Piv txwv ntawm Cov Lus Nug Sib Tham Txog Inductance
Inductance yog ib lub tswv yim tseem ceeb hauv hluav taws xob thiab electromagnetism. Nws ntsuas lub peev xwm ntawm lub voj voog los tsim lub zog electromotive (EMF) los teb rau qhov hloov pauv hluav taws xob. Hauv tsab xov xwm no, peb yuav tham txog ntau qhov piv txwv thiab kev sib tham tob tob kom nkag siab zoo dua txog lub tswv yim ntawm inductance.
Kev Taw Qhia Txog Inductance
Ua ntej peb tham txog cov piv txwv, cia peb kawm seb inductance yog dab tsi. Inductance yog muab lub cim \(L\) thiab ntsuas hauv Henrys (H). Inductance tuaj yeem tshwm sim hauv ob hom tseem ceeb: tus kheej inductance thiab kev sib koom ua ke inductance.
– Kev tswj tus kheej: Kev tswj tus kheej yog qhov inductance tsim los ntawm lub kauj ntawm nws tus kheej thaum muaj kev hloov pauv ntawm cov hluav taws xob tam sim no. Qhov no yog muab los ntawm cov qauv:
\[ V_L = L \frac{dI}{dt} \]
qhov twg \(V_L \) yog qhov hluav taws xob induced, \(L \) yog qhov inductance, thiab \(\frac{dI}{dt} \) yog tus nqi ntawm kev hloov pauv ntawm tam sim no.
– Kev sib koom ua ke ntawm inductance: Kev sib koom ua ke ntawm inductance tshwm sim thaum ob lub kauj cuam tshuam rau ib leeg qhov induction. Cov qauv yog:
\[V_{L1} = M \frac{dI_2}{dt} \]
dan
\[V_{L2} = M \frac{dI_1}{dt} \]
qhov twg \(M\) yog qhov sib koom ua ke ntawm ob lub kauj.
Cov Lus Nug Piv Txwv Txog Inductance
Yuav kom nkag siab zoo dua txog inductance, cia peb saib qee qhov piv txwv ntawm cov teeb meem.
Piv txwv lus nug 1: Kev tswj tus kheej
Ib lub kauj muaj 200 tig thiab qhov tam sim no hloov pauv ntawm 0 txog 5 A hauv 2 vib nas this. Yog tias qhov sib nqus flux yog 5 Weber, xam qhov inductance ntawm lub kauj.
Kev Sib Tham:
Tus inductance \(L\) tuaj yeem suav los ntawm kev siv kev sib raug zoo ntawm magnetic flux (\( \Phi \)), tus naj npawb ntawm kev tig (\(N\)), thiab tam sim no (\(I\)).
\[ \Phi = L \times I \]
Nws yog paub,
\( N = 200 \)
\( Kuv = 5 \) A
\( \Phi = 5 \) Weber
Yog li ntawd,
\[ L = \frac{\Phi}{I} \]
\[ L = \frac{5}{5} \]
\[ L = 1 \text{ Henry} \]
Lub kauj muaj qhov inductance ntawm 1 Henry.
Piv txwv lus nug 2: Lub zog hauv Inductance
Ib lub solenoid uas muaj inductance ntawm 3 H muab hluav taws xob ntawm 2 A. Xam lub zog khaws cia rau hauv lub solenoid.
Kev Sib Tham:
Lub zog khaws cia rau hauv ib qho inductor yog muab los ntawm qhov equation:
\[ W = \frac{1}{2} LI^2 \]
Nws yog paub,
\( L = 3 \) H
\( Kuv = 2 \) A
Yog li ntawd,
\[ W = \frac{1}{2} \times 3 \times 2^2 \]
\[ W = \frac{1}{2} \times 3 \times 4 \]
\[ W = \frac{1}{2} \times 12 \]
\[ W = 6 \text{ Joules} \]
Yog li, lub zog khaws cia rau hauv solenoid yog 6 Joules.
Piv txwv 3: Kev sib koom ua ke ntawm Inductance
Ob lub kauj, A thiab B, muaj qhov sib txuas ntawm 0,5 H. Yog tias tam sim no hauv kauj A hloov pauv raws li qhov sib npaug \( I_{A}(t) = 3t \), xam lub zog electromotive hauv kauj B ntawm \(t = 4 \) s.
Kev Sib Tham:
Lub zog electromotive (EMF) hauv kauj B tuaj yeem suav los ntawm:
\[V_{L_B} = M \frac{dI_A}{dt} \]
Nws yog paub,
\( M = 0,5 \) H
\( I_{A}(t) = 3t \)
Tus nqi hloov pauv ntawm tam sim no \( \frac{dI_A}{dt} \) yog qhov tsis hloov pauv, uas yog 3 A/s.
Yog li ntawd,
\[ V_{L_B} = 0,5 \times 3 \]
\[ V_{L_B} = 1,5 \text{ V} \]
Yog li, lub zog electromotive hauv coil B ntawm \(t = 4\) s yog 1,5 Volts.
Piv txwv teeb meem 4: RL Series Circuit
Xav txog ib lub voj voog RL series uas muaj ib lub resistor nrog qhov tsis kam ntawm 5 ohms thiab ib lub inductor nrog qhov inductance ntawm 2 H. Yog tias lub voltage yog 10 V DC thiab lub qhov hloov kaw ntawm \(t = 0 \), xam qhov tam sim no hauv lub voj voog ntawm \(t = 1 \) vib nas this.
Kev Sib Tham:
Thaum lub qhov hloov kaw lawm, qhov tam sim no hauv RL Circuit Court nce raws li qhov sib npaug:
\[ Kuv(t) = \frac{V}{R} \left( 1 – e^{-\frac{R}{L}t} \right) \]
Nws yog paub,
\( V = 10 \) V
\( R = 5 \) ohm
\( L = 2 \) H
Yog li ntawd,
\[ Kuv(t) = \frac{10}{5} \left( 1 – e^{-\frac{5}{2} \times t} \right) \]
\[ Kuv(t) = 2 \left( 1 – e^{-2.5 \times t} \right) \]
Ntawm \(t = 1 \) vib nas this,
\[ Kuv(1) = 2 \sab laug( 1 – e^{-2.5 \times 1} \sab xis) \]
\[ Kuv(1) = 2 \left( 1 – e^{-2.5} \right) \]
\[ Kuv(1) \kwv yees li 2 \sab laug( 1 – 0.0821 \sab xis) \]
\[ Kuv(1) \kwv yees li 2 \times 0.9179 \]
\[ Kuv(1) \approx 1.8358 \text{ A} \]
Tam sim no hauv lub voj voog ntawm ≡(t = 1) vib nas this yog li 1.8358 A.
Xaus
Inductance yog ib lub tswv yim tseem ceeb hauv physics uas piav qhia txog yuav ua li cas hloov pauv hluav taws xob tam sim no tuaj yeem tsim hluav taws xob hla lub teb magnetic. Nrog cov piv txwv uas peb tau tham, peb tuaj yeem pom tias inductance siv li cas hauv ntau qhov xwm txheej, los ntawm cov kauj yooj yim mus rau cov voj voog RL nyuaj. Kev nkag siab txog inductance tseem ceeb tsis yog rau cov tub ntxhais kawm thiab cov engineers xwb, tab sis kuj rau txhua tus neeg uas xav paub txog electronics thiab electromagnetism. Yog tias xyaum txaus, koj txoj kev nkag siab txog inductance thiab nws cov ntawv thov tuaj yeem tob dua thiab nkag siab ntau dua.
