Su'aalo Tusaale ah oo Ka Hadlaya Inductance iyo Transformers-ka
Inductance iyo transformers waa laba fikradood oo muhiim u ah korontada, gaar ahaan marka la eego wareegyada AC (current-ka beddelan). Fahmidda sida ay u shaqeeyaan waxay ka caawin doontaa codsiyo kala duwan oo wax ku ool ah, laga bilaabo naqshadeynta wareegga elektaroonigga ah ilaa codsiyada qalabka guryaha iyo warshadaha. Maqaalkan, waxaan ka wada hadli doonnaa tusaalooyin dhibaatooyin iyo xalal la xiriira inductance iyo transformers.
Hordhac ku saabsan Inductance
Inductance waa awoodda qayb koronto, sida gariiradda, si ay u soo saarto EMF (xoog elektromotive) oo la soo saaray marka isbeddel ku yimaada hadda uu dhex maro. Qayb leh inductance waxaa loo yaqaan inductor. Cutubka inductance waa Henry (H).
Qaacidada aasaasiga ah ee la xiriirta inductance waa:
\[ V_L = L \frac{dI}{dt} \]
Halkee:
– \(V_L \) waa danabka la kiciyay (volts)
– \( L \) waa soo-jiidashada (Henry)
– \( \frac{dI}{dt} \) waa heerka isbeddelka hadda marka loo eego waqtiga (ampers ilbiriqsikiiba)
Su'aal Tusaale ah 1: Xisaabinta Danabka La Soo Saaray
Su'aal:
Inductor leh inductance 5 H waxaa la siiyaa koronto ka beddesha 3 A ilaa 6 A 2 ilbiriqsi gudahood. Xisaabi danabkii ka dhashay!
Xalka:
Marka hore, waxaan u baahanahay inaan go'aamino heerka isbeddelka hadda (\(\frac{dI}{dt}\)):
\[ I_1 = 3 \, \qoraalka{A}, \, I_2 = 6 \, \qoraalka{A}, \, \Delta t = 2 \, \qoraalka{ilbiriqsiyo} \]
\[ \frac{dI}{dt} = \frac{I_2 – I_1}{\Delta t} = \frac{6 – 3}{2} = 1.5 \, \text{A/sec} \]
Hadda waxaan ku beddelnaa qiimayaasha la yaqaan qaacidada korantada ee la soo saaray:
\[ V_L = L \frac{dI}{dt} = 5 \jeer 1.5 = 7.5 \, \text{V} \]
Sidaas darteed, danab la soo saaray waa 7.5 V.
Hordhac ku saabsan Transformers-ka
Transformer-ku waa qalab koronto oo loo isticmaalo in lagu beddelo heerarka danabka AC heer ilaa heer kale iyadoo la adeegsanayo mabda'a kicinta elektromagnetic-ka. Transformer-ku wuxuu ka kooban yahay laba gariirad, gariirad aasaasi ah iyo gariirad labaad, oo ku wareegsan xudunta birta.
Qaacidada aasaasiga ah ee loogu talagalay transformer-ka ku habboon waa:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Halkee:
– \(V_p \) waa danabka ku yaal gariiradda koowaad
– \( V_s \) waa danabka ku jira gariiradda labaad
– \( N_p \) waa tirada wareegyada ee gariiradda koowaad
– \( N_s \) waa tirada wareegyada ee gariiradda labaad
Su'aal Tusaale 2: Xisaabinta Danabka Labaad
Su'aal:
Transformer-ku wuxuu leeyahay 500 wareeg oo gariiradda koowaad ah iyo 100 wareeg oo gariiradda labaad ah. Haddii danabka gelinta gariiradda koowaad uu yahay 230 V, waa maxay danabka wax soo saarka ee gariiradda labaad?
Xalka:
Isticmaal qaacidada isbeddelka ku habboon:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Xuduudaha la yaqaan waa:
- \ ( V_p = 230 \, \ qoraal {V} \)
– \( N_p = 500 \)
– \( N_s = 100 \)
Waxaan u baahanahay inaan helno \( V_s \):
\[ \frac{230}{V_s} = \frac{500}{100} \]
Fududeynta jajabka dhanka midig:
\[ \frac{230}{V_s} = 5 \]
Hadda, xalli \(V_s \):
\[ V_s = \ frac{230}{5} = 46 \, \ qoraal {V} \]
Markaa, danab soo saar ah oo ku yaal gariiradda labaad waa 46 V.
Tusaale 3: Xisaabinta Tirada Wareegyada Labaad
Su'aal:
Transformer-ka hoos u dhaca ayaa loo isticmaalaa in lagu yareeyo danabka laga bilaabo 240 V ilaa 24 V. Haddii tirada wareegyada gariiradda koowaad ay tahay 800 wareeg, immisa wareeg ayaa ku jira gariiradda labaad?
Xalka:
Isticmaal qaacidada isbeddelka ku habboon:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Xuduudaha la yaqaan waa:
- \ ( V_p = 240 \, \ qoraal {V} \)
– \( V_s = 24 \, \qoraal{V} \)
– \( N_p = 800 \)
Waxaan u baahanahay inaan helno \( N_s \):
\[ \frac{240}{24} = \frac{800}{N_s} \]
Fududeynta jajabka bidixda:
\[ 10 = \frac{800}{N_s} \]
Xal u hel \( N_s \):
\[ N_s = \ frac{800}{10} = 80 \]
Markaa, tirada wareegyada gariiradda labaad waa 80 wareeg.
Su'aal Tusaale 4: Xisaabinta Awoodda ee Transformer-ka Ku Habboon
Su'aal:
Transformer-ka ku habboon wuxuu leeyahay danab gelin ah oo ah 120 V oo ku yaal gariiradda koowaad oo leh hadda 2 A iyo danab soo saar ah oo ah 12 V oo ku yaal gariiradda labaad. Xisaabi hadda socda ee gariiradda labaad iyo awoodda laga soo saaro gariiradda labaad.
Xalka:
Marka hore, waxaan xisaabineynaa awoodda ku jirta gariiradda koowaad (\(P_p\)):
\[ P_p = V_p \times I_p = 120 \, \text{V} \times 2 \, \text{A} = 240 \, \text{W} \]
Transformer-ka ku habboon, awoodda aasaasiga ah waxay la mid tahay awoodda labaad:
\[ P_s = P_p = 240 \, \qoraal{W} \]
Hadda, waxaan xisaabinaynaa hadda ku jirta gariiradda labaad (\(I_s\)) annagoo adeegsanayna awoodda:
\[ P_s = V_s \times I_s \]
\[ 240 = 12 \ jeer I_s \]
Xal u hel \(I_s\):
\[ I_s = \frac{240}{12} = 20 \, \qoraal{A} \]
Markaa, hadda ku socota gariiradda labaad waa 20 A, awoodda laga soo saaro gariiradda labaadna waa 240 W.
Jimicsiyada
Ka dib markii la fahmo tusaalooyin ku saabsan xallinta dhibaatooyinka kor ku xusan, waa kuwan qaar ka mid ah dhibaatooyinka dhaqanka ee la samayn karo si loo xoojiyo fahamkaaga ku saabsan inductance iyo transformers-ka.
1. Inductor leh induction 10 H waxaa la siiyaa koronto ka beddesha 4 A ilaa 10 A 3 ilbiriqsi gudahood. Xisaabi danabka la kiciyay ee ka dhashay!
2. Transformer-ka kor u kaca wuxuu leeyahay 200 oo wareeg oo gariiradda koowaad ah iyo 1000 wareeg oo gariiradda labaad ah. Haddii danabka la gelinayo uu yahay 120 V, waa maxay danabka wax soo saarka ee gariiradda labaad?
3. Tirada wareegyada gariiradda koowaad ee transformer-ka waa 400 wareeg, tirada wareegyada gariiradda labaadna waa 100 wareeg. Haddii danabka gariiradda labaad uu yahay 15 V, waa maxay danabka gariiradda koowaad?
4. Transformer-ka ku habboon wuxuu leeyahay danab gelin ah oo ah 240 V oo ku yaal gariiradda koowaad oo leh hadda 3 A iyo danab soo saar ah oo ah 60 V oo ku yaal gariiradda labaad. Xisaabi hadda socda ee gariiradda labaad iyo awoodda laga soo saaro gariiradda labaad.
Markaad dhammaystirto layliyadan, waxaad si qoto dheer u fahmi doontaa sida ay u shaqeeyaan inductance iyo transformers-ku iyo codsiyadooda xaaladaha kala duwan ee wax ku oolka ah. Aqoontani muhiim ma aha oo kaliya tacliinta laakiin sidoo kale waa mid muhiim u ah dhinacyada kala duwan ee farsamada nolol maalmeedka iyo shaqada xirfadeed ee injineernimada korontada.
