Imibuzo Ehlukahlukene Yengxoxo Yamanje
I-Pendahuluan
I-Alternating current (AC) uhlobo lwamandla kagesi olushintsha indlela ngezikhathi ezithile. Ngokungafani namandla aqondile (DC), ageleza ohlangothini olulodwa, ukugeleza kwamandla kagesi okushintshashintshayo ngesivinini neziqondiso ezihlukene. I-AC isetshenziswa kabanzi ekusatshalalisweni kwamandla kagesi ngenxa yezinzuzo zayo ekudluliseni ibanga elide kanye nekhono lokushintsha kalula i-voltage yayo kusetshenziswa ama-transformer. Lesi sihloko sizokunikeza izibonelo eziningana zezinkinga kanye nezingxoxo ezihlobene namandla kagesi okushintshanisa ukuze ujulise ukuqonda kwakho ngalesi sihloko.
Isibonelo Umbuzo 1: Ukuvama kanye Nesikhathi Sokushintshana Kwamanje
Umbuzo:
I-current eshintshanayo inemvamisa engu-50 Hz. Bala isikhathi se-current.
Ingxoxo:
Imvamisa (f) kanye nenkathi (T) yamanje alternating anobuhlobo obulandelayo:
\[ T = \frac{1}{f} \]
Ngokuphindaphinda (f) okungu-50 Hz:
\[ T = \frac{1}{50} \]
\[ T = 0,02 \umbhalo{ imizuzwana} \]
Ngakho-ke, isikhathi samandla ashintshanayo singamasekhondi angu-0,02.
Isibonelo Umbuzo 2: Ukucindezeleka Okukhulu Nokucindezeleka Okuphumelelayo
Umbuzo:
I-alternating current ine-voltage ephezulu (i-Vmax) engu-311 V. Bala i-voltage esebenzayo (i-Veff) yale current.
Ingxoxo:
I-voltage esebenzayo (i-Veff) yamandla ashintshanayo iyisikwele esimaphakathi se-voltage yayo ephezulu futhi ingabalwa kusetshenziswa ifomula:
\[ V_{\text{eff}} = \frac{V_{\text{max}}}{\sqrt{2}} \]
Uma i-Vmax yaziwa ukuthi ingu-311 V, khona-ke:
\[ V_{\text{eff}} = \frac{311 \umbhalo{ V}}{\sqrt{2}} \]
\[ V_{\text{eff}} = \frac{311 \umbhalo{ V}}{1,414} \]
\[ V_{\text{eff}} \cishe 220 \text{ V} \]
Ngakho-ke, i-voltage esebenzayo yamanje alternating ingu-220 V.
Isibonelo Umbuzo 3: Amandla Kagesi Esisekelweni Esiphikisayo
Umbuzo:
Kumjikelezo ophikisanayo kuphela, ukugeleza kwamandla kagesi (i-Ieff) okusebenzayo kungu-5 A kanti i-voltage ephumelelayo (i-Veff) ingu-220 V. Bala amandla kagesi amuncwa yisekethe.
Ingxoxo:
Amandla kagesi (P) amuncwa yisekethe yokumelana kuphela angabalwa kusetshenziswa ifomula:
\[ P = V_{\text{eff}} \times I_{\text{eff}} \]
Nge-Veff ka-220 V kanye ne-Ieff ka-5 A, bese kuba:
\[ P = 220 \umbhalo{ V} \izikhathi 5 \umbhalo{ A} \]
\[ P = 1100 \umbhalo{ W} \]
Ngakho-ke, amandla kagesi amuncwa yisekethe angama-watts ayi-1100.
Isibonelo Inkinga 4: Ukungavimbeli Esigabeni Sochungechunge lwe-LR
Umbuzo:
Isekethe iqukethe i-resistor (R) engama-ohms ayi-10 kanye ne-inductor (L) ene-inductance engu-0,1 H exhunywe ochungechungeni. Uma ugesi oshintshanayo onemvamisa engu-50 Hz ugeleza kusekethe, bala inani eliphelele le-impedance yesekethe.
Ingxoxo:
Ingqikithi ye-impedance (Z) ku-sekhethi ye-LR yochungechunge ingabalwa kusetshenziswa ifomula:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
Di mana:
\[ X_L = \omega L \]
kanye ne-\(\omega\) imvamisa ye-angular enikezwe yi:
\[ \omega = 2\pi f \]
Nge-f ye-50 Hz:
\[ \omega = 2\pi \izikhathi ezingu-50 \]
\[ \omega = 100\pi \umbhalo{ ama-radians/isekhondi} \]
Ukukhishwa (L) kwe-0,1 H:
\[ X_L = 100\pi \izikhathi 0,1 \]
\[ X_L = 10\pi \umbhalo{ ohm} \]
Ngakho-ke, i-total impedance (Z) ithi:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
\[ Z = \sqrt{10^2 + (10\pi)^2} \]
\[ Z = \sqrt{100 + (100\pi^2)} \]
\[ Z = \sqrt{100 + 986.96} \]
\[ Z \cishe \sqrt{1086.96} \]
\[ Z \cishe 32.97 \umbhalo{ ohm} \]
Ngakho-ke, i-impedance iyonke yesekethe icishe ibe ngu-32,97 ohms.
Isibonelo Inkinga 5: I-Power Factor ku-Series RLC Circuits
Umbuzo:
Uma unikezwe isekethe ye-RLC ewuchungechunge enamanani angu-R = 20 ohms, L = 50 mH, kanye no-C = 100 μF exhunywe emthonjeni we-AC voltage onemvamisa engu-60 Hz. Bala isici samandla kusekethe.
Ingxoxo:
Isici samandla kusekethe ye-RLC sinqunywa yi
\[ \cos(\phi) = \frac{R}{Z} \]
Isinyathelo sokuqala ukubala ingqikithi ye-impedance (Z) yesekethe:
\[ \omega = 2\pi f \]
Di mana
\[ f = 60 \umbhalo{ Hz} \]
\[ \omega = 2\pi \izikhathi ezingu-60 \]
\[ \omega = 120\pi \umbhalo{ rad/s} \]
Bese ubala i-inductive (XL) kanye ne-capacitive (XC) reactance:
\[ X_L = \omega L \]
\[ X_L = 120\pi \izikhathi 0,05 \]
\[ X_L = 6\pi \umbhalo{ ohm} \]
\[ X_C = \frac{1}{\omega C} \]
\[ X_C = \frac{1}{120\pi \times 100 \times 10^{-6}} \]
\[ X_C = \frac{1}{0,012\pi} \]
\[ X_C \cishe 26,525 \umbhalo{ ohm} \]
Umehluko phakathi kwe-inductive kanye ne-capacitive reactance \(X_L – X_C\):
\[ X = X_L – X_C \]
\[ X = 6\pi – 26,525 \]
\[ X \cishe -7,903 \umbhalo{ ohm} \]
Bese ubala i-total impedance (Z):
\[ Z = \sqrt{R^2 + X^2} \]
\[ Z = \sqrt{20^2 + (-7,903)^2} \]
\[ Z = \sqrt{400 + 62,41} \]
\[ Z \cishe \sqrt{462,41} \]
\[ Z \cishe 21,51 \umbhalo{ ohm} \]
Bese kuba yi-power factor (cos(φ)):
\[ \cos(\phi) = \frac{R}{Z} \]
\[ \cos(\phi) = \frac{20}{21,51} \]
\[ \cos(\phi) \cishe 0,93 \]
Ngakho-ke, isici samandla esisekugcineni singaba ngu-0,93.
Isiphetho
I-alternating current inezici ezithile ezihlukanisa i-direct current, njengemvamisa, isikhathi, kanye nenani elisebenzayo. Ekuhlaziyweni kwesekethe ye-AC, sibheka izingxenye ezivimbelayo, ezibangela ukuguquka, kanye nezibangela amandla. Ngaphezu kwalokho, ukubala i-impedance kanye ne-power factor kubalulekile ekwakhiweni nasekuhlaziyeni ukusebenza kwesekethe. Ngokuqonda izibonelo ezingenhla, singaqonda kalula imiqondo eyisisekelo ye-alternating current kanye nokusetshenziswa kwayo kubunjiniyela kagesi.
