Ihe Nlereanya nke Ajụjụ Mkparịta ụka Inductionance
Inductance bụ echiche dị mkpa na ọkụ eletrik na electromagnetism. Ọ na-atụ ikike sekit nwere ịmepụta ike electromotive (EMF) n'ihi mgbanwe ọkụ eletrik. N'isiokwu a, anyị ga-ekpuchi ọtụtụ ihe atụ na mkparịta ụka miri emi iji ghọta nke ọma echiche nke inductance.
Okwu Mmalite nke Inductance
Tupu anyị ekwuo maka ihe atụ, ka anyị leba anya n'ihe inductance bụ. A na-enye inductance akara \(L\) ma a na-atụ ya na Henrys (H). Inductance nwere ike ime n'ụdị abụọ bụ isi: inductance onwe na inductance ibe ya.
– Ntinye onwe: Ntinye onwe bụ ntinye onwe onye nke coil na-emepụta n'onwe ya mgbe mgbanwe na ọkụ eletrik mere. Nke a bụ site na nha anya:
\[V_L = L \frac{dI}{dt} \]
ebe \(V_L \) bụ voltaji e tinyere n'ime ya, \(L \) bụ inductance, na \( \frac{dI}{dt} \) bụ ọnụego mgbanwe nke ugbu a.
– Induction nkeonwe: Induction nkeonwe na-eme mgbe eriri abụọ metụtara induction nke ibe ha. Usoro nhazi ahụ bụ:
\[ V_{L1} = M \frac{dI_2}{dt} \]
dan
\[ V_{L2} = M \frac{dI_1}{dt} \]
ebe \( M \) bụ njikọta nkekọ n'etiti eriri abụọ ahụ.
Ajụjụ Ihe Nlereanya nke Induction
Iji ghọta nke ọma ihe na-eme ka induction dị, ka anyị leba anya n'ụfọdụ nsogbu dị iche iche.
Ajụjụ Ihe Nlereanya nke 1: Ịkwalite Onwe Gị
Kọịl nwere ntụgharị 200, ọkụ eletrik na-agbanwe site na 0 ruo 5 A n'ime sekọnd 2. Ọ bụrụ na ọkụ magnetik bụ 5 Weber, gbakọọ inductance nke kọịl ahụ.
Azịza:
Enwere ike ịgbakọ inductance \(L\) site na iji mmekọrịta dị n'etiti magnet flux (\( \Phi \)), ọnụọgụ nke ntụgharị (\(N\)), na ugbu a (\(I\)).
\[ \Phi = L \ugboro I \]
A maara,
\( N = 200 \)
\( I = 5 \) A
\( \Phi = 5 \) Weber
Maca,
\[ L = \frac{\Phi}{I} \]
\[ L = \frac{5}{5} \]
\[ L = 1 \ederede{ Henry} \]
Okporo ígwè ahụ nwere inductance nke 1 Henry.
Ajụjụ Ihe atụ nke 2: Ike dị na Inductance
A na-enye solenoid nwere inductance nke 3 H na ọkụ eletrik nke 2 A. Gbakọọ ike echekwara na solenoid.
Azịza:
A na-enye ike echekwara na inductor site na usoro nha anya:
\[ W = \frac{1}{2} LI^2 \]
A maara,
\( L = 3 \) H
\( I = 2 \) A
Maca,
\[ W = \frac{1}{2} \ugboro atọ \ugboro 2^2 \]
\[ W = \frac{1}{2} \ugboro atọ \ugboro anọ \]
\[ W = \frac{1}{2} \ugboro 12 \]
\[ W = 6 \ederede{ Joules} \]
Ya mere, ike echekwara na solenoid bụ 6 Joules.
Ihe atụ nke atọ: Nduzi mmekọrịta
Kọlụ abụọ, A na B, nwere njikọ chiri anya nke 0,5 H. Ọ bụrụ na ọkụ dị na kọlụm A agbanwee dịka nha anya \( I_{A}(t) = 3t \), gbakọọ ike electromotive dị na kọlụm B na \( t = 4 \) s.
Azịza:
Enwere ike ịgbakọ ike electromotive (EMF) dị na coil B site na:
\[ V_{L_B} = M \frac{dI_A}{dt} \]
A maara,
\( M = 0,5 \) H
\( I_{A}(t) = 3t \)
Ọnụego mgbanwe nke ugbu a \( \frac{dI_A}{dt} \) bụ ihe na-agbanwe agbanwe, ya bụ 3 A/s.
Maca,
\[V_{L_B} = 0,5 \ugboro 3 \]
\[V_{L_B} = 1,5 \ederede{V} \]
Ya mere, ike electromotive dị na coil B na \( t = 4 \) s bụ 1,5 Volts.
Ihe atụ Nsogbu nke 4: Sekit Usoro RL
Tụlee usoro sekit RL nke nwere resistor nwere nguzogide nke 5 ohms na inductor nwere inductance nke 2 H. Ọ bụrụ na voltaji ahụ bụ 10 V DC ma mechie mgbanwe ahụ na \( t = 0 \), gbakọọ ugbu a na sekit ahụ na \( t = 1 \) sekọnd.
Azịza:
Mgbe emechiri mgba ọkụ ahụ, ọkụ dị na sekit RL na-abawanye dịka nha nhata si dị:
\[ I(t) = \frac{V}{R} \left(1 – e^{-\frac{R}{L}t} \nri) \]
A maara,
\( V = 10 \) V
\( R = 5 \) ohm
\( L = 2 \) H
Maca,
\[ I(t) = \frac{10}{5} \left( 1 – e^{-\frac{5}{2} \times t} \right) \]
\[ I(t) = 2 \aka ekpe( 1 – e^{-2.5 \ugboro t} \nri) \]
Na sekọnd \(t = 1 \),
\[ I(1) = 2 \aka ekpe( 1 – e^{-2.5 \ugboro 1} \nri) \]
\[ I(1) = 2 \aka ekpe(1 – e^{-2.5} \aka nri) \]
\[ I(1) \ihe dị ka 2 \aka ekpe( 1 – 0.0821 \nri) \]
\[ I(1) \ihe dị ka ugboro abụọ 0.9179 \]
\[ I(1) \ihe dịka 1.8358 \ederede{ A} \]
Ọkụ dị na sekit ahụ na sekọnd 1 (t = 1) bụ ihe dịka 1.8358 A.
Mmechi
Inductance bụ echiche dị mkpa na fiziki nke na-akọwa otu ọkụ eletrik na-agbanwe agbanwe nwere ike isi mepụta voltaji n'ofe ubi magnetik. Site na ihe atụ ndị anyị tụlere, anyị nwere ike ịhụ otu esi etinye inductance n'ọtụtụ ọnọdụ bara uru, site na coils dị mfe ruo na sekit RL dị mgbagwoju anya. Ịghọta inductance dị mkpa ọ bụghị naanị maka ụmụ akwụkwọ na ndị injinia, kamakwa maka onye ọ bụla nwere mmasị na eletrọniki na electromagnetism. Site na omume zuru oke, nghọta gị banyere inductance na ngwa ya nwere ike ịghọ nke miri emi ma dịkwuo nghọta.
