Tambayoyi Misali Game da Inductance da Transformers
Inductance da transformers muhimman ra'ayoyi ne guda biyu a fannin wutar lantarki, musamman a yanayin da'irar AC (mai canza wutar lantarki). Fahimtar yadda suke aiki zai taimaka a aikace-aikace daban-daban, tun daga ƙirar da'irar lantarki zuwa aikace-aikace a cikin na'urorin gida da na masana'antu. A cikin wannan labarin, za mu tattauna misalai na matsaloli da mafita da suka shafi inductance da transformers.
Gabatarwa ga Inductance
Inductance ikon wani ɓangaren lantarki ne, kamar na'ura, don samar da EMF (ƙarfin lantarki) da aka haifar lokacin da canjin wutar lantarki ke ratsawa ta cikinsa. Ana kiran wani ɓangaren da ke da inductance inductor. Naúrar inductance ita ce Henry (H).
Tsarin da ke da alaƙa da inductance shine:
\[V_L = L \frac{dI}{dt} \]
Ina:
– \(V_L \) shine ƙarfin lantarki da aka haifar (volts)
– \( L \) shine inductance (Henry)
– \( \frac{dI}{dt} \) shine saurin canjin wutar lantarki dangane da lokaci (amperes a kowace daƙiƙa)
Misali Tambaya ta 1: Lissafin Wutar Lantarki Mai Inganci
Tambaya:
Ana samar da inductor mai inductance na 5 H tare da wutar lantarki wanda ke canzawa daga 3 A zuwa 6 A cikin daƙiƙa 2. A ƙididdige ƙarfin lantarki da aka haifar!
Mafita:
Da farko dai, muna buƙatar tantance saurin canjin wutar lantarki (\(\frac{dI}{dt}\)):
\[I_1 = 3 \, \text{A}, \, I_2 = 6 \, \text{A}, \, \Delta t = 2 \, \text{seconds} \]
\[ \frac{dI}{dt} = \frac{I_2 – I_1}{\Delta t} = \frac{6 – 3}{2} = 1.5 \, \text{A/sec} \]
Yanzu mun maye gurbin dabi'un da aka sani a cikin tsarin ƙarfin lantarki da aka haifar:
\[V_L = L \frac{dI}{dt} = 5 \sau 1.5 = 7.5 \, \text{V} \]
Saboda haka, ƙarfin lantarki da aka haifar shine 7.5 V.
Gabatarwa ga Masu Canza Wutar Lantarki
Na'urar canza wutar lantarki (transformer) na'urar lantarki ce da ake amfani da ita don canza matakan ƙarfin AC daga mataki ɗaya zuwa wani ta amfani da ƙa'idar shigar da wutar lantarki ta hanyar lantarki (electromagnetic induction). Na'urar canza wutar lantarki ta ƙunshi na'urori biyu, na'urar farko da na'urar sakandare, waɗanda aka kewaye a tsakiyar ƙarfe.
Tsarin da ya dace da na'urar transformer shine:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Ina:
– \(V_p \) shine ƙarfin lantarki akan babban na'urar
– \(V_s \) shine ƙarfin lantarki akan na'urar ta biyu
– \( N_p \) shine adadin juyawa a cikin babban na'urar
– \( N_s \) shine adadin juyawa a cikin na'urar ta biyu
Misali Tambaya ta 2: Lissafin Wutar Lantarki ta Biyu
Tambaya:
Na'urar transformer tana da juyawa 500 a cikin na'urar farko da juyawa 100 a cikin na'urar ta biyu. Idan ƙarfin wutar lantarki na shigarwa zuwa na'urar farko shine 230 V, menene ƙarfin fitarwa zuwa na'urar ta biyu?
Mafita:
Yi amfani da dabarar transformer mai kyau:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Sigogi da aka sani sune:
- \( V_p = 230 \, \ rubutu {V} \)
– \( N_p = 500 \)
– \( N_s = 100 \)
Muna buƙatar nemo \( V_s \):
\[ \frac{230}{V_s} = \frac{500}{100} \]
Sauƙaƙa ɓangaren da ke hannun dama:
\[ \frac{230}{V_s} = 5 \]
Yanzu, warware don \(V_s \):
\[ V_s = \ frac{230}{5} = 46 \, \rubutu {V} \]
Saboda haka, ƙarfin fitarwa akan na'urar ta biyu shine 46 V.
Misali na 3: Lissafin Adadin Juyawa na Biyu
Tambaya:
Ana amfani da na'urar canza wutar lantarki mai sauka ƙasa don rage ƙarfin lantarki daga 240 V zuwa 24 V. Idan adadin juyawa a cikin na'urar farko shine juyawa 800, juyawa nawa ne a cikin na'urar ta biyu?
Mafita:
Yi amfani da dabarar transformer mai kyau:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Sigogi da aka sani sune:
- \( V_p = 240 \, \ rubutu {V} \)
– \( V_s = 24 \, \rubutu{V} \)
– \( N_p = 800 \)
Muna buƙatar nemo \( N_s \):
\[ \frac{240}{24} = \frac{800}{N_s} \]
Sauƙaƙa ɓangaren da ke hagu:
\[ 10 = \frac{800}{N_s} \]
Warware don \( N_s \):
\[ N_s = \ frac{800}{10} = 80 \]
Don haka, adadin juyawa a cikin na'urar ta biyu shine juyawa 80.
Misali Tambaya ta 4: Lissafin Ƙarfi a cikin Na'urar Canzawa Mai Kyau
Tambaya:
Na'urar canza wutar lantarki mai kyau tana da ƙarfin shigarwa na V 120 a kan na'urar farko mai ƙarfin lantarki na 2 A da kuma ƙarfin fitarwa na V 12 a kan na'urar ta biyu. Lissafa wutar da ke gudana a cikin na'urar ta biyu da kuma ƙarfin da aka samar a cikin na'urar ta biyu.
Mafita:
Da farko, muna ƙididdige ƙarfin da ke cikin babban coil (\(P_p\)):
\[ P_p = V_p \times I_p = 120 \, \text{V} \times 2 \, \text{A} = 240 \, \text{W} \]
A cikin na'urar transformer mai kyau, ƙarfin farko yana daidai da ƙarfin sakandare:
\[ P_s = P_p = 240 \, \rubutu{W} \]
Yanzu, muna ƙididdige wutar lantarki a cikin na'urar ta biyu (\(I_s\)) ta amfani da wutar lantarki:
\[ P_s = V_s \times I_s \]
\[ 240 = sau 12 I_s \]
Warware don \(I_s\):
\[ I_s = \frac{240}{12} = 20 \, \text{A} \]
Don haka, wutar lantarki da ke gudana a cikin na'urar ta biyu ita ce 20 A, kuma ƙarfin da aka samar a cikin na'urar ta biyu shine 240 W.
Darussa
Bayan fahimtar wasu misalan magance matsalolin da ke sama, ga wasu matsalolin aiki da za a iya yi don zurfafa fahimtar ku game da inductance da transformers.
1. Ana samar da inductor mai induction na 10 H tare da wutar lantarki wanda ke canzawa daga 4 A zuwa 10 A cikin daƙiƙa 3. A ƙididdige ƙarfin lantarki da aka haifar!
2. Na'urar transformer mai hawa sama tana da juyawa 200 a cikin na'urar farko da juyawa 1000 a cikin na'urar ta biyu. Idan ƙarfin wutar lantarki na shigarwa shine 120 V, menene ƙarfin fitarwa a na'urar ta biyu?
3. Adadin juyawa a cikin babban na'urar transformer shine juyawa 400, kuma adadin juyawa a cikin na'urar ta biyu shine juyawa 100. Idan ƙarfin lantarki a cikin na'urar ta biyu shine 15 V, menene ƙarfin lantarki a cikin na'urar ta farko?
4. Na'urar canza wutar lantarki mai kyau tana da ƙarfin shigarwa na 240 V akan na'urar farko mai ƙarfin lantarki na 3 A da kuma ƙarfin fitarwa na 60 V akan na'urar ta biyu. Lissafa wutar da ke gudana a cikin na'urar ta biyu da kuma ƙarfin da aka samar a cikin na'urar ta biyu.
Ta hanyar kammala waɗannan darussa, za ku sami ƙarin fahimtar yadda inductance da transformers ke aiki da kuma aikace-aikacensu a cikin yanayi daban-daban na aiki. Wannan ilimin yana da matuƙar muhimmanci ba kawai a fannin ilimi ba har ma a fannoni daban-daban na fasaha na rayuwar yau da kullun da kuma aikin ƙwararru a fannin injiniyan lantarki.
