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  • 8/3/2019 Ly Thuyet Vat Ly_full

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    Li m au

    Theo chu trng cua Bo Giao Duc & ao Tao, t nam 2007 hnh thc thi c anh gia ket quahoc tap cua cac em hoc sinh oi vi mon Vat Ly se chuyen t hnh thc thi t luan sang hnh thcthi trac nghiem. e giup cac em hoc sinh hoc tap, ren luyen tot cac k nang giai cac bai toan tracnghiem, ngi bien soan xin tran trong gi ti cac bac phu huynh, cac quy thay co, cac em hocsinh mot so tai lieu trac nghiem mon Vat Ly THPT Trong tam la cac tai lieu danh cho cac ky thitot nghiep va ai hoc. Vi noi dung ay u, bo cuc sap xep ro rang t c ban en nang cao, ngibien soan hi vong cac tai lieu nay se giup ch cho cac em trong viec on luyen va at ket qua caotrong cac k thi.

    Mac du a het sc co gang va can trong trong khi bien soan nhng van khong the tranh khoinhng sai sot ngoai y muon, rat mong nhan c s gop y xay dng t pha ngi oc.

    Xin chan thanh cam n!

    CAC TAI LIEU A BIEN SOAN:

    @ Bai tap trac nghiem dao ong c hoc song c hoc (400 bai).

    @ Bai tap trac nghiem dao ong ien song ien t (400 bai).

    @ Bai tap trac nghiem quang hnh hoc (400bai).

    @ Bai tap trac nghiem quang ly vat ly hat nhan (400 bai).

    @ Bai tap trac nghiem c hoc chat ran ban khoa hoc t nhien (250 bai).

    @ Bai tap trac nghiem toan tap vat ly 12 (1200 bai).

    @ Tuyen tap 40 e thi trac nghiem vat ly danh cho on thi tot nghiep va ai hoc (2 tp).

    @ e cng on tap cau hoi ly thuyet suy luan vat ly 12 dung cho thi trac nghiem.

    @ Vn kin hi tho Hng dn thi trc nghim(ST).

    @ Bai tap trac nghiem vat ly 11 theo chng trnh sach giao khoa nang cao.

    @ Bai tap trac nghiem vat ly 10 theo chng trnh sach giao khoa nang cao.

    Noi dung cac sach co s tham khao tai lieu va y kien ong gop cua cac tac gia va ongnghiep. Xin chan thanh cam n!

    Moi y kien xin vui long lien he:': 0210.471.167 - 08.909.22.16 090.777.54.69*: [email protected]

    GV: BUI GIA NOI

    (Bo mon vat ly)

    Thanh Pho Ho Ch Minh, thng06 nam 2007

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    DAO ONG C HOC

    Cau 1 :nh ngha dao ong ieu hoa. Viet phng trnh, neu nh ngha cac ai lng trongphng trnh. Thanh lap cong thc tnh van toc va gia toc trong dao ong ieu hoa. Trnh baymoi lien he gia chuyen ong tron eu va dao ong ieu hoa.1. NH NGHA - VIET PHNG TRNH

    Dao ong ieu hoa la dao ong co ly o x bien oi theo thi gian tuan theo nh luat hnhsin (hay cosin).

    Phng trnh dao ong ieu hoa: x = Asin(wt + j) A : bien o hay gia tr cc ai cua ly o. j : pha ban au la ai lng xac nh v tr, van toc luc t = 0. (wt + j) : pha dao ong la ai lng xac inh v tr, van toc luc t. T la chu ky cua dao ong. No la khoang thi gian ngan nhat sau o trang thai dao ong

    lap lai nh cu hay thi gian e vat thc hien c 1 lan dao ong. f la tan so. No la so dao ong ma vat thc hien trong mot n v thi gian. w la tan so goc cua dao ong. La ai lng trung gian cho phep xac nh tan so va chu ky

    cua dao ong theo cong thc : w = 2Tp = 2pf

    2. VAN TOC - GIA TOC- Van toc : v = x = Aw cos(wt + j)- Gia toc : a = x = - Aw2sin(wt + j)

    3. LIEN HE GIA CHUYEN ONG TRON EU VA DAO ONG IEU HOAXet iem M chuyen ong eu tren vong tron (O, A) vi

    van toc goc w : t = 0 : M co ly o goc la j. t : M co ly o goc la (wt + j).

    Goi P la hnh chieu cua M xuong truc xOx, ta co:xp = OP = OMsin(wt + j) xp = Asin(wt + j)Ta thay chuyen ong cua P la mot dao ong ieu hoa.

    Noi khac i dao ong ieu hoa co the coi nh la hnh chieu cuamot chuyen ong tron eu xuong mot truc nam trong mat phangquy ao.

    Cau 2 :* Nhan xet ve pha dao ong gia v va x, gia a va x.* Cho biet nhng iem giong nhau va khac nhau gia dao ong ieu hoa va dao ong

    tuan hoan.

    1. Nhan xet ve pha dao ong gia v va x; gia a va x

    * v = A w cos (wt + j) = A w sin [(wt + j) +2p

    ]

    x = A sin (wt + j) v va x la 2 ai lng vuong pha* a = - A w2 sin (wt + j) = A w2 sin [(wt + j) + p ]

    x = A sin (wt + j) a va x la 2 ai lng ngc pha

    x

    C (D)

    Mo

    M

    AP

    jwt

    x'

    O

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    2. iem giong nhau va khac nhau cua hai dao ong ieu hoa va dao ong tuan hoan* Giong nhau :

    - eu co s lap lai nhng khoang thi gian bang nhau.- Hai ao ong eu co chu ky, tan so.

    * Khac nhau:- Dao ong ieu hoa mo ta bang inh luat hnh sin va co quy ao luon la ng

    thang, trong khi dao ong tuan hoan th khong nhat thiet phai can ieu kien o.

    - Dao ong ieu hoa la tap con cua dao ong tuan hoan, dao ong tuan hoan lai latap con cua cac dao ong noi chung.

    Cau 3 : Dao ong cua con lac lo xo nam ngang* Mo ta cau tao va th nghiem.* Thiet lap phng trnh dao ong.

    1. Mo ta cau tao th nghiem ve con lac lo xo- Xet mot he gom lo xo co o cng K, mot au gan vao mot iem co nh, au kia mang

    qua cau khoi lng m, gia qua cau co mot cai ranh cho phep no chuyen ong doc theo mot

    thanh ngang khong ma sat. F- Chon goc O la v t luc qua cau ng yen.- Keo qua cau ra khoi v tr can bang en ly o x = A roi

    buong tay, qua cau chuyen ong nhanh dan ve pha O, vt qua Odo quan tnh, roi chuyen ong cham dan en khi van toc bang 0,sau o chuyen ong nhanh an ve pha O roi lai cham dan en khivan toc bang 0. Sau o chuyen ong lap lai nh cu.2. Thiet lap phng trnh dao ong cua con lac lo xo

    a. Phan tch lc v tr x hon bi chu tac dung cua 3 lc : trong lc P mg=

    ur r,

    phan lc Nur

    cua thanh ngang va lc an hoi Fur

    cua lo xo. V Pur

    va Nur

    can bang nhau nen ch conlc F lam cho hon bi dao ong. Theo nh luat Hooke th F = - Kx, vi K la o c ng cua lo xocon dau tr ch lc F luon luon hng ve v tr can bang.

    b. Lap phng trnh chuyen ongTheo nh luat 2 Newton: P N F ma+ + =

    ur ur ur r(*)

    Chon chieu dng nh hnh ve, chieu (*) xuong

    - Kx = mx x = -F

    xm

    -

    at w2 =K

    m

    Suy ra x = w2x Hay x + w2x = 0

    ay la phng trnh vi phan mo ta chuyen ong cua con lac lo xoNghiem cua phng trnh vi phan co dang: x = Asin(wt + j)Vay chuyen ong cua con lac lo xo la mot ao ong ieu hoa.

    Cau 4 :* Lap cong thc lien he gia w va T.* Viet cong thc chu k dao ong cua con lac lo xo co chieu dai l treo vat m. Neu tang

    chiu dai lo xo la 2l va van treo vat m th chu ky dao ong cua con lac lo xo thenao.

    mNur

    Pur

    KO

    m

    Fur

    KO

    Ox

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    1. Quan he gia w va T:

    Ta co : x = A sin(wt + j) x = A sin(wt + j +2p) x = A sin [w( t +2pw

    ) + j]

    Vay li o tai thi iem t bang ly o thi iem ( t +2pw

    ), nen khoang thi gian 2pw

    goi

    la chu ky cua ao ong ieu hoa.p

    =

    w

    2T

    2. Cong thc chu ky cua con lac lo xo:

    * V w =Km

    T =2 m2

    Kp

    = pw

    * He soan hoi cua lo xo:

    K = ESl

    vi E la suat young. chieu dai tang 2 lan th o cng giam 2 lan: K =K2

    T =m2 . 2 T 2K

    p = . Vay chu ky tang 2 lan.

    Cau 5: Lap moi lien he gia ly o, bien o va tan so cua vat dao ong ieu hoa

    Ta co : x = A sin(wt + j) sin2(wt+j)=2

    2

    xA

    v = A w cos(wt + j) cos2(wt + j) =2

    2 2

    vA w

    2 2

    2 2 2

    x v1

    A A+ =

    w

    Cau 6:* Dao ong cua con lac n: Cau tao va lap phng trnh dao ong* So sanh hai phng trnh cua con lac lo xo va con lac n* Dao ong cua con lac n co phai la dao ong t do khong?

    1. CAU TAO VA PHNG TRNH DAO ONG CUA CON LAC N:a. Cau tao: Con lac n gom hon bi co khoi

    lng m treo vao day dai co khoi lng va o dan khongang ke.

    b. Lap phng trnh:

    Hp lc tac dung len vat m co ly o goc aP :tronglc

    F P mavi:lccangday

    = + t =

    t

    rur r r r

    r

    Chieu hp lc len tiep tuyen:- mgsin a = m aT la gia toc tiep tuyen: aT = s - gsin a = s (*)

    ieu kien: a0 nho (a0 < 100)

    OPur

    Tur

    Fur

    aoa

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    sin a = a =sl''

    - gs

    s''=l

    =>g

    s'' s 0+ =l

    at w2 =gl

    s + w2 s = 0 (1)

    Phng trnh (1) la phng trnh vi phan mo ta ao ong cua con lac n. No co nghiem :s = s0 sin(wt + j) (2)

    Phng trnh (2) la phng trnh dao ong cua con lac n. Phng trnh cho thay con lacn ao ong ieu hoa vi chu ky: T = 2p

    l

    g

    2. SO SANH:* Giong nhau: Hai phng trnh cua con lac lo xo va con lac n co dang toan hoc giong

    nhau va eu mo ta dao ong ieu hoa.* Khac nhau:

    Tan so goc khac nhau. oi vi con lac lo xo th w = Km

    ch phu thuoc vao he kn ( lo

    xo va vat), trong khi oi vi con lac n th w =gl ch phu thuoc vao g.

    Khi khong ma sat th dao ong con lac lo xo la dao ong ieu hoa, trong khi dao ongcua con lac n ch gan ung la dao ong ieu hoa khi bien o nho.

    3. OI VI DAO ONG NHO :(a0 < 100) th chu ky con lac n khong phu thuoc bien o, ma phu thuoc o ln gia toc

    trong lc g. Tai v tr conh oi vi trai at g khong oi, dao ong cua con lac n c coi ladao ong t do.

    Cau 7: Khao sat nh tnh va nh lng s bien oi nang lng trong dao ong ieu hoa cuacon lac lo xo.

    1. KHAO SAT NH TNH: (S bien oi nang lng) Keo hon bi t v tr can bang O en b B

    th lc keo thc hien cong va truyen chohon bi mot nang lng ban au la the nangan hoi.

    Tha hon bi tc la lc keo mat i th lc an hoi keohon bi chuyen ong nhanh dan ve vtr can bang O. ong nang hon bi tang, the nang lo xo giam.

    Tai v tr can bang O, thenang lo xo bang khong, ong nang hon bi cc ai Do quan tnh hon bi tiep tuc chuyen ong en b B', lc an hoi fr oi chieu lam hon bi

    chuyen ong cham dan: ong nang hon bi giam, thenang lo xo tang. Tai b B', hon bi dng lai, lo xo nen toi a, ong nang hon bi bang khong the nang lo xo

    cc ai. Sau o hon bi di tac dung l c an hoi lai chuyen ong ve v tr can bang O va qua trnh

    nh tren c lap lai.Vay: Trong qua trnh dao ong cua con lac lo xo co s chuyen hoa gia ong nang va thenang

    cb

    O BB

    +

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    2. KHAO SAT NH LNG: (S bao toan nang lng)

    *) ong nang hon bi: E =12

    mv2 vi v = Aw cos(wt + j) E =12

    mA2w2cos2(wt + j)

    *) The nang lo xo: Et =12

    Kx2 vi x = Asin(w + j) va K = mw2

    => Et =1

    2mw2A2sin2(wt + j)

    *) C nang: E = Et +E E =12

    mw2A2 [cos2(wt + j) + sin2(wt + j)]

    E =12

    mw2A2

    Vay:Trong suot qua trnh dao ong c nang caa con lac la khong oi va t le vi bnhphng cua bien o dao ong

    Cau 8:

    * ong nang va thenang cua con lac lo xo bien oi ieu haa vi tan sogoc bao nhieu .* Neu khoi lng tang 4 1an va bien o giam 2 lan th c nang con lac lo xo oi thenao.

    1. Ta co:

    * E =12

    mA2w2 cos2 (wt + j)

    1 cos(2 t 2 )v cos2 ( t + )

    21 1 cos(2 t 2 )

    2 2

    + w + j=

    = + w + j

    E =14

    m A2w2 +14

    mA2 w2cos (2wt + 2j)

    Vay E bien oi ieu hoa vi tan so goc w0 = 2w va f0 = 2f => chu k T0 = 0,5T* Tng t Et bien oi ieu hoa vi tan sogoc w0 = 2w va f0 = 2f => chu k T0 = 0,5T* E , Et bien oi ieu hoa cung tan so nhng ngc pha nhau.

    2. C nang: E =12

    m A2w2.

    Khi m = 4 m w=K Km' 4m 2

    w= =

    A = A2

    A2 = 2A4

    Vay E = 12

    .4m. 2 2A.4 4

    w

    E = 2 21 1

    ( mA )4 2

    w E =E4

    Vay c nang giam 4 lan.

    Cau 9: Khao sat nh tnh va nh lng s bien oi nang lng cua con lac n trong khi daoong. Chng minh ra ng neu dao ong cua con lac n la dao ong ieu hoa th c nang cua nokhong oi va t le vi bnh phng cua bien o dao ong.

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    1. KHAO SAT NH TNH: (S bien oi nang lng) Keo con lac n lech khoi v tr can bang mot goc a0 th lc keo thc hien mot cong va

    truyen cho con lac n mot thenang trong trng. Tha nhe hon bi th lc keo mat i, hon bi chuyen ong nhanh dan va v tr can bang va

    thenang giam dan trong khi ong nang tang. Hon bi ve v tr can bang, thenang bang khong, ong nang cc ai. Do quan tnh hon bi len cao dan. Thenang hon bi tang, ong nang giam. Khi hon bi len v tr cao nhat B th dng lai. ong nang bang khong va the nang cc ai. Sau o hon bi chuyen ong nhanh dan eu ve v tr can bang O va qua trnh nh tren tai

    dien.Vay:Trong qua trnh dao ong co s chuyen hoa gia the nang va ong nang

    2. KHAO SAT NH LNG: (S bao toan nang lng)

    Thenang : Et = mgh vi h = l - l cos a = l (1 - cosa) = 2lsin2 2a

    Et =12

    mg l a2 v w2 =g s

    va a =l l

    Et =2

    2 22

    1 s 1mg m s

    2 2= wl

    l

    Mat khac: s = sosin(wt + j) Et = 12

    mw2 20s sin2(wt + j)

    ong nang: E = 12

    mv2 vi v =sowcos(wt + j) E = mw2 20s cos2(wt + j)

    C nang: E = Et + E 2 201E m s2= w Vay:Trong qua trnh dao ong ieu hoa c nang cua con lac n la khong oi va t le vi

    bnh phng cua bien o dao ong

    Cau 10:- Phat bieu cac nh ngha: dao ong t do, dao ong cng bc, he dao ong- Dao ong t do va dao ong cng bc co iem nao giong nhau va khac nhau

    1. Phat bieu nh ngha:v Dao ong t do: la dao ong ma chu ky ch phu thuoc cac ac tnh cua he dao o ng

    nhng khong phu thuoc cac yeu to ben ngoaiv Dao ong cng bc: la dao ong chu tac dung cua lc cng bc bien thien tuan

    hoan F = Fosin(wt + j) vi Fo la bien o ngoai lc.v He giao ong: la he co kha nang thc hien dao ong t do. Sau khi b kch thch he dao

    ong se t no thc hien dao ong theo chu ky rieng cua no.2. Dao ong t do va dao ong cng bc co iem nao giong va khac nhau:v Giong nhau: eu co tnh tuan hoan (dao ong ieu hoa)v Nhac nhau: Chu ky va tan socua dao ong cng bc phu thuoc ngoai lc tac dung

    trong khi dao ong t do th khong.

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    Cau 11: Bieu dien dao ong ieu hoa bang phng Phap gian o vect quay Fresnel

    Phng phap vect quay da tren tnh chat: mot dao ong ieu hoa co the c coi nhhnh chieu cua mot chuyen ong tron eu xuong mot truc namtrong mat phang quy ao.

    - Gia s can bieu dien dao ong: x = Asin(wt + j)

    Ta ve mot truc nam ngang (D

    ) va mot truc thang ngx'x cat (D) tai O. Ve mot vect Ar co goc tai O: co o dai bangbien o A va tao vi truc (D) mot goc bang j tai thi iem t = 0.Cho vect A

    rquay eu theo chieu dng lng giac vi van toc

    goc w. Luc o chuyen ong cua hnh chieu au mut vect Ar

    xuong truc x'x la mot dao ong ieu hoa:

    x = OP = Asin(wt + j)- Ta ket luan rang dao ong ieu hoa x = Asin(wt + j) c bieu dien bang vect quay A

    r

    Cau 12: Tong hp hai dao dao ong ieu hoa cung phng, cung tan so bang phng phap

    vect quay.

    1. TONG HP HAI DAO ONG IEU HOA CUNG PHUNG CUNG TAN SO BANGPHNG PHAP VECT QUAY:

    Xet vat tham gia 2 dao ong ieu hoa cung phng, cung a so:x1 = A1sin(wt + jl)x2 = A2sin(wt + j2)

    Dao ong tong hp: x = x1 + x2. Tm x bang phng phapvect quay. Ta ve cac vect bieu dien x1, x2, x nh hnh ve:

    Ta thay1 2 1 2M OM hang= j - j =

    Cho hai vect 1 2A ,Ar r

    , quay quanh O theo chieu dngvi van toc goc w khong oi. Khi o hnh bnh hanh OM1MM2khong bien dang nen vect tong hp co o ln khong oi va cungquay quanh O theo chieu ng vi van toc goc w.

    V tong ai so cac hnh chieu cua hai vect 1 2A ,Ar r

    xuong truc x'Ox bang hnh chieu cua vect 1Ar

    xuong truc onen chuyen ong tong hp cua hai ao ong ieu hoa cung phng va cung a so la mot daoong ieu hoa cung phng va cung a so.

    Do o vect 1Ar

    bieu dien dao ong ieu hoa tong hp va goc j bieu dien pha ban au

    cua ao ong tong hp.2. BIEN O VA PHA BAN AU CUA DAO ONG TONG HP:

    Co 1 2OM OM OM= +uuuur uuuuur uuuuur

    Chieu xuong truc (D) va truc xx:Acosa = A1cosj1 + A2cosj2 (1)Asina = A1sinj1 + A2sinj2 (2)(l)2 + (2)2 cho 2 22 1 2 1 2 1 2A A A 2A A cos( )= + + j - j

    x

    (D)

    Mo (t = 0)

    MP

    jwt

    x'

    O

    +

    x

    (D)

    A2

    A1

    A

    M1

    MM2

    O

    jj1

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    (2)(1)

    cho 1 1 2 21 1 2 2

    A sin A sintgA cos A cos

    j + jj =

    j + j

    Neu x1 va x2 dao ong cung pha : j1 - j2 = K2p A = A1 + A2 Neu x1 va x2 dao ong ngc pha : j1 - j2 = (2K + 1)p A = 1 2A A- Neu x1 va x2 dao ong bat ky : 1 2A A- < A < (A1 + A2)

    Cau 13: Dao ong tat dan: nh ngha, nguyen nhan, ac iem.

    1. nh ngha:Dao ong tat dan la dao ong co bien o giam dan theo thi gian.

    2. Nguyen nhan:Trong thc te cac vat eu dao ong trong mot moi trng xac nh nen cac tac dung ma

    sat cua moi trng o. Do phai thc hien cong e thang ma sat nen nang lng he c giam danlam cho bien o giam dan va cuoi cung vat dng lai v tr can bang.3. ac iem: Lc ma sat nho th dao ong tat dan cham.V du: con lac ao ong trong khong kh.

    Lc ma sat ln th dao ong tat dan nhanh.V du: con lac dao ong trong nc.

    Lc ma sat qua ln th con lac khong dao ongV du: con lac dao ong trong nht.

    Cau 14:- Trnh bay ve dao ong cng bc. Bien o dao ong cng bc phu thuoc vao yeu tonao?- S cong hng c hoc la g? Neu mot v du ve cong hng co li va co hai- Hay cho biet cac iem giong nhau va khac nhau gia dao rieng cng bc va s t dao ong.1. Dao ong cng bc:

    Thong thng, mot he dao ong chu tac dung lc ma sat cua moi trng nen sinh co ng

    am lam giam c nang va dao ong b tat an.Muon duy tr dao ong, ta tac dung len he mot ngoai lc bien thien tuan hoan: F =F0sin(wt + j) vi F0 la bien o cua ngoai lc; w la tan so goc

    Trong thi gian Dt rat ngan, dao ong cua he la mot dao ong phc tap do s tong hpcua dao ong rieng cua he va dao ong cua ngoai lc.

    Sau thi gian Dt, dao ong rieng tat han va he ch dao ong vi a so cua ngoai lc. o laao ong cng bc.

    a. nh ngha: Dao ong cng bc la dao ong gay ra bi mot ngoai lc bien thien tuanhoan F = F0sin(wt + j) goi la lc cng bc.

    x

    t

    x

    t

    x

    t

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    b. ac iem: Co tan so bang tan socua ngoai lc Co bien o phu thuoc s chenh lech gia tan so f cua lc cng bc va tan so dao

    ong rieng f0 cua he ao ong.2. Cong hng c:

    a. nh ngha: S cong hng la hien tng bien o cua dao ong cng bc tang otngot khi a socua lc cng bc xap x bang tan so rieng cua he dao ong.

    b. Th du ve cong hng:v Cong hng co li: Mot em nho cung co the a vong cho mot ngi ln len rat cao.

    Neu em tac dung len vong mot ngoai lc co tan so f0 gan bang ung tan so rieng f0cua vong, ngha la lc keo cua tay an nhp vi nhp ong a cua vong, sau motthi gian, bien o dao ong cua vong rat ln. Neu muon dng sc e ay vong motlan len cao nh vay, em nho se khong lam c.

    v Cong hng co hai: Chiec cau, be may, khung xe,... la nhng he thong dao ong cotan so rieng. Neu e chung dao ong cng bc vi mot vat dao ong khac at lenchung (v du: mot may phat ien ln), chung co the rung len rat manh va co the bgay.

    3. iem giong nhau va khac nhau gia dao ong cng bc va s t dao ong:v Giong nhau: Duy tr dao ong lau nh c bu nang lng (e thang lc ma sat)v Khac nhau: S t dao ong khong can tac dung cua ngoai lc trong khi dao ong cng

    bc la do ngoai lc tac dung.

    Cau 15:- Neu nguyen nhan e dao ong khong tat dan.- Neu bien phap ky thuat e duy tr dao cong cua con lac ong ho va bien phap k thuat lam cho

    dao ong khung xe oto chong tat.1. DAO ONG DUY TR:

    a. nh ngha: Dao ong co bien o khong thay oi theo thi gian gi la dao ong duy trcon goi la t dao ong.

    b. Nguyen tac duy tr dao ong: la phai tac dung vao con lac mot lc tuan hoan co tanso bang tan so rieng cua con lac.

    Lc tuan hoan nho khong lam bien oi tan sorieng cua con lac, lc cung cap nang lng chocon lac trong moi na chu ky e bu ap nang lng mat i do ma sat.2. NG DUNG:

    a. Bien phap ky thuat e duy tr dao ong cua con lac ong ho: La len day cot cuaong ho. Khi len day cot la ta cung cap mot the nang an hoi cho con lac. Sau o moi khi con lacat ti bien o sau mot na chu ky th ay cot dan ra mot chut va mot phan the nang cua no

    truyen cho con lac nh cac c cau thch hp.b. Bien phap ky thuat lam dao ong cua khung xe o to chong tat: Khi o to b xoc th loxo giam xoc b nen hay dan. e lam cho dao ong cua khung xe oto chong tat khi qua cho b xocth ngi ta dung mot thiet b gom piston chuyen ong theo chieu thang ng trong mot xylanhcha ay dau nht. Piston gan vi khung xe, xylanh gan vi truc banh xe. Khi khung xe dao ongtren lo xo giam xoc th piston cung dao ong trong xylanh va nh dau nht dao ong trong khungxe chong tat.

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    SONG C VA AM HOC

    Cau 1 : Song c hoc la g? Giai thch s tao thanh song tren mat nc. V sao qua trnh truyensong la mot qua trnh truyen nang lng. Thanh lap phng trnh dao ong cua mot iem trenphng truyen song?

    1. NH NGHA SONG: Song c hoc la nhng dao ong an hoi lan truyen trong moi trngvat chat theo thi gian.2. GIAI THCH S TAO THANH SONG TREN MAT NC: Hien tng song nc:

    - Nem hon a nho xuong ho nc yen lang ta thay xuat hien nhng song nc hnh tron tni hon a ri lan rong ra tren moi trng nc vi bien o giam dan

    - Cai phao nhap nho theo song nhng khong truyen i. Giai thch:

    Gia cac phan t nc co lc tng tac nen khi mot phan t M ao ong va nho len caoth cac lc tng tac keo cac phan t ke can nholen theo nhng cham hn mot chut, cac lc o

    cung keo M ve can bang. Ket qua la dao ong lan rong ra tren moi trng nc.Phao ch nhap nho theo song ma khong truyen i la v trong moi trng truyen song thtrang thai dao ong truyen i con phan t vat chat cua moi trng ch dao ong quanh v tr canbang cua no.3. GIAI THCH V SAO QUA TRNH TRUYEN SONG LA MOT QUA TRNH TRUYENNANG LNG: Nang lng truyen song tai mot iem t le vi bnh phng cua bien o song tai o. V

    vay song truyen en iem nao th lam cho cac phan t vat chat cua moi trng tai iemo dao ong vi mot bien o nhat nh tc la truyen cho cac phan t o mot nang lng.Do o qua trnh truyen song cung la mot qua trnh truyen nang lng.

    Theo nh luat bao toan nang lng th nang lng song truyen i t nguon do phai trairong ra cho cac phan t cua moi trng nen nang lng song cang xa nguon cang nho.

    4. LAP PHNG TRNH DAO ONG CUA MOT IEM TREN PHNG TRUYENSONG:

    Do song truyen i theo moi phng nh nhau nen ta ch xet mot phng truyen song Ox.Xet iem M tren phng truyen song Ox cach nguon song O mot khoang OM = x.

    Phng trnh nguon song O: u0 = asin2pft Phng trnh song tai M: u(M) (t) = u(t - q) vi q = x

    v

    uM = asin2pf(t -x

    v) = asin(2pft 2 x

    v

    f

    p ) V l = vf

    uM = asin(2pft -2 xpl

    )

    Cau 2: Neu cac nh ngha: cua song c hoc, song doc, song ngang, cac song ket hp s giaothoa cua cac song, song dng, chu ky cua song, tan so cua song, bc song, van toc truyen song,bien o song. nh ngha 2 dao ong lech pha, cung pha, ngc pha1. NEU CAC NH NGHA: Song c la nhng dao ong an hoi lan truyen trong moi trng vat chat theo thi gian. Song ngang la song co phng dao ong vuong goc vi phng truyen song. Song doc la song co phng dao ong trung vi phng truyen song. Song ket hp la cac song co cung phng, cung tan sova co o lech pha khong oi.

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    S giao thoa cua song la s tong hp cua hai hay nhieu song ket hp trong khong gian, trong oco nhng cho conh ma bien o song c tang cng hay giam bt.

    Song dng la song co cac nut va cac bung co nh trong khong gian. Chu ky T cua song la chu ky dao ong chung cua cac phan t vat chat co song truyen qua va

    bang chu ky dao ong cua nguon song. Tan so f cua song la tan so dao ong chung cua cac phan t vat chat co song truyen qua va

    bang tan sodao ong cua nguon song. Bc song l la khoang cach gan nhat gia hai iem dao ong cung pha (hay ngc pha) tren

    cung mot phng truyen song, no cung la quang ng ma song truyen i c trong mot chuky cua song.

    Van toc truyen song v la van toc truyen pha dao ong Bien o song A tai mot iem la bien o dao ong cua cac phan t vat chat tai iem o khi

    song truyen qua.

    Lien he gia T, f, v va l la: l = v.T = vf

    2. THE NAO LA HAI DAO ONG LECH PHA, CUNG PHA, NGC PHA: Hai dao ong lech pha la hai ao ong co o lech pha khong oi va khac khong Hai dao ong cung pha la hai dao ong co o lech pha bang 0 hay bang k2p Hai dao ong ngc pha la hai dao ong co o lech pha bang p hay bang (2k + 1)p Khi Dj = j1 - j2 > 0 th dao ong 1 sm pha hn dao ong 2 hay dao ong 2 tre pha hn dao

    ong 1 .

    Cau 3: nh ngha o lech pha gia hai song. Chng minh rang o lech pha la yeu to quantrong trong viec giai thch hien tng giao thoa song nc.1. nh ngha o lech pha gia hai song:

    o lech pha la ai lng ac trng cho s khac nhau ve trang thai gia hai hai dao ongva c xac nh bang hieu cac pha ban au: Dj = j1 - j2

    2. Vai tro o lech pha gia 2 song trong viec giai thch hien tng giao thoa:* Phng trnh song tai M do hai nguon ket hp S1, S2 tao ra lan lt la:

    U1M = a sin (2pft - 12 dp

    l) v U2M = a sin (2pft - 2

    2 dpl

    )

    * Phng trnh song tong hp tai M:

    uM = u1m + u2m uM = 2a cospl

    (d1 - d2)sin [2pft -pl

    (d1 + d2)]

    ay la mot dao ong ieu hoa co:

    Pha ban au: j = - pl

    (d1 + d2)

    Bien o: A = 2a 1 2cos (d d )p

    -

    V: Dj = j2M - j1M =2pl

    (d1 d2) (d1 d2) =2

    l Djp

    A = 2a cos2

    Dj

    Ta thay:Tai M hai song cung pha th Dj = k2p A = 2aTai M hai song ngc pha th Dj = (2k + l)p A = 0

    Vay trong hien tng giao thoa cua 2 song, o lech pha cua 2 song thanh phan tai iem haisong o gap nhau se quyet nh o ln cua bien o dao ong tong hp tai o.

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    Cau 4: Mo ta hai hien tng ac trng cua lu trnh truyen song: hien tng giao thoa va hien

    tng nhieu xa.1. HIEN TNG GIAO THOA CUA SONG NC:

    a. Th nghiem: Dung mot am thoa co motnhanh noi vi mau thep hnh ch U co hai au cham

    nhe vao mat nc tai S1 va S2. Khi am thoa rung cacvong tron song phat ra t S1 va S2 lan truyen tren matnc.

    Hai nguon S1 va S2 cung tan so, co o lech phakhong oi goi la hai nguon song ket hp. Hai song do chung tao ra goi la hai song ket hp. Trongvung giao nhau cua hai song ket hp.

    Trong vung giao nhau cua hai song ket hpxuat hien cac ng hyperbol co bien o cc ai, bieno bang khong nam xen ke nhau nhan S1, S2lam tieuiem goi la hien tng giao thoa song nc. Cacng hyperbol goi la van giao thoa song.

    b. Giai thch: Tai iem M trong vung giao thoa song t nguon S1 va S2 truyen en cophng trnh lan lt la:

    u1M = asin(2pft - 12 dp

    l) va u2M = asin(2pft - 2

    2 dpl

    )

    Phng trnh song giao thoa tai M:

    uM = u1M + u2M - a[sin(2pft - 12 dp

    l) + sin(2pft - 22 dp

    l)]

    uM = 2acos 1 2(d d )p -

    lsin[2pft - p

    l(d1 + d2)]

    Bien o song tai M: A = 2a 1 2(d d )

    cosp -

    l

    M la van cc ai: Amax 1 2(d d )cos cos k p - = pl

    1 2(d d ) kp - = pl

    (d1 d2) = kp M la van ng yen: A = 0 1 2(d d )cos cos(2k 1)

    2

    p - p= +

    l 1 2(d d ) (2k 1)

    2

    p - p= +

    l (d1 d2) = (2k+1)

    2

    p

    V:1 2

    d d- = hang sonen M tren ng hyperbol nhan S1, S2 lam tieu iem.

    c. ieu kien co hien tng giao thoa:- Hai song co cung tan so

    - Hai song co o lech pha khong oi theo thi gianCac song co tnh chat tren goi la song ket hp. Cac nguon tao ra song ket hp goi languon ket hp.2. HIEN TNG NHIEU XA:

    Khi gap mot chng ngai vat co kch thc nho so vi bc song th song co the i vongqua ve pha sau vat nh khong gap g ca. Neu vat can co kch thc ln hn so vi bc song thsong cung i vong qua vat nhng ngay pha sau vat co mot vung khong co song. Hien tng songi vong qua vat can goi la hien tng nhieu xa. Khi b nhieu xa cac tia song b uon cong i.

    S1

    S2

    f

    M

    S1 S2

    d2d1

    k = 3 2 1 0 -1 - 2 -3

    S2S1

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    Cau 5: Khai niem ve song dng. Giai thch cach hnh thanh song dng tren mot si day va neuieu kien e co song dng. Cach xac nh van toc truyen song bang hien tng song dng.1. KHAI NIEM VE SONG DNG:

    Khi mot song ti va song phan xa cua no truyen theo cung mot phng th chung giaothoa vi nhau. Ket qua la tren phng truyen song co nhng iem conh ma cac phan t vat

    chat tai o luon dao ong vi bien o cc ai (goi la bung) va nhng iem co nh khac ma cacphan t vat chat tai o luon ng yen (goi la nut). Cac ao ong nay tao thanh mot song khongtruyen i trong khong gian goi la song dng.

    Vay:Song dng la song co cac nut va bung co nh trong khong gian2. GIAI THCH CACH HNH THANH SONG DNG TREN MOT SI DAY VA NEU IEU KIENE CO SONG DNG:

    a. Cach hnh thanh song dng:Buoc au M cua si day co nh vao tng va cho au P

    dao ong.- Thay oi a so dao ong cua P en mot luc nao o ta

    thay si day dao ong on nh trong o co nhng cho dao ong rat

    manh va nhng cho hau nh khong dao ong.b. Giai thch: Dao ong truyen t A en B tren ay didang mot song ngang. en B song N Phan xa truyen ngc lai A.Song ti va song phan xa thoa man ieu kien song ket hp vangc pha nhau tai B (B co nh) hai song nay giao nhau tao nen song dng.

    Ket qua cho thay: A, B la hai iem luon ng yen, cac iem tren si day AB cach A va B nhng

    khoang bang mot so nguyen lan na bc song (k2

    l) luon luon ng yen (goi la cac nut cua song dng),

    cac iem tren AB nam cach A va B nhng khoang cach bang mot so le phan t bc song [(2k + 1)4

    l] th

    dao ong vi bien o cc ai (goi la cac bung cua song dng). Khoang cach gia 2 nut hay 2 bung lien

    tiep nhau la 2l . oi vi song doc tuy hnh anh song dng co khac nhng no van gom co cac nut va bung.

    Khoang cach gia hai nut tren tiep van bang2

    l

    c. ieu kien co song dng: e co song dng vi hai iem nut hai au day phai co ieu kien:

    l= Zl lk ( )vi

    2la chieu dai day

    e co song dng vi mot nut au nay va mot bung au kia phai co ieu kien:(2k 1) (k Z)

    4l

    = + l

    3. CACH XAC NH VAN TOC TRUYEN SONG BANG HIEN TNG SONG DNG:Hien tng song dng cho phep ta a c bc song 1 mot cach chnh xac. oi vi song

    am va cac song khac, viec do tan so f cung n gian. Biet l va f ta xac nh van toc truyen songtheo he thc: v = lf

    V du: Vi mot si day an hoi co hai au co nh. Quan sat song tren day ta em c so

    bang (k). Biet chieu dai l cua si day ta thay: 2k2 kl

    = l =l

    l Vay: v = lf = 2 fkl

    AB

    2

    Hnh ve co: 4 bung, 4 nut va 3 bo song

    4

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    Cau 6: The nao la dao ong am va song am? Moi trng truyen am va van toc am, vai tro cua

    bau an va cac day an cua chiec an ghi - ta.

    1. DAO ONG VA SONG AM:a. Song am: La cac song doc c hoc truyen trong cac moi trng kh, long hay ran.

    Song am nghe c co tan so nam trong khoang t 16Hz en 20.000HzSong am co tan so nho hn 16Hz goi la cac song ha am. Song am co tan so ln hn20.000Hz goi la cac song sieu am. Tai ta khong nghe c ha am va sieu am.

    b. Dao ong am: La cac dao ong c hoc cua cac vat ran, long, kh v.v co tan so namtrong khoang noi tren.

    Cac vat co dao ong am, co kha nang tao ra song am trong moi trng bao quanh goi lacac vat phat dao ong am.2. MOI TRNG TRUYEN AM - VAN TOC AM:

    a. Moi trng truyen am: Song am truyen c truyen ca ba moi trng ran, long vakh, nhng khong truyen c trong chan khong.

    b. Van toc truyen cua song am: Phu thuoc vao tnh an hoi va mat o cua mi trng: Van toc am trong chat ran ln

    hn trong chat long va trong chat long ln hn trong chat kh Van toc am thay oi theo nhiet o Nhng vat lieu nh bong, nhung, tam xop v.v truyen am kem v tnh an hoi cua

    chung kem. Chung c dung e lam cac vat lieu cach am.3. VAI TRO CUA DAY AN VA BAU AN TRONG CHIEC AN GHI TA:

    Trong an ghi ta cac day an ong vai tro vat phat dao ong am. Dao ong nay thong qua gia, ay an gan tren mat bau an se lam cho mat bau an ao ong.

    Bau an ong vai tro hp cong hng co kha nang cong hng oi vi nhieu tan so khacnhau va tang cng nhng am co cac a soo.

    Bau an ghi ta co hnh dang rieng va lam bang go ac biet nen no co kha nang conghng va tang cng mot sohoa am xac nh, tao ra am sac ac trng cho loai an nay.

    Cau 7: Nhng ac trng sinh ly cua am va s phu thuoc cua chung vao nhng ac trng vat lcua am1. O CAO CUA AM: la mot ac trng sinh l cua am, phu thuoc vao ac tnh vat ly cua am ola tan so. Am co tan socang ln th cang cao (cang thanh) Am co tan socang nho th cang thap (cang tram)

    2. AM SAC: Moi ngi, moi nhac cu phat ra nhng am thanh co sac thai khac nhau (du cung mot cao o)

    ma tai co the phan biet c. ac tnh o c goi la am sac. Th nghiem cho biet neu nhac cu va ngi phat ra cung mot am co tan so f1 th ong thi

    cung phat ra cac am co tan so f2 = 2f1, f3 = 3f1, ... am co a so f1 la am c ban, am co tanso f2, f3 goi la cac hoa am th 2, th 3,.. Do o, am phat ra la s tong hp cua cac am cban va cac hoa am cua no (vi cac bien o khac nhau) nen ng bieu dien cua no codang phc tap nhng chu ky nhat nh va moi dang tao ra mot am sac nhat nh.

    Vay am sac la mot ac trng sinh ly cua am, no phu thuoc vao ac tnh vat ly cua am latan sova bien o cua am c ban va cac hoa am cua no.

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    3. O TO CUA AM:a. Nang lng am:Song am mang theo nang lng truyen i t nguon am en tai ngi nghe. Nang lng

    nay t le vi bnh phng bien o song. Cng o am la nang lng am c song am truyentrong mot n v thi gian qua mot n v dien tch at vuong goc vi phng truyen am, ky hieuI, n v W/m2.

    b. o to cua am: Muon gay cam giac am, cng o am phai ln hn mot gia tr cc tieu nao o c

    goi la ngng nghe. Ngng nghe phu thuoc vao a so am. o to cua am la mot ac tnh sinh ly cua am, no phu thuoc vao cng o cua am va

    tan socua am.V du:- Vi am co tan sof t 1000Hz 1500Hz th ngng nghe I0 = 10-12W/m2- Vi am co tan sof = 1000Hz th ngng nghe I0 = 10-7W/m2

    - Vi am co tan so 1000Hz co cng o I = 10-7W/m2 ln gap 105 lan ngng nghe la motam kha to nghe rat ro. Vi mot am co tan sof = 50Hz cung co cng o 10-7 W/m2 th ch miva bang ngng nghe I0 cua no nen ch hi nghe. o to cua am con phu thuoc vao tan soam.

    Tai nghe tnh nhat oi vi cac am co tan so trong khoang 1000Hz en 5000Hz va ngheam co tan socao (am cao) thch hn am co tan sothap (am tram). Neu cng o am len ti 10W/m2 th oi vi moi tan so eu gay ra cam giac cho tai,

    gia tr nay goi la ngng au. Mien nam gia ngng nghe va ngng au la mien nghe c.c. Mc o am:

    e ac trng cho o to cua am ta thng dung mot ai lng la mc cng o am (k hieu L).Mc cng o am la logarit thap phan cua t socng o am va ngng nghe.

    L(B) =0 0

    I Ilg ;L(dB) 10 lgI I

    =

    n v la Ben (B) hay exiben (dB), 1dB = 1 B10

    Cau 8:* Van toc truyen am trong khong kh 350C va 200C co khac nhau khong? Tai sao.* So sanh van toc truyen am trong kh oxy va kh hidro cung nhiet o. Giai thch.* Thay oi o cang day an hoi th bc song cua song dng co oi khong. Tai sao (cho tan so

    song dng khong oi).

    1. Van toc truyen am trong khong kh 350C va 200C khac nhau v van toc truyen am

    thay oi theo nhiet o (van toc t le can bac 2 cua nhiet o tuyet oi).2. Van toc truyen am t le nghch vi khoi lng phan t cua chat kh. Ta thay kh hydroco khoi lng phan t nho hn oxy nen van toc truyen am trong hydro nhanh hn.

    3. Theo cong thc Melde :T

    v =m

    vi T la lc cang day va m la khoi lng cua mot n

    v chieu dai day. Vay khi lc cang T oi th van toc v oi. V v = lf bc song l oi.

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    DONG IEN XOAY CHIEU

    Cau 1 :1. Nguyen tac tao ra dong ien xoay chieu. Hieu ien the va cng o dong ien xoay chieu.

    2. The nao la cng o dong ien hieu dung, hieu ien the hieu dung? V sao oi vi dongien xoay chieu ngi ta s dung cac ai lng nay?

    1. NGUYEN TAC TAO RA DONG IEN XOAY CHIEUNguyen tac tao ra dong ien xoay chieu da

    tren hien tng cam ng ien t.Cho mot khung day kim loai co N vong

    day, co dien tch S quay vi van toc goc w khongoi trong t trng eu B

    ursao cho truc xoay xx

    vuong goc vi ng cam ng cua t trng.v Luc t = 0: Phap tuyen nr cua khung day

    trung phng chieu cua t trng Bur

    .v Luc t : Phap tuyen nr hp vi vect Bur

    mot goc (wt).- Khi o t thong qua khung day la : F = NBScoswt.- Theo nh luat cam ng ien t trong khung day xuat hien S cam ng :

    E = -F = wNBSsinwtat Eo = NBSw : Bien o suat ien ong hay suat ien ong cc ai. e = EosinwtVay : Suat ien ong cam ng trong khung day la ai lng bien oi ieu hoa c goi la

    suat ien ong xoay chieu.Noi hai au khung day vi mach ngoai th trong mach ngoai co mot dong ien xoay

    chieu.2. HIEU IEN THE XOAY CHIEU VA CNG O DONG IEN XOAY CHIEU

    - V suat ien ong xoay chieu bien thien ieu hoa vi tan so goc w nen hieu ien the mano gay ra mach ngoai cung bien thien ieu hoa vi tan sogoc w.u = Uosin(wt + ju)

    - Dong ien xoay chieu trong mach ngoai cung bien thien ieu hoa vi tan so goc w.i = Iosin(wt + ji) trong o ju = ji + j

    j la goc lech pha gia u, i va no tuy thuoc tnh chat cua mach ien. V ien trng truyentrong day dan co van toc vao khoang 3.108 m/s nen moi thi iem nhat nh ien trng moiiem tren mach noi tiep la nh nhau, do o cng o dong ien moi iem tren mach noi tiep lanh nhau.3. CNG O HIEU DUNG VA HIEU IEN THE HIEU DUNG

    Cho mot dong ien xoay chieu i = Iosinwt chay qua ien tr thuan R trong thi gian t thnhiet lng toa ra tren ien tr la :22

    0 0I IQ R t R t2 2

    = =

    Bay gi cho dong ien khong oi co cng o I chay qua ien tr thuan R nh tren saocho cung trong thi gian t th nhiet lng toa ra cung la : Q = RI2t

    So sanh : I = 0I2

    Br

    x

    x'

    t = 0t

    OBr

    nr

    nr wt

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    Vay: Xet ve tac dung nhiet trong mot thi gian dai th dong ien xoay chieu

    i = Iosinwt tng ng vi dong ien khong oi I = 0I2

    . Cng o dong ien I goi la cng o

    hieu dung cua dong ien xoay chieu.nh ngha : Cng o hieu dung cua dong ien xoay chieu bang cng o cua mot dong

    ien khong oi ma neu chung lan lt i qua cung mot ien tr trong cung mot thi gian th toa racung mot nhiet lng.

    Tng t suat ien ong hieu dung va hieu ien thehieu dung lan lt la:0 0E UE ; U2 2

    = =

    4. LY DO S DUNG CAC GIA TR HIEU DUNG CUA CNG O DONG IEN XOAYCHIEU VA HIEU IEN THE XOAY CHIEU

    Vi dong ien xoay chieu, ta khong the xac nh cng o tc thi cua no v no bien oirat nhanh cung nh khong the lay gia tr trung bnh cua cng o v trong chu ky gia tr nay bangkhong. Ta cung khong the dung ampe ke hay von ke khung quanh e o cng o hay hieu ienthe xoay chieu, v moi khi dong ien oi chieu th chieu quay cua kim cung thay oi nhng doquan tnh ln cua kim va khung day nen kim khong theo kp s oi chieu nhanh cua dong ienva kim se ng yen.

    Vi dong ien xoay chieu, ta khong can quan tam tac dung tc thi cua no tng thiiem ma ch quan tam tac dung cua dong ien xoay chieu trong thi gian dai. Mat khac, tacdung nhiet cua dong ien th t le vi bnh phng cua cng o dong ien, khong phu thuocchieu dong ien; do o co the so sanh dong ien xoay chieu vi dong ien khong oi gay ra tacdung nhiet tng ng.

    o la cac ly do e a ra khai niem cua cng o hieu dung cua dong ien xoay chieu.

    Cau 2 :1. Trnh bay cong suat cua dong ien xoay chieu.

    Xet cac trng hp rieng :- Mach ch co R.- Mach ch co C.- Mach ch co L.- Mach RLC mac noi tiep trong ieu kien co cong hng ien.

    2. Neu y ngha cua he socong suat.3. V sao khi chetao cac dung cu ien nh quat, tu lanh, ong c ngi ta co gang tang he

    so cong suat.1. CONG SUAT CUA DONG IEN XOAY CHIEU

    at mot hieu ien the xoay chieu 2 au mot oan mach. Dung von ke, ampe ke, watt

    ke e o hieu ien the hieu dung U 2 au oan mach; cng o hieu dung I cua dong ien quamach; cong suat tieu thu P cua oan mach th thay :* Neu oan mach ch co ien tr thuan th : P = UI.* Neu oan mach co them cuon cam hay tu ien hay ca hai th : P < UI.* Cac ket qua o cho ta : P = UI vi K 1.* Thc nghiem cho thay gia he so K va goc lech pha j (cua u va i) co moi lien he : k =

    cosj.

    Vay : P = UIcosj cosj : goi la he socong suatR

    cosZ

    j =

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    Ta xet cac trng hp rieng :* Vi mach ch co R : cosj = 1 P = UI* Vi mach ch co C : cosj = 0 P = 0* Vi mach ch co L : cosj = 0 P = 0* Vi mach RLC mac noi tiep trong ieu kien co cong hng :

    ZL = ZC cosj = 1 P = UI2. Y NGHA CUA HE SO CONG SUATKhi U va I co mot gia tr nhat nh th t P = UIcosj, ta thay P cang ln khi cosj cang ln.

    * cosj = 1 j = 0 : ay la trng hp oan mach ch co R hay oan mach co RLCmac noi tiep trong ieu kien cong hng.

    Khi o cong suat tieu thu tren oan mach ln nhat va bang UI.

    * cosj = 0 j =2p

    : ay la trng hp oan mach ch co C hay L, hay co L, C.

    Khi co cong suat tieu thu tren oan mach nho nhat va bang khong.Luc nay nguon ien co the cung cap cho oan mach mot cong suat kha ln tc la U va I cua

    oan mach kha ln, nhng oan mach van khong tieu thu mot phan nao cua cong suat o, congha la dong ien khong co hieu qua co ch trong khi co mot phan nho cua cong suat van b hao

    ph vo ch tren ng day ien truyen tai.* 0 < cosj < 1 tc la

    2p

    - < j < 0 hay 0 < j 0,85).

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    Cau 3 :1. Trnh bay nguyen tac hoat ong, cau tao va bieu thc suat ien ong cua may phat ien

    xoay chieu 1 pha.2. Trnh bay nguyen tac cau tao va hoat ong cua may phat ien xoay chieu 3 pha. V sao

    dong ien xoay chieu lai c s dung rong rai trong thc te.

    1. MAY PHAT IEN XOAY CHIEU 1 PHAa. Nguyen tac hoat ongMay phat ien xoay chieu kieu cam ng hoat ong da vao hien tng cam ng ien t.Cho khung day kim loai co N vong day co dien

    tch S quay vi van toc goc w khong oi trong mottrng eu B sao cho truc quay cua khung day vuonggoc ng cam ng cua t trng.

    Khi o t thong qua khung day dao ong ieuhoa lam phat sinh trong khung day mot suat ien ongxoay chieu.

    Suat ien ong trong mot khung day la rat nho.

    e co suat ien ong u ln dung c trong congnghiep va i song, ngi ta bo tr trong may phat ien nhieu cuon day dan, moi cuon gom nhieuvong day va nhieu nam cham ien tao thanh nhieu cap cc N S khac nhau. Cac cuon day trongmay phat ien c mac noi tiep nhau va hai au c noi vi mach tieu thu bang mot c caurieng goi la bo gop.

    b. Cau tao- Bo gop la he thong vanh khuyen choi quet : hai vanh khuyen at ong truc vi khung

    day va cung quay vi khung day. Noi au day A vi vanh khuyen 1 va au day B vi vanhkhuyen 2. Hai choi quet a, b co nh t len 2 vanh khuyen va c noi vi mach ngoai. Khikhung day quay, hai vanh khuyen trc tren hai choi quet va dong ien t khung day chuyen qua

    vanh khuyen, choi quet ra mach ngoai.- Phan cam tao ra t trng: trong may phat ien nho, phan cam la nam cham vnh cu;trong may phat ien ln, phan cam la nam cham ien.

    - Phan ng tao ra dong ien.- Cac cuon day cua phan cam va phan ng eu quan tren loi lam bang thep Silic e tang

    cng t thong qua cuon day. e tranh dong Foucault cac loi c ghep bang nhieu tam thepmong cach ien vi nhau.

    - Phan cam va phan ng co the la bo phan ng yen hay bo phan chuyen ong cua may.Bo phan ng yen goi la stato, bo phan chuyen ong goi la roto.

    - Goi p la so cap cc cua phan cam va quay vi van toc quay n (vong/s) th tan so dongien phat ra la: f = np

    c. Bieu thc suat ien ong- Luc t = 0 gia s phap tuyen nr cua khung day trung vi t trng B

    r.

    - Luc t 0 th nr quay vi mot goc wt va t thong bien oi qua khung day la :F = NBScoswt

    - Theo nh luat cam ng ien t trong khung xuat hien suat ien ong cam ng tc thi :e = -F = NBSwsinwt at Eo = NBSw e = EosinwtKhi o gia hai au A, B cua khung xuat hien hieu ien the tc thi :

    u = e = Uosinwt

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    2 CAU TAO VA HOAT ONG CUA MAY PHAT IEN XOAY CHIEU 3 PHAa. nh nghaDong ien xoay chieu ba pha la he thong gom ba dong ien xoay chieu mot pha, 3 dong

    ien nay tao bi 3 suat ien ong co cung bien o, cung tan so nhng lech nhau ve pha mot goc

    bang23p

    rad hay 120o tc la lech nhau ve thi gian13

    chu ky.

    b. Cau tao : gom 2 phan- Phan cam (Roto) la nam cham ien.- Phan ng (Stato) gom 3 cuon day giong nhau c at lech

    nhau 120o tren vong tron.c. Hoat ongKhi Roto quay, vao luc cc N oi dien vi 1 cuon 1 th t

    thong qua cuon 1 cc ai. Roto quay them 120o hay tnh ve thi gian

    laT3

    th t thong qua cuon 2 cc ai va sau thi gian13

    na th t

    thong qua cuon 3 cc ai. Nh vay t thong qua cac cuon day lech nhau13

    chu ky ve thi gian

    hay lech nhau 120o ve pha. Do o suat ien ong trong 3 cuon day cung lech nhau 120o.Neu noi cac au day cua 3 cuon vi 3 mach ngoai giong nhau th 3 dong ien trong 3

    mach cung lech pha nhau la 120o :i1 = Iosinwt

    i2 = Iosin2t3p w -

    i3 = Iosin4t3p w -

    d. Ly do s dung rong rai dong ien xoay chieu

    - oi vi cac ng dung thc tien nh thap sang, un nau, chay cac may quat, may cong cuth dong ien xoay chieu cung cho ket qua tot nh dong ien khong oi.- Dong ien xoay chieu de san xuat hn (may phat ien xoay chieu co cau tao n gian

    hn may phat ien mot chieu).- Dong ien xoay chieu co the tai i xa c vi hao ph t va chi ph nho va viec phan

    phoi ien cung thuan tien hn nh may bien the.- Khi can co dong ien mot chieu, ngi ta co the chnh lu do ng ien xoay chieu e tao

    ra dong ien mot chieu.- Dong ien xoay chieu de tang hay giam hieu ien thenh may bien thehn so vi dong

    ien mot chieu.- Dong ien xoay chieu co the cung cap mot cong suat rat ln.- oi vi dong ien xoay chieu 3 pha con co them u iem :

    * Co cach mac day tiet kiem : hnh sao, tam giac.* Tao t trng quay e van ong ong c khong ong bo 3 pha.

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    Cau 4 : Cach mac mach ien 3 pha. Dong ien 3 pha co u iem g so vi dong ien 1 pha.1. CACH MAC MACH IEN 3 PHA

    a. Cach mac hnh saoBa iem au cua 3 cuon day noi vi nhau va a ra ngoai bang 1 day trung hoa, ba iem

    cuoi a ra ngoai bang 3 day khac nhau goi la 3 day pha.

    - Tai tieu thu thng c noi vi mot day trung hoa (day nguoi) va mot day pha (daynong).

    Cng o dong ien tren day trung hoa : i = i1 + i2 + i3- Neu tai oi xng tc la tai tieu thu tren 3 mach ngoai bang nhua th i = 0.- Neu tai khong oi xng th i 0 nhng thng rat nho => day trung hoa thng nho hn

    day pha v no tai dong ien nho hn.b. Cach mac tam giac- iem cuoi cua cuon day 1 c noi vi iem au cua cuon day 2, iem cuoi cua cuon

    day 2 noi vi iem au cua cuon 3 va iem cuoi cua cuon 3 noi vi iem au cua cuon 1.

    - Ba iem noi o c noi vi 3 mach ngoai bang 3 day pha. Cach mac nay can 3 tai tieuthu phai giong nhau (tai oi xng).

    - Ta co the mac mot tai hnh tam giac vao mot may phat ien mac hnh sao hay ngc lai.

    - Ngi ta chng minh c : d pU U 3= Ud la hieu ien the gia 2 day pha.Up la hieu ien the gia day trung hoa va day pha.

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    2. U IEM CUA DONG IEN 3 PHA SO VI DONG IEN MOT PHA- Bang cach mac hnh sao hay tam giac, ta tai c ba dong ien ma ch can ba day noi,

    do o tiet kiem c day dan va hao ph ien nang tren day.- Tao ra t trng quay e s dung trong ong c khong ong bo ba pha la loai ong c

    co cong suat ln, de san xuat hn ong c dung dong ien mot pha, chieu quay cua chung co thethay oi de dang.Cau 5 : Trnh bay* Nguyen tac hoat ong cua ong c khong ong bo.* Nguyen tac cau tao cua ong c khong ong bo 3 pha.* u iem cua dong c khong ong bo 3 pha.* So sanh roto va stato cua may dao ien 3 pha va cua ong c khong ong bo ba pha.

    1. NGUYEN TAC HOAT ONGBien ien nang thanh c nang tren c s hien tng cam ng ien t va s dung t

    trng t trng quay.* Th nghiem :Quay eu mot nam cham ch U vi van toc goc w

    quanh truc xx th t trng Bur gia hai nhanh cua no cungquay eu vi van toc goc w.

    Khi o mot khung day at gia hai nhanh co truc quayla xx quay nhanh dan cung chieu quay cua nam cham va khiat ti van toc wo < w th gi nguyen van toc o. Ta noi khung day quay khong ong bo vi ttrng quay.

    * Giai thchKhi nam cham bat au quay (t trng quay) th t thong qua khung bien thien lam xuat

    hien dong ien cam ng.Theo nh luat Lenz, dong ien nay chong lai s bien thien cua t thong sinh ra no, ngha

    la chong lai s chuyen ong tng oi gia nam cham va khung day, do o lc ien t tac dunglen khung day lam khung quay cung chieu vi nam cham.

    Neu khung day at ti van toc w th t thong qua no khong bien thien na, dong ien camng mat i, lc t cung mat i, khung day quay cham lai nen thc te khung day ch at ti motvan toc goc on nh wo < w.

    Ta noi khung day quay khong ong bo vi nam cham.ong c hoat ong theo nguyen tac tren goi la ong c khong ong bo.

    2. T TRNG QUAY CUA DONG IEN 3 PHACho dong ien xoay chieu 3 pha i vao trong 3 cuon day

    dan giong nhau at lech nhau 120o tren mot vong tron.

    Gia s thi iem t = T4 th t trng cua cuon day 1

    co gia tr cc ai dng B01 va hng t trong ra ngoai cuon day.Khi o, t trng cua cuon day 2 va 3 co gia tr am.

    B2 = B3 = 01B2

    -

    Vay : T trng tong hp Bur

    cua 3 cuon day co hng

    trung vi t trng Bur

    tc la hng t cuon day 1 ra ngoai.

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    - Ly luan tng t, ta thay sau13

    chu ky th Bur

    hng t cuon day 2 ra va sau13

    chu ky

    na th Bur

    hng t cuon day 3 ra.- Tom lai, t trng tong hp B

    urcua 3 cuon day quay quanh tam O vi tan so bang tan so

    goc cua dong ien 3 pha.3. CAU TAO CUA ONG C KHONG ONG BO BA PHA

    * Gom 2 phan chnh :- Stato gom 3 cuon day giong nhua quan tren loi sat lech nhau 120o tren mot vong tron etao ra t trng quay.

    - Roto la hnh tru co tac dung nh mot cuon day quan tren loi thep.Khi mac ong c vao mang ien 3 pha th t trng quay do Stato gay ra lam cho Roto

    quay quanh truc. Chuyen ong quay cua roto c truc may truyen ra ngoai va c s dung evan hanh cac may cong cu 4. U IEM CUA ONG C KHONG ONG BO BA PHA

    - Cau tao n gian, de che tao.- S dung tien li, khong can vanh khuyen, choi quet.- Co the thay oi chieu quay de dang.

    5. SO SANH ROTO VA STATO CUA MAY PHAT IEN XOAY CHIEU 3 PHA VA O NGC KHONG ONG BO 3 PHA

    - Stato cua may phat va cua ong c giong nhau : gom 3 cuon day dan giong nhau quantren loi sat at lech nhau 120o tren vong tron.

    - Roto khac nhau : Roto cua may phat la nam cham ien, con cua ong c la hnh tru cotac dung nh mot cuon day quan tren loi thep.

    Cau 6 : May bien the* nh ngha va cau tao* Nguyen tac hoat ong, s bien oi hieu ien the va cng o dong ien qua may bien the.

    * Cong dung cua may bien the.

    1. NH NGHABien the la mot thiet b dung e thay oi hieu ien thecua dong ien xoay chieu.

    2. CAU TAO- Mot loi thep ky thuat do nhieu la thep mong hnh

    khung ch nhat ghap sat va cach ien vi nhau (e tangien tr cua loi sat, tranh c hao ph do dong ienphuco).

    - Hai cuon day ong quan tren loi thep: cuon s

    cap n1 vong la cuon mac vao mang ien xoay chieu; cuonth cap nhieu vong la cuon noi vi tai tieu thu.3. NGUYEN TAC HOAT ONG

    - Hoat ong cua may bien the da tren hien tng cam ng ien t.- Khi cuon s cap c mac vao nguon ien xoay chieu th dong ien trong cuon s cap

    lam phat sinh mot t trng bien thien trong loi thep.- T thong bien thien cua t trng o truyen qua cuon th cap. Neu mach th cap noi vi

    tai th trong tai co dong ien cam ng.

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    4. S BIEN OI HIEU IEN THE VA CNG O DONG IENa. Hieu ien the- Goi n1, e1, u1, i1 la so vong day, suat ien ong, hieu ien the, cng o dong ien cua

    cuon s cap. Goi n2, e2, u2, i2 la so vong day, suat ien ong, hieu ien the, cng o dong iencua cuon th cap.

    - Theo nh luat cam ng ien t : e1 = -F1 = -n1d

    dt

    F va e2 = -F2 = -n2

    d

    dt

    F

    - Theo nh luat Ohm : u1 = e1 vi r1 = 0

    - Khi mach th cap h : u2 = e2. 1 1 12 2 2

    u e nu e n

    = = 1 12 2

    U nU n

    =

    - Neu n1 > n2 U1 > U2 : may ha the- Neu n1 < n2 U1 < U2 : may tang the.

    b. Cng o dong ienNeu bo qua hao ph nang lng trong may bien the th cong suat trong mach s cap va th

    cap bang nhau : P1 = P2 U1I1 = U2I2 = =1 2 22 1 1

    I U nI U n

    Vay :Dung lam may bien the lam hieu ien the tang bao nhieu lan th cng o dong iengiam bay nhieu lan va ngc lai.5. CONG DUNG:

    May bien the dung e tao hieu ien the thch hp trong sinh hoat, trong ky thuat va nhat lae truyen tai ien nang i xa vi hao ph nho.

    Cau 7 : Vai tro cua may bien the trong viec van tai ien nang i xa va s dung ien.

    1. CONG SUAT HAO PH TREN NG DAY TAIKhi a dong ien t nha may en ni tieu thu (thng rat xa) se phai mat nang lng

    hao ph tren ng day toa nhiet. Goi P la cong suat cung cap cua nha may.Goi U la hieu ien the hai au ng day.

    - Cng o dong ien tren ng day : I =PU

    - Cong suat hao ph tren ng day co ien tr R : P = RI2 = R2

    2

    PU

    Ta thay e giam cong suat hao ph tren ng day th :- Giam R tc la tang tiet dien day. Cach nay rat ton kem.- Tang U bang cach dung may bien the a hieu ien the nha may len rat cao. Gan en

    ni tieu thu lai giam hieu ien thetng bc en gia tr thch hp.

    2. S O HE THONG CHUYEN TAI VA PHAN PHOI IEN NANG

    Tangthe

    Hathe

    Hathe

    Hathe

    11 KV 110 V 35 KV 6 KV 220V

    Nha may ien

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    Cau 8:1. S can thiet cua dong ien mot chieu.

    2. Trnh bay phng phap chnh ludong ien xoay chieu bang diod.3. u iem va nhc iem cua phng phap nay.

    1. S CAN THIET CUA DONG IEN MOT CHIEUMot songanh ky thuat sau ay van phai dung dong ien mot chieu :- Ma ien, uc ien, vo tuyen ien, nap ien cho acquy, san xuat hoa chat, tinh che kim

    loai- ong c ien mot chieu v chung co u iem hn ong c ien xoay chieu cho co

    moment khi ong ln va thay oi c van toc de dang.- Mot so mach ien t hoac mot sobo phan can ien ap mot

    chieu.2. PHNG PHAP CHNH LU BANG DIOD

    a. Chnh lu na chu ky :- Trong na chu ky au cua dong ien xoay chieu th A la

    cc dng, B la cc am: dong ien truyen t A qua dido D, qua Rve B.

    - Trong na chu ky sau cua dong ien xoay chieuth A la cc am, B la cc dng: khi o khong co dongien qua R.

    Vay dong ien qua R la dong ien 1 chieu nhapnhay co dang :

    b. Chnh lu 2 na chu ky- Trong na chu ky cua dong ien xoay chieu th A la cc dng, B la cc am: dong ien

    i t A ti M qua diod D1 ti N qua R ti Q qua diod D3 ti P roi ve B.

    - Trong na chu ky sau cua dong ien xoay chieu th A la cc am, B la cc dng: dongien i t B ti P qua diod D2 ti N qua R ti Q qua diod D4 en M roi ve A.Vay dong ien qua R cung la dong 1 chieu van con nhap nhay. e dong ien mot chieu bt

    nhap nhay, ta dung bo loc.

    3. U VA NHC IEM CUA PHNG PHAP CHNH LU* u iem :La phng phap kinh te, thiet b de che tao, t ton kem, gon, van chuyen de dang.Co the tao ra dong ien mot chieu cong suat ln.* Nhc iem :Dong ien mot chieu c tao ra van con nhap nhay. Ta co the lam giam

    s nhap nhay bang cach dung bo loc.

    R

    P n

    Io

    O

    i

    t

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    Cau 9 :1. Trnh bay nguyen tac cau tao va hoat ong cua may phat ien mot chieu.

    2. Tai sao phng phap chnh lu c dung pho bien hn may phat ien mot chieu.3. u iem va nhc iem cua phng phap nay.

    1. MAY PHAT IEN MOT CHIEUa. Cau taoMot khung day co the quay xung quanh truc oi xng cua no

    trong mot t trng eu vi van toc goc w khong oi sao cho truc vuonggoc t trng.

    Bo gop ien gom hai vanh ban khuyen va hai choi quet e layien ra mach ngoai.

    b. Hoat ongDa tren hien tng cam ng ien t. Khi t thong qua khung day bien thien ieu hoa th

    lam phat sinh trong khung mot suat ien ong cam ng cung bien thien ieu hoa. Dong ientrong khung la dong xoay chieu nhng do bo tr hai vanh ban khuye n, nen khi dong ien trong

    khung oi chieu th vanh ban nguyet oi chieu quet, nen choi a luon luon co dong ien i ramach ngoai va choi b luon luon co dong ien t mach ngoai i vao. Vay choi a la cc dng,choi b la cc am cua may phat ien mot chieu nay. Dong ien phat ra la dong nhap nhay :

    * Trong ky thuat may phat ien co nhieu khungday at lech nhau va mac noi tiep nhau tao ra dong ienmot chieu hau nh khong nhap nhay.

    * Neu cho dong ien mot chieu chay vao khungday th di tac dung cua lc ien t khung day se quay:may phat ien mot chieu tr thanh ong c ien motchieu.

    2. LY DO PHNG PHAP CHNH LU C DUNG PHO BIEN HN MAY PHATIEN MOT CHIEUSo vi may phat ien mot chieu, phng phap chnh lu c dung pho bien hn, v no co

    cac u iem :* La phng phap kinh te nhat, tien li nhat.* Thiet b chnh lu de chetao nhat, t ton kem, gon, van chuyen de dang.* Co the tao ra dong ien mot chieu co cong suat ln.Trong khi may phat ien mot chieu che tao phc tap, ton kem hn nen khong kinh te va

    khong tien li. Co gop thng xuyen co tia la ien, nen chong h hong va lam anh hng encac thiet b ien t khac lan can.

    Io

    O

    i

    t

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    DAO ONG IEN T SONG IEN T

    Cau 1 :1. Khao sat s bien thien cua ien tch tren 2 ban tu ien va s bien thien cua cng o dong

    ien trong mach dao ong.2. Khao sat nang lng ien t trong mach dao ong.V sao dao ong trong mach lai tat dan

    1. S BIEN THIEN IEN TCH VA DONG IEN TRONGMACH DAO ONG

    - Mach dao ong gom tu C mac noi tiep vi cuon cam L.- Noi K vi A th nguon ien P tch cho tu ien mot ien

    tch cc ai Qo.- Sau o noi K vi B th tu ien phong ien lam phat

    sinh dong ien i = q

    .Dong ien nay tang dan lam xuat hien trong cuon cammot suat ien ong t cam : e = -Li = -Lq

    - Ap dung nh luat Ohm : u - e = 0 u = +e = -LqVi u la hieu ien thegia 2 au cuon day, ong thi cung la hieu ien thegia 2 au tu

    ien nen :q

    uC

    = q

    Lq"C

    = - 1

    q" q 0LC

    + =

    at 21

    LCw = 2q" q 0+ w =

    - Phng trnh vi phan nay co nghiem : ( )oq Q sin t= w + j

    Phng trnh cho thay ien tch tu ien bien thien ieu hoa vi tan so goc w. V1LC

    w = ch phu thuoc vao ac tnh cua mach, nen dao ong ien trong mach goi la dao ong

    rieng.- Cng o dong ien :i = q = Qowcos(wt + j) = Iocos(wt + j)

    vi Io = Qow : cng o cc ai.

    Vay :Dong ien i cung bien thien ieu hoa vi tan so goc w nhng sm pha2p

    so vi ien

    tch.

    2. KHAO SAT NANG LNG IEN T TRONG MACH DAO ONGNang lng trong mach dao ong gom nang lng ien trng tap trung tu ien va nang

    lng t trng tap trung cuon cam.

    - Nang lng ien trng : ( )22

    20E

    Q1 qW . sin t2 C 2C

    = = w + j

    - Nang lng t trng : ( )2 2 2 2B 01 1

    W Li LQ cos cos t2 2

    = = w w + j

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    v 21

    LCw = ( )

    220

    B

    QW cos t

    2C= w + j

    - Nang lng cua mach dao ong :20

    E B

    QW W W W2C

    = + = =

    Vay :* Nang lng ien trng va nang lng t trng bien thien ieu hoa theo thi gian vi

    cung mot tan so, va tan sonay gap 2 lan tan so dao ong cua mach.* Nang lng cua mach dao ong la khong oi.* Trong mach dao ong luon luon co s chuyen hoa gia nang lng ien trng trong tu

    ien va nang lng t trng trong cuon day.3. NGUYEN NHAN TAT DAN CUA DAO ONG IEN T TRONG MACH DAO ONG

    Thc te cuon cam, day noi eu co ien tr R (du nho) lam tieu hao nang lng trongmach, ong thi mot phan nang lng cua mach b bc xa ra khong gian xung quanh di dangsong ien t lam nang lng cua mach dao ong giam dan, do o dao ong ien t trong machtat dan.Cau 2 : So sanh dao ong cua con lac lo xo va dao ong cua mach LC vecac mat : cac ai

    lng bien thien, phng trnh dao ong rieng, tan so dao ong rieng, nang ng dao ongrieng, tac nhan lam tat dao ong, ieu kien cong hng nhon.a. Ve cac ai lng bien thien- Cung bien thien ieu hoa vi cung tan so.* con lac lo xo : li o, van toc, gia toc.* mach LC : ien tch cua tu, cng o dong ien qua cuon cam, hieu ien the.b. Phng trnh dao ong rieng- Co cung mot dang :* con lac : x + w2x = 0 x = Asin(wot + j)* mach LC : q + w2oq = 0 q = Qosin(wt + j)

    c. Tan sodao ong rieng- eu ch phu thuoc cau tao cua he.

    * con lac : oKm

    w =

    * mach LC : o1LC

    w =

    d. Nang lng dao ong riengLa tong cua hai dang nang lng, cac dang nang lng eu bien thien tuan hoan vi cung

    tan sonhng tong co gia tr khong oi moi thi iem.

    * con lac : W = E + Et = 21 KA2

    * mach LC : W = WE + WB =20Q1 .

    2 C

    e. Tac nhan lam tat dan dao ongLam cho nang lng dao ong b tieu hao.* con lac : lc ma sat lam nang lng con lac chuyen hoa thanh nhiet.* mach LC : toa nhiet tren ien tr R cua cuon cam hoac s bc xa song ien t cua tu.

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    Cau 3 :1. Phat bieu 2 gia thiet cua Maxwell ve ien trng bien thien va t trng bien thien. ac

    iem cua ien trng xoay. The nao la dong ien dch?2. The nao la ien trng t trng.

    1. HAI GIA THUYET CUA MAXWELL VE T TRNG BIEN THIEN VA IENTRNG BIEN THIENa. Gia thuyet ve t trng bien thienMoi t trng bien thien theo thi gian eu lam xuat hien mot

    ien trng xoay, tc la mot ien trng ma cac ng sc bao quanhcac ng cam ng.

    b. Gia thuyet ve ien trng bien thienMoi ien trng bien thien theo thi gian eu lam xuat hien mot