Chitsanzo cha Mafunso Okambirana za Inductance
Kusinthasintha kwa magetsi ndi lingaliro lofunikira kwambiri pamagetsi ndi maginito amagetsi. Kumayesa kuthekera kwa dera kupanga mphamvu yamagetsi (EMF) poyankha kusintha kwa magetsi. M'nkhaniyi, tikambirana zitsanzo zingapo ndi zokambirana zakuya kuti timvetse bwino lingaliro la kusinthasintha kwa magetsi.
Chiyambi cha Inductance
Tisanakambirane zitsanzo, tiyeni tione tanthauzo la inductance. Inductance imapatsidwa chizindikiro \(L\) ndipo imayesedwa mu Henrys (H). Inductance imatha kuchitika m'njira ziwiri zazikulu: kudzipangira wekha ndi kugwirirana kwapawiri.
– Kudziyendetsa: Kudziyendetsa ndi kulowetsa komwe kumapangidwa ndi coil yokha pamene kusintha kwa magetsi kumachitika. Izi zimaperekedwa ndi equation:
\[ V_L = L \frac{dI}{dt} \]
kumene \( V_L \) ndi voltage yoyambitsidwa, \( L \) ndi inductance, ndipo \( \frac{dI}{dt} \) ndi liwiro la kusintha kwa mphamvu yamagetsi.
– Kusinthasintha kwa ma inductance: Kusinthasintha kwa ma inductance kumachitika pamene ma coil awiri amakhudza kusinthasintha kwa ma inductance. Equation ndi iyi:
\[ V_{L1} = M \frac{dI_2}{dt} \]
dani
\[ V_{L2} = M \frac{dI_1}{dt} \]
kumene \( M \) ndi inductance yolumikizana pakati pa ma coil awiriwa.
Mafunso a Chitsanzo cha Inductance
Kuti timvetse bwino za inductance, tiyeni tiwone zitsanzo za mavuto ena.
Chitsanzo Funso 1: Kudziyendetsa
Coil ili ndi ma turns 200 ndipo mphamvu yamagetsi imasiyana kuyambira 0 mpaka 5 A mu masekondi awiri. Ngati mphamvu ya maginito ndi 5 Weber, werengani kuchuluka kwa inductance ya coil.
Kukambirana:
Kuchuluka kwa mphamvu ya magetsi (L) kungawerengedwe pogwiritsa ntchito ubale womwe ulipo pakati pa maginito (\( \Phi \)), chiwerengero cha ma turns (\(N \)), ndi mphamvu yamagetsi (\(I \)).
\[ \Phi = L \nthawi I \]
Ndizodziwika kuti,
\( N = 200 \)
\( Ine = 5 \) A
\( \Phi = 5 \) Weber
Kotero,
\[ L = \frac{\Phi}{I} \]
\[ L = \frac{5}{5} \]
\[ L = 1 \lemba{ Henry} \]
Chozunguliracho chili ndi inductance ya 1 Henry.
Chitsanzo Funso 2: Mphamvu mu Inductance
Solenoid yokhala ndi inductance ya 3 H imaperekedwa ndi magetsi a 2 A. Werengani mphamvu yosungidwa mu solenoid.
Kukambirana:
Mphamvu yosungidwa mu inductor imaperekedwa ndi equation:
\[ W = \frac{1}{2} LI^2 \]
Ndizodziwika kuti,
\( L = 3 \) H
\( Ine = 2 \) A
Kotero,
\[ W = \frac{1}{2} \nthawi 3 \nthawi 2^2 \]
\[ W = \frac{1}{2} \nthawi 3 \nthawi 4 \]
\[ W = \frac{1}{2} \nthawi 12 \]
\[ W = 6 \malemba{ Ma Joule} \]
Chifukwa chake, mphamvu yosungidwa mu solenoid ndi 6 Joules.
Chitsanzo 3: Kusinthasintha kwa Magulu
Ma coil awiri, A ndi B, ali ndi inductance yogwirizana ya 0,5 H. Ngati mphamvu yamagetsi mu coil A isintha malinga ndi equation \( I_{A}(t) = 3t \), werengani mphamvu yamagetsi mu coil B pa \(t = 4 \) s.
Kukambirana:
Mphamvu yamagetsi (EMF) mu coil B ikhoza kuwerengedwa ndi:
\[ V_{L_B} = M \frac{dI_A}{dt} \]
Ndizodziwika kuti,
\( M = 0,5 \) H
\( Ine_{A}(t) = 3t \)
Mlingo wa kusintha kwa mphamvu yamagetsi \( \frac{dI_A}{dt} \) ndi wokhazikika, womwe ndi 3 A/s.
Kotero,
\[ V_{L_B} = 0,5 \nthawi 3 \]
\[ V_{L_B} = 1,5 \malemba{ V} \]
Kotero, mphamvu ya electromotive mu coil B pa \(t = 4 \) s ndi 1,5 Volts.
Chitsanzo Vuto 4: RL Series Circuit
Taganizirani za dera la RL lotsatizana lomwe lili ndi resistor yokhala ndi kukana kwa 5 ohms ndi inductor yokhala ndi inductance ya 2 H. Ngati magetsi ali 10 V DC ndipo switch yatsekedwa pa \(t = 0 \), werengerani mphamvu mu dera pa \(t = 1 \) masekondi.
Kukambirana:
Pamene switch yatsekedwa, mphamvu yamagetsi mu RL circuit imawonjezeka malinga ndi equation:
\[ I(t) = \frac{V}{R} \left( 1 – e^{-\frac{R}{L}t} \right) \]
Ndizodziwika kuti,
\( V = 10 \) V
\( R = 5 \) ohm
\( L = 2 \) H
Kotero,
\[ I(t) = \frac{10}{5} \left( 1 – e^{-\frac{5}{2} \times t} \right) \]
\[ Ine(t) = 2 \kumanzere( 1 – e^{-2.5 \nthawi t} \kumanja) \]
Pa masekondi a \(t = 1 \),
\[ I(1) = 2 \kumanzere( 1 – e^{-2.5 \nthawi 1} \kumanja) \]
\[ I(1) = 2 \kumanzere( 1 – e^{-2.5} \kumanja) \]
\[ I(1) \pafupifupi 2 \kumanzere( 1 – 0.0821 \kumanja) \]
\[ I(1) \pafupifupi 2 \nthawi 0.9179 \]
\[ I(1) \pafupifupi 1.8358 \malemba{ A} \]
Mphamvu yamagetsi mu dera pa masekondi a t = 1 ndi pafupifupi 1.8358 A.
Mapeto
Kusinthasintha kwa magetsi ndi lingaliro lofunikira mu fizikisi lomwe limafotokoza momwe magetsi osinthika angapangire magetsi kudutsa mphamvu yamaginito. Ndi zitsanzo zomwe takambiranazi, titha kuwona momwe kusinthasintha kwa magetsi kumagwiritsidwira ntchito pazinthu zambiri zothandiza, kuyambira ma coil osavuta mpaka ma RL circuits ovuta. Kumvetsetsa kusinthasintha kwa magetsi ndikofunikira osati kwa ophunzira ndi mainjiniya okha, komanso kwa aliyense amene ali ndi chidwi ndi zamagetsi ndi maginito. Mukachita mokwanira, kumvetsetsa kwanu kwa kusinthasintha kwa magetsi ndi momwe amagwiritsidwira ntchito kumatha kukhala kozama komanso komveka bwino.
