Misali na Tambayoyin Tattaunawar Mai Gudanar da Inductor
Inductor wani abu ne da ake amfani da shi a cikin da'irori na lantarki don adana makamashi a cikin nau'in filin maganadisu. Duk da cewa ƙa'idodin asali na inductor suna da sauƙi, fahimtar da ƙididdige halayensa a cikin aikace-aikace daban-daban na iya zama ƙalubale. Wannan labarin yana da nufin tattauna misalai da yawa na matsaloli da tattaunawa game da inductor don fayyace ra'ayi da aikace-aikacensa a cikin injiniyan lantarki.
Asali Ma'anar Masu Inductor
Inductor, wanda galibi ana kiransa coil ko coil na waya, yana da ikon tsayayya da canje-canje a cikin wutar lantarki da ke ratsa ta. Wannan ya faru ne saboda ƙa'idar Faraday ta induction na lantarki. Lokacin da wutar lantarki ta canza a cikin inductor, filin maganadisu da wannan wutar ke samarwa shi ma yana canzawa, wanda hakan ke haifar da emf (ƙarfin lantarki) wanda ke adawa da canjin wutar lantarki.
Tsarin da ake amfani da shi wajen kwatanta inductor a cikin da'irar lantarki shine:
\[V = L \frac{di}{dt} \]
Ina:
– \(V \) shine ƙarfin lantarki a fadin inductor (volts),
– \( L \) shine induction na inductor (henry),
– \(\frac{di}{dt} \) shine canjin halin yanzu akan lokaci (amperes a kowace daƙiƙa).
Yanzu bari mu ga yadda ake amfani da inductor a wasu misalan matsaloli.
Misali na 1: Ƙarfin wutar lantarki a kan Inductor
Tambaya:
Ana wucewa da inductor mai induction na H2 ta hanyar canjin wutar lantarki a saurin A/s 3. Menene ƙarfin lantarki a kan inductor?
Tattaunawa:
Yi amfani da dabarar inductor ta asali:
\[V = L \frac{di}{dt} \]
An sani:
– \( L = 2 \) H
– \(\frac{di}{dt} = 3 \) A/s
\[ V = 2 sau 3 \]
\[ V = 6 \]
Saboda haka, ƙarfin lantarki a fadin inductor shine 6 V.
Misali Tambaya ta 2: Makamashin da aka Adana a cikin Inductor
Tambaya:
Nawa ne makamashin da ake adanawa a cikin inductor na H4 idan wutar lantarki ta ratsa shi ta kai 5A?
Tattaunawa:
Ana iya ƙididdige kuzarin da aka adana a cikin inductor ta amfani da dabarar:
\[ E = \frac{1}{2} LI^2 \]
Ina:
– \( E \) shine makamashi (joules),
– \( L \) shine inductance (henry),
– \( I \) shine halin yanzu (amperes).
An sani:
– \( L = 4 \) H
– \( I = 5 \) A
\[ E = \frac{1}{2} \sau 4 \sau 5^2 \]
\[ E = sau 2 \ sau 25 \]
\[ E = 50 \]
Don haka, kuzarin da aka adana a cikin inductor shine joules 50.
Misali Matsala ta 3: Da'irar Jerin RL
Tambaya:
Da'irar jerin RL ta ƙunshi resistor 10 Ω da kuma inductor 2 H. Idan aka yi amfani da tushen ƙarfin lantarki na 20 V, menene kwararar wutar lantarki mai ƙarfi a cikin da'irar?
Tattaunawa:
Ga jerin da'irar RL, ana iya ƙididdige wutar lantarki mai ƙarfi ta amfani da dokar Ohm saboda a yanayin da aka daidaita, inductor yana aiki kamar wayar da ke jagorantar al'ada (sifili impedance).
\[V = IR \]
An sani:
– \( V = 20 \) V
– \( R = 10 \) Ω
\[ I = \frac{V}{R} \]
\[ I = \frac{20}{10} \]
\[ I = 2 \]
Saboda haka, matsakaicin ƙarfin lantarki da ke gudana a cikin da'irar shine 2 A.
Misali na 4: Mitar Mai Raɗaɗi na Da'irar RLC ta Jeri
Tambaya:
Da'irar RLC mai jerin suna da resistor 5 Ω, inductor 150 mH, da kuma capacitor 100 μF. Menene mitar resonant na da'irar?
Tattaunawa:
Ana iya ƙididdige mitocin amsawa \( f_0 \) na da'irar RLC ta jerin ta amfani da dabarar:
\[ f_0 = \frac{1}{2 \pi \sqrt{LC}} \]
Ina:
– \( L \) shine inductance (henry),
– \( C \) shine ƙarfin aiki (farads).
An sani:
– \( L = 150 \) mH = 0.15 H
– \( C = 100 \) μF = 100 × 10^-6 F
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \sau 100 \sau 10^{-6}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \sau 10^{-4}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.15 \sau 10^{-4}}} \]
\[ f_0 = \frac{1}{2 \pi \sqrt{0.000015}} \]
\[ f_0 = \frac{1}{2 \pi \times 0.00387} \]
\[ f_0 = \frac{1}{0.0243} \]
\[ f_0 \kimanin 41.15 \]
Don haka, mitar amsawar da'irar jerin RLC tana da kusan 41.15 Hz.
Misali Tambaya ta 5: Abubuwan da suka Cancanta a cikin Da'irori na RL
Tambaya:
Da'irar RL ta ƙunshi resistor mai ƙarfin 8 Ω da kuma inductor mai ƙarfin 100 mH. Idan aka yi amfani da ƙarfin lantarki na mataki na 24 V, tsawon lokacin da wutar lantarki za ta ɗauka kafin ta kai kashi 63.2% na ƙimar ƙarshe?
Tattaunawa:
Lokacin da ake buƙata don isa 63.2% na ƙimar ƙarshe a cikin da'irar RL shine ma'aunin lokaci \( \tau \), inda:
\[ \tau = \frac{L}{R} \]
An sani:
– \( L = 100 \) mH = 0.1 H
– \( R = 8 \) Ω
\[ \tau = \frac{0.1}{8} \]
\[ \tau = 0.0125 \, s \]
Don haka, lokacin da ake buƙata don wutar lantarki ta kai kashi 63.2% na ƙimar ƙarshe shine daƙiƙa 0.0125.
Kammalawa
Ta hanyar misalan da ke sama, mun tattauna fannoni daban-daban da suka shafi inductors, ciki har da ƙarfin lantarki a cikin inductor, makamashin da aka adana, halayensa a cikin da'irori na RL, da kuma mitar resonant a cikin da'irori na RLC. Fahimtar waɗannan ra'ayoyi da lissafi yana da mahimmanci ga duk wanda ke neman aiki a injiniyan lantarki ko na lantarki. Inductors suna taka muhimmiyar rawa a cikin aikace-aikace da yawa, gami da matattara, da'irori na oscillator, da masu canza wutar lantarki. Ta hanyar fahimtar yadda suke aiki da yadda ake ƙididdige sigoginsu, za mu iya tsara da'irori masu inganci da aiki.
