Tare da f na 50 Hz:
\[ \omega = 2\pi \sau 50 \]
\[ \omega = 100\pi \text{ radians/second} \]
Inductance (L) na 0,1 H:
\[ X_L = 100\pi \sau 0,1 \]
\[ X_L = 10\pi \text{ ohm} \]
Don haka, jimlar impedance (Z) shine:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
\[Z = \sqrt{10^2 + (10\pi)^2} \]
\[Z = \sqrt{100 + (100\pi^2)} \]
\[ Z = \sqrt{100 + 986.96} \]
\[ Z \kimanin \sqrt{1086.96} \]
\[ Z \kimanin 32.97 \rubutu{ ohm} \]
Don haka, jimlar impedance na da'irar shine kusan 32,97 ohms.
Misali Matsala ta 5: Ma'aunin Ƙarfi a cikin Da'irori na RLC na Jeri
Tambaya:
An ba da jerin da'irar RLC tare da ƙimar R = 20 ohms, L = 50 mH, da C = 100 μF da aka haɗa zuwa tushen ƙarfin lantarki na AC tare da mita na 60 Hz. Lissafa ƙarfin lantarki a cikin da'irar.
Tattaunawa:
Ana ƙayyade ƙarfin wutar lantarki a cikin da'irar RLC ta hanyar
\[ \cos(\phi) = \frac{R}{Z} \]
Mataki na farko shine a ƙididdige jimlar impedance (Z) na da'irar:
\[ \omega = 2\pi f \]
Da mana
\[ f = 60 \rubutu{ Hz} \]
\[ \omega = 2\pi \sau 60 \]
\[ \omega = 120\pi \text{ rad/s} \]
Sannan a ƙididdige amsawar inductive (XL) da capacitive (XC):
\[ X_L = \omega L \]
\[ X_L = 120\pi \sau 0,05 \]
\[ X_L = 6\pi \text{ ohm} \]
\[ X_C = \frac{1}{\omega C} \]
\[ X_C = \frac{1}{120\pi \sau 100 \sau 10^{-6}} \]
\[ X_C = \ frac{1}{0,012\pi} \]
\[ X_C \kimanin 26,525 \rubutu{ ohm} \]
Bambanci tsakanin amsawar inductive da capacitive \(X_L - X_C\):
\[ X = X_L – X_C \]
\[ X = 6\pi – 26,525 \]
\[ X \approx -7,903 \text{ohm} \]
Sannan a lissafta jimlar impedance (Z):
\[ Z = \sqrt{R^2 + X^2} \]
\[ Z = \sqrt{20^2 + (-7,903)^2} \]
\[ Z = \sqrt{400 + 62,41} \]
\[ Z \kimanin \sqrt{462,41} \]
\[ Z \kimanin 21,51 \rubutu{ ohm} \]
Sai kuma ƙarfin lantarki (cos(φ)):
\[ \cos(\phi) = \frac{R}{Z} \]
\[ \cos(\phi) = \frac{20}{21,51} \]
\[ \cos(\phi) \kimanin 0,93 \]
Don haka, ƙarfin wutar lantarki a cikin da'irar shine kusan 0,93.
Kammalawa
Canjin wutar lantarki yana da takamaiman halaye waɗanda suka bambanta shi da direct current, kamar mita, period, da kuma tasiri mai tasiri. A cikin nazarin da'irar AC, muna la'akari da abubuwan da ke da juriya, inductive, da capacitive. Bugu da ƙari, ƙididdige impedance da power factor yana da mahimmanci don tsara da kuma nazarin aikin da'irar. Ta hanyar fahimtar misalan da ke sama, za mu iya fahimtar mahimman ra'ayoyin canjin wutar lantarki da aikace-aikacensa a cikin injiniyan lantarki cikin sauƙi.
