Cov Lus Nug Piv Txwv Sib Tham Txog Inductance thiab Transformers
Inductance thiab transformers yog ob lub tswv yim tseem ceeb hauv hluav taws xob, tshwj xeeb tshaj yog nyob rau hauv cov ntsiab lus ntawm AC (alternating current) circuits. Kev nkag siab txog lawv ua haujlwm li cas yuav pab tau rau ntau yam kev siv, los ntawm kev tsim hluav taws xob circuit mus rau cov ntawv thov hauv tsev neeg thiab cov khoom siv hauv kev lag luam. Hauv tsab xov xwm no, peb yuav tham txog cov teeb meem piv txwv thiab cov kev daws teeb meem ntsig txog inductance thiab transformers.
Kev Taw Qhia Txog Inductance
Inductance yog lub peev xwm ntawm ib qho khoom siv hluav taws xob, xws li lub kauj, los tsim ib qho EMF (electromotive force) thaum muaj kev hloov pauv ntawm tam sim no ntws los ntawm nws. Ib qho khoom siv uas muaj inductance hu ua inductor. Lub chav ntawm inductance yog Henry (H).
Cov mis yooj yim ntsig txog inductance yog:
\[ V_L = L \frac{dI}{dt} \]
Qhov twg:
- \( V_L \) yog qhov tshwm sim ntawm qhov hluav taws xob (volts)
- \( L \) yog qhov inductance (Henry)
- \( \frac{dI}{dt} \) yog tus nqi ntawm kev hloov pauv ntawm tam sim no nrog rau lub sijhawm (amperes ib ob)
Piv txwv lus nug 1: Xam qhov hluav taws xob induced
Lo lus nug:
Ib qho inductor nrog inductance ntawm 5 H muab nrog tam sim no uas hloov ntawm 3 A mus rau 6 A hauv 2 vib nas this. Xam qhov hluav taws xob induced uas tshwm sim!
Kev daws teeb meem:
Ua ntej tshaj plaws, peb yuav tsum txiav txim siab qhov kev hloov pauv ntawm tam sim no (\(\frac{dI}{dt}\)):
\[ I_1 = 3 \, \text{A}, \, I_2 = 6 \, \text{A}, \, \Delta t = 2 \, \text{seconds} \]
\[ \frac{dI}{dt} = \frac{I_2 – I_1}{\Delta t} = \frac{6 – 3}{2} = 1.5 \, \text{A/sec} \]
Tam sim no peb hloov cov nqi paub rau hauv cov qauv hluav taws xob induced:
\[ V_L = L \frac{dI}{dt} = 5 \times 1.5 = 7.5 \, \text{V} \]
Yog li, qhov hluav taws xob induced yog 7.5 V.
Kev Taw Qhia rau Transformers
Lub transformer yog ib lub cuab yeej hluav taws xob siv los hloov cov theem AC voltage ntawm ib theem mus rau lwm qib siv lub hauv paus ntsiab lus ntawm electromagnetic induction. Lub transformer muaj ob lub kauj, ib lub kauj thawj zaug thiab ib lub kauj thib ob, qhwv ib puag ncig lub plawv hlau.
Cov mis yooj yim rau lub transformer zoo tagnrho yog:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Qhov twg:
- \( V_p \) yog qhov voltage ntawm lub kauj thawj
- \( V_s \) yog qhov voltage ntawm lub kauj thib ob
- \( N_p \) yog tus naj npawb ntawm cov tig hauv lub kauj thawj zaug
- \( N_s \) yog tus naj npawb ntawm cov tig hauv lub kauj theem nrab
Piv txwv lus nug 2: Xam qhov hluav taws xob theem ob
Lo lus nug:
Ib lub transformer muaj 500 tig hauv lub kauj thawj thiab 100 tig hauv lub kauj thib ob. Yog tias qhov hluav taws xob nkag mus rau lub kauj thawj yog 230 V, qhov hluav taws xob tso tawm mus rau lub kauj thib ob yog dab tsi?
Kev daws teeb meem:
Siv cov qauv zoo tagnrho transformer:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Cov kev ntsuas paub yog:
- \(V_p = 230 \text{V} \)
– \( N_p = 500 \)
– \( N_s = 100 \)
Peb yuav tsum nrhiav \( V_s \):
\[ \frac{230}{V_s} = \frac{500}{100} \]
Ua kom yooj yim rau feem ntawm sab xis:
\[ \frac{230}{V_s} = 5 \]
Tam sim no, daws rau \(V_s\):
\[V_s = \frac{230}{5} = 46 \, \text{V} \]
Yog li, qhov hluav taws xob tso zis ntawm lub kauj thib ob yog 46 V.
Piv txwv 3: Xam Tus Naj Npawb ntawm Kev Tig Thib Ob
Lo lus nug:
Ib lub transformer step-down siv los txo qhov voltage ntawm 240 V mus rau 24 V. Yog tias tus naj npawb ntawm cov tig hauv lub kauj thawj zaug yog 800 tig, muaj pes tsawg lub tig hauv lub kauj thib ob?
Kev daws teeb meem:
Siv cov qauv zoo tagnrho transformer:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Cov kev ntsuas paub yog:
- \(V_p = 240 \text{V} \)
– \( V_s = 24 \, \text{V} \)
– \( N_p = 800 \)
Peb yuav tsum nrhiav \( N_s \):
\[ \frac{240}{24} = \frac{800}{N_s} \]
Ua kom yooj yim rau feem ntawm sab laug:
\[ 10 = \frac{800}{N_s} \]
Daws rau \( N_s \):
\[ N_s = \frac{800}{10} = 80 \]
Yog li, tus naj npawb ntawm cov tig hauv lub kauj theem nrab yog 80 tig.
Piv txwv lus nug 4: Xam lub zog hauv lub Transformer zoo tagnrho
Lo lus nug:
Ib lub transformer zoo tagnrho muaj qhov hluav taws xob nkag ntawm 120 V ntawm lub kauj thawj nrog rau tam sim no ntawm 2 A thiab qhov hluav taws xob tso tawm ntawm 12 V ntawm lub kauj thib ob. Xam cov tam sim no ntws hauv lub kauj thib ob thiab lub zog tsim tawm hauv lub kauj thib ob.
Kev daws teeb meem:
Ua ntej, peb xam lub zog hauv lub kauj thawj (\(P_p\)):
\[ P_p = V_p \times I_p = 120 \, \text{V} \times 2 \, \text{A} = 240 \, \text{W} \]
Hauv ib lub transformer zoo tagnrho, lub zog thawj zaug yog sib npaug rau lub zog thib ob:
\[ P_s = P_p = 240 \, \text{W} \]
Tam sim no, peb xam qhov tam sim no hauv lub kauj theem nrab (\(I_s\)) siv lub zog:
\[ P_s = V_s \times I_s \]
\[ 240 = 12 \times I_s \]
Daws rau \(I_s\):
\[ I_s = \frac{240}{12} = 20 \, \text{A} \]
Yog li, tam sim no ntws hauv lub kauj thib ob yog 20 A, thiab lub zog tsim tawm hauv lub kauj thib ob yog 240 W.
Kev tawm dag zog
Tom qab nkag siab qee qhov piv txwv ntawm kev daws cov teeb meem saum toj no, ntawm no yog qee qhov teeb meem xyaum uas tuaj yeem ua tau los ua kom koj nkag siab tob txog inductance thiab transformers.
1. Ib lub inductor uas muaj inductance ntawm 10 H muab nrog lub zog tam sim no uas hloov ntawm 4 A mus rau 10 A hauv 3 vib nas this. Xam qhov hluav taws xob uas tau los ntawm induced!
2. Lub transformer step-up muaj 200 tig hauv lub kauj thawj thiab 1000 tig hauv lub kauj thib ob. Yog tias lub zog nkag yog 120 V, lub zog tso zis ntawm lub kauj thib ob yog dab tsi?
3. Tus naj npawb ntawm cov tig hauv lub kauj thawj zaug ntawm lub transformer yog 400 tig, thiab tus naj npawb ntawm cov tig hauv lub kauj thib ob yog 100 tig. Yog tias qhov hluav taws xob hla lub kauj thib ob yog 15 V, qhov hluav taws xob hla lub kauj thawj zaug yog dab tsi?
4. Ib lub transformer zoo tagnrho muaj qhov hluav taws xob nkag ntawm 240 V ntawm lub kauj thawj nrog rau tam sim no ntawm 3 A thiab qhov hluav taws xob tso tawm ntawm 60 V ntawm lub kauj thib ob. Xam qhov tam sim no ntws hauv lub kauj thib ob thiab lub zog tsim tawm hauv lub kauj thib ob.
Thaum koj ua tiav cov kev cob qhia no, koj yuav nkag siab tob dua txog kev ua haujlwm ntawm inductance thiab transformers thiab lawv cov kev siv hauv ntau yam xwm txheej. Kev paub no tseem ceeb heev tsis yog hauv kev kawm xwb tab sis kuj tseem ceeb rau ntau yam kev txawj ntse ntawm lub neej txhua hnub thiab kev ua haujlwm hauv kev tsim hluav taws xob.
