Imibuzo Yezibonelo Exoxa Ngezilinganiso Zamanje Ezishintshanayo
I-Pendahuluan
I-alternating current (AC) uhlobo lwamandla kagesi angashintsha indlela ngezikhathi ezithile. Ngokungafani ne-direct current (DC), egeleza ohlangothini olulodwa, i-AC ine-waveform ye-sinusoidal futhi ibalulekile ekusetshenzisweni okuhlukahlukene kwansuku zonke, kusukela emakhaya kuya ezimbonini. Ukwazi ukuthi ungasebenza kanjani nge-alternating current equations kubalulekile ekuqondeni izici eziningana ezibalulekile ze-electronics kanye nogesi. Lesi sihloko sizoxoxa ngezibonelo eziningana zezinkinga kanye nezixazululo zokucacisa umqondo we-alternating current equations.
Isibalo Esijwayelekile Sokushintshana Kwamanje
Ukushintshana kwamandla kagesi kuvame ukuvezwa yi-equation ye-sinusoidal:
\[ i(t) = I_m \sin(\omega t + \phi) \]
Kuphi:
– \( i(t) \) ugesi osheshayo njengomsebenzi wesikhathi.
– \( I_m \) inani eliphakeme (eliphezulu) lamanje.
– \( \omega \) yijubane le-angular, elinamayunithi ama-radians ngomzuzwana.
– \(t \) yisikhathi.
– \( \phi \) yisigaba sokuqala samanje.
Isibonelo Umbuzo 1: Ukunquma Isikhathi Esikhona Ngesikhathi Esithile
Umbuzo:
Uma ubheka i-alternating current equation \( i(t) = 10 \sin(100\pi t + \pi/3) \). Thola ubukhulu bamanje ngesikhathi \(t = 0.01 \) imizuzwana.
Ingxoxo:
Kuyaziwa:
\[ I_m = 10 \, \umbhalo{A} \]
\[ \omega = 100\pi \, \text{rad/s} \]
\[ \phi = \pi/3 \]
\[t = 0.01 \, \umbhalo{imizuzwana} \]
Faka la manani ku-equation yamanje:
\[ i(0.01) = 10 \sin(100\pi \times 0.01 + \pi/3) \]
\[ i(0.01) = 10 \isono(\pi + \pi/3) \]
\[ i(0.01) = 10 \isono(4\pi/3) \]
Kuphawulwe ukuthi:
\[ \isono(4\pi/3) = -\sono(\pi/3) \]
\[ \isono(\pi/3) = \sqrt{3}/2 \]
Ngakho-ke:
\[ \isono(4\pi/3) = -\sqrt{3}/2 \]
\[ i(0.01) = 10 \izikhathi -\sqrt{3}/2 \]
\[ i(0.01) = -5\sqrt{3} \]
\[ i(0.01) \cishe -8.66 \, \umbhalo{A} \]
Ngakho-ke, ubukhulu bamanje ngesikhathi \( t = 0.01 \) imizuzwana cishe \(-8.66 \, \text{A} \).
Isibonelo Umbuzo 2: Ukunquma Ijubane Eliyindilinga kanye Nokuphindaphinda
Umbuzo:
Ukuze uthole ugesi oshintshanayo ovezwe yi-equation \( i(t) = 5 \cos(200\pi t – \pi/4) \), nquma ijubane le-angular (ω) kanye nemvamisa (f) yamandla kagesi.
Ingxoxo:
Kunikezwe:
\[ i(t) = 5 \cos(200\pi t – \pi/4) \]
Ijubane le-angular (\( \omega \)) liyi-coefficient ka \( t \) empikiswaneni ye-cosine, okungu- \( 200 \pi \).
\[ \omega = 200\pi \, \text{rad/s} \]
Imvamisa (f) ingatholakala ngokusebenzisa ubudlelwano:
\[ \omega = 2\pi f \]
\[ f = \frac{\omega}{2\pi} \]
Faka esikhundleni senani lejubane le-angular:
\[ f = \frac{200\pi}{2\pi} \]
\[ f = 100 \, \umbhalo{Hz} \]
Ngakho-ke, ijubane le-angular lamanje lingu-\( 200\pi \, \text{rad/s} \) kanti imvamisa yamanje ingu-\( 100 \, \text{Hz} \).
Isibonelo Umbuzo 3: Ukunquma Inani le-RMS
Umbuzo:
Ukuze uthole ugesi oshintshanayo onikezwe yi-\( i(t) = 7 \sin(50t) \), nquma inani le-RMS (impande yesikwele esimaphakathi).
Ingxoxo:
Kuyaziwa:
\[ i(t) = 7 \sin(50t) \]
Inani le-RMS lomsinga we-sinusoidal yileli:
\[ I_{\text{RMS}} = \frac{I_m}{\sqrt{2}} \]
lapho \( I_m \) kuyinani lamanje eliphakeme.
Inani eliphakeme kakhulu lamanje \( I_m \) lingu-7 A.
Ngakho-ke:
\[ I_{\text{RMS}} = \frac{7}{\sqrt{2}} \]
\[ I_{\text{RMS}} = \frac{7 \sqrt{2}}{2} \]
\[ I_{\text{RMS}} \cishe 4.95 \, \text{A} \]
Ngakho-ke, inani le-RMS lalowo mshini wamanje licishe libe ngu-4.95 A.
Isibonelo Umbuzo 4: Ukubala Amandla Aphakathi
Umbuzo:
Isekethe kagesi iqukethe i-resistor engu-10 ohm futhi inomsinga oshintshanayo \( i(t) = 6 \sin(120\pi t) \). Bala amandla ajwayelekile asetshenziswa yi-resistor.
Ingxoxo:
Njengoba kunikezwe amandla kagesi:
\[ i(t) = 6 \sin(120\pi t) \]
Inani lamanje eliphakeme kakhulu (\( I_m \)) lingu-6 A.
Inani le-RMS lamanje yileli:
\[ I_{\text{RMS}} = \frac{I_m}{\sqrt{2}} \]
\[ I_{\text{RMS}} = \frac{6}{\sqrt{2}} \]
\[ I_{\text{RMS}} = 3\sqrt{2} \]
Isivikelo (\( R \)) = 10 ohms.
Amandla ajwayelekile (\(P \)) ku-resistor angabalwa ngo:
\[ P = I_{\text{RMS}}^2 \times R \]
\[ P = (3\sqrt{2})^2 \izikhathi eziyi-10 \]
\[ P = 18 \izikhathi ezingu-10 \]
\[ P = 180 \, \umbhalo{W} \]
Ngakho-ke, amandla ajwayelekile asetshenziswa yi-resistor angama-180 W.
I-Penutup
Kulesi sihloko, sixoxe ngezinkinga eziningana zezibonelo futhi saxoxa ngezibalo zamandla ashintshanayo. Ukwazi ukuthi ungabala kanjani amandla kagesi ngeyunithi ngayinye, ijubane le-angular, imvamisa, inani le-RMS, kanye namandla ajwayelekile kubalulekile ekuqondeni amandla ashintshanayo kanye nokusetshenziswa kwawo empilweni yansuku zonke. Ukuqonda le mibono kusisiza ukuklama nokuhlaziya izifunda ezahlukene zikagesi ezisebenzisa amandla ashintshanayo.
