bổ trợ kiến thức vật lí phần 2 điện xoay chiều chu văn biên

Tinh do lech pha ciia dien ap giua hai dau doan mach AB so voi dong dien qua mach va cong sua't tieu thu dien cua doan mach AB va doan mach X... Goi i la cuong do dong dien tuc thoi tron

T " ^—

5 A^T" CHU VAN BIEN

Gi^o vien chuong trinh bo tro Itien thurc V$t li 12,

kenh yffZ - Dai Truy^n hinh Viet Nam

Bo tra hion IMi « i i

LUYEN m DAI HOC IKEN KENHWi

PHAN LOAI VA fHUONG PHAP GlAl CAC BAI T O A N

CO BAN, DIEN HINH, HAY, LA VA KHO

• Danh cho ttn sinh lOp 12 On tap va thi Bai hqc, Cao dang

V' 0 Blen scan theo nOl dung va cau tnic 6& tN ciia BO GD E DT,

1 ,

NHA XUAT BAN DAI HOC QUOC GIA HA NQI

1) Quan he gia tri hieu dung

Mach chi c6 R thi u va i cung pha va R = ^ = ~ "

In

2 / A2

u U„

V i du 1 : Dat vao hai dau mot cuon cam thuan L mot dien ap xoay chieu c6 gia

tri hieu d u n g U khong doi va tan so f thay doi Khi f = 60 H z thi cuong do hieu d u n g qua L la 2,4 A De cuong do hieu d u n g qua L bang 3,6 A thi tan

so C L i a dong dien phai bang MI- v '

V i du 2 : M o t tu dien khi mac vao nguon u = uV2 cos(100Kt + 7t) (V) thi cuong

do hieu d u n g qua mach la 2A Neu mac tu vao nguon u = Ucos(1207tt + 0,5::) (V) thi cuong do hieu d u n g qua mach la bao nhieu?

A 1,2N/2A B 1,2A ' C V2 A D 3,5 A

""'XHuongdan ••*'-,''-:''>:^'<':':<-'y z,:^''-:'''-<':•'''••'

I = - ^ = c o C U ^ j ; ' = " ' ^ y ; = k = ^ ^ I , = l , 2 V 2 ( A ) = > C h o n A

Zc [ l 2 = ( 0 2 C U 2 Ij (0|U,

V i du 3: Doan mach dien xoay chieu tan so fi = 60 H z chi c6 m o t tu dien Neu

tan so la h thi d u n g khang cua tu dien tang them 20% Tan so

A f2 = 72 Hz B. f2 = 50 Hz. C f2 = 10 Hz D f2 = 2 5 0 Hz

BS trg kiSn thiic V$t If LTBH trBn kenh VTV2 t^p 2 - Chu V^n Bi&n

moi, d la khodng each giua hai ban tu va S la dien tich doi dien gifm cdc ban tu)

1) Khi chat dien moi trong tu la ichong khi thi ZQ = 1

Neii nhung cdc bdn tu ngdp vao trong dien moi long (c6 hang so dien moi s) va cdc

= ZCQ nen cuang do hieu

yeu tokhdc khong doi thi dien dung cua tu C = ^ —

dung qua tula I ' = coCU = E I

New nhiing x phan tram dien tich cdc bdn tu ngdp vao trong dien moi long (c6 hang

so dien moi s) vd cdc yeu tokhdc khong doi thi bo tu C gom hai tu Ci, Ci ghep song

( l - x ) S „ E X S

song: C i = • • = ( l - x ) C o , C 2 = - • = E x C n

9.10\47td 9.10^47id

^ C = + C 2 = (1 - X + ex)Co ' '.,1'n<<'-ti

Cwang do hieu dung qua mqch h'lc nay Id V = coCU = (1 - x + 8 x ) I

Neu ghep sdt vdo mot bdn tu mot td'm dien moi c6

hang so dien moi sco be day bang x phan tram be'

day cua lop khong khi vd cdc yeu tokhdc khong

dot thi bo tu C gom hai tu Ci, Ci ghep noi tiep:

Ba trg kiSn thurc V^t li LTDtl tren henh VtV2 t^p 2 - Chu Vdn Bien

:i=0<=>u = ±U

(Do thi quan he ii, i la duong clip)

[u = 0 <=> i = ±I()

V i d u 1: (DH-20n) Dat dien ap u = uV2cosa)t vao hai dau mot tu dien tiii

cuang do dong dien qua no c6 gia tri hieu dung la I Tai thoi diem t, dien ap

a hai dau tu dien la u va cuong do dong dien qua no la i He thuc lien he

giua cac dai luong la

V i d u 2: Dat vao hai dau doan m c i c h chi c6 cuon cam thuan mot dien ap xoay

chieu u = UdCOslOOTit (V) Biet gia trj dien ap va cuong do dong dien tai thai

diei-n t^ la u^ =50^ (V), -Jl (A) va tai thoi diem t2 la U2 = 50 (V),

I

— C h e n B . y ,, , ,„

I „ = 2 ( A ) • tii'VidnmpiS

V i d u 3: Dat vao hai dau mot cuon cam thuan c6 do t u cam 0,3/;: (H) mot dien

ap xoay chieu Biet dien ap c6 gia trj tuc thai 60-J6 (V) thi dong dien c6 gia

trj tuc thoi V 2 (A) va khi dien ap c6 gia tri tuc thai 60>/2 (V) thi dong dien

CO gia tri tuc thoi %/6 (A) Hay tinh tan so cua dong dien

* Nguvc Igi nujch chi c6 L hoac C

(Dexdc dinh dwgc L iiay C thi nen Iwu y: Neu f tang thi Zi tdng nen I gidm con

ZQ gidm nen I tang)

V i du 4: M o t hop X chi chua mot trong 3 phan t u la dien tro thuan hoac tu dien hoac cuon cam thuan Dat vao hai dau hop X mot dien ap xoay chieu chi c6 tan so f thay doi K h i f = 50 H z thi dien ap tren X va dong dien trong mach 6

thoi diem ti c6 gia trj Ian lugt la: ij = l A , Uj = 100 V, 6 thai diem t2 thi:

i , = A, U2 = lOOV Khi f = lOOHz thi cuang dp dong dien hieu dung

trong mach la 0,5 V2 A H o p X chua

A dien tro thuan R = 100 Q ' ' "

B cuon cam thuan c6 do t u cam I/TT (H)

C tu dien c6 dien d u n g C = IO-VTI (F)

D tu dien c6 dien dung C = 100 ^3 /TI (F) C

V i d u 5: (DH-2010) Dat di§n ap u = Uocoscot vao hai dau cuon cam thuan c6 do

tu cam L thi cuang do dong dien qua cuon cam la

A i = HLcos coL

Bo trfi kien thijrc V,jt li I roil iren kcnh VTV2 t^p 2 - Chu V^n Blen

1 = —^cos cot

2 coL -cos 2 •Chon C

Vi du 6: Dat dien ap u = Uocos(1207Tt - TT/4) (V) vao hai dau mgt tu dien thi von

kenhiet (c6 dien tro rat Ion) mac song song voi tu dien chi 120^/2 (V), ampe

kenhiet (c6 dien tro bang 0) mac noi tiep voi tu dien chi 2 ( A ) Chon ket

C Dong dien tuc thai qua tu dien la i = 4cos(1007it + 7i/4) ( A )

D Dien ap cue dai giira hai dau tu dien la 120 y/l (V), dong dien cue dai qua

V i du 7: Do thj bieu dien cuong do tuc thoi cua dong dien xoay chieu chi c6

cuon cam thuan c6 cam khang ZL = 50 Q o hinh ve ben Viet bieu thue dien

ap tuc thoi giira hai dau cuon cam ' " : i ( A )

i = IQ cos (cot + cp) = 1,2 cos (cot + cp)(A)

Liicdau, i = — ycidang.dive i = 0nernp = —

V i du 8: Mot doan mach mSc noi tiep gom: tu dien eo dung khang Z c va cuon

cam thuan c6 cam khang Zi, = 0,5Zc Dien ap giira hai dau tu:

uc = 100eos(1007it + 7t/6) V Dien ap giiia hai dau doan mach la:

A u = 200eos(1007it - 57t/6) V • •' B u = 200cos(100Txt - 7r/3) V

C.u = 100eos(1007it-571/6) V D u = 50cos(1007it + 7:/6) V

Huong dan , 1+: • |«~.- :fUSU.:dt' •

U p

Dien ap giij'a hai dau doan mach: u = U L + = Z L + u^

u = 0,5uc + U c = 0,5uc = 50 cos 1007Ct +

-6, (V)=>ChonD j j i ,:v

Chu y:

1) NcU cho • thi du'a vao he thi'fc \

(dm) in:t)\i ^n;.iC) !'-<i,:,) en npiu u\p iBsi oi\'> UM

= 1- Thay U Q ^ I Q Z L

hoac Uo=IoZc

Mach chi c6 C thi i sdm pha hcfn u Id K/2

Mach chi c6 L thi i tre pha hcfn u Id n/2 /.I

h/.'AM.ii'^y'AH Huongdan );|^:Kr;i;flj!p*iJ,r.):^i;^»;.fi!a ,

Cdch 1: Gidi tuan tu: iriJ'rrs! hamh it'jil: ••.!,!'•

1 1 : : :

Bo trfl kicn Ihitc V^t li LTDH tren hcnii VTV2, t^p 2 - Chu Vdn Bicn

-Cdch 2: Gidi nhanh (van tat):

Dua vao he thuc: -4r + = 1- Thny U() = l o Z c 150

V i d u 10: Dat vao hai dau tu dien c6 dien dung 1/{3n) (mF) mot dien ap xoay

chieu Biet dien ap c6 gia t r i tiic thoi 60^6 (V) thi dong dien c6 gia t r i tuc

thoi yfl (A) va khi dien ap c6 gia tri tuc thai SOs/l (V) thi dong dien c6 gia

tri tuc thoi -^6 (A) Ban dau dong dien tuc thoi bang gia tri cue dai, bieu

thii'c C L i a dong dien la

A i = 2^y3cos(^007tt + 7t/2) (A) B i = 2 V2 coslOOTtt (A)

C i = 2V2cos507it(A) D i = 2 ^/3 cos(507it + 7r/2)(A) ,

V i ban dau dong dien tiic thoi bang gia trj eye dai, bieu thiic ciia dong dien

CO dang i = I,, cos cot thay so vao ta dugc i = 2V2 COSSOTTI ( A ) => Clion C

V i d u 11: Dat vao hai ban tu dien c6 dien d u n g 100/(37r) (|aF) m o t dien ap xoay

chieu u = Uiicos(1007it + (pu) (V) thi dong dien qua tu c6 bieu thuc

i = 2V2 cos{1007tt + 7x/3) (A)

1) T i n h dien ap giiia hai ban t u tai thoi diem t = 5 (ms) t •

2) Xac d i n h cac thai diem de dien ap u = 600 (V) » I ',/

3) Xac d j n h thoi diem Ian t h u 2014 de u = -300 V2 (V)

4) Xac d j n h thoi diem ian t h u 2014 de |u| = 300 V2 (V)

Huang dan

1) T i n h d u n g Ichang: Z c = — = 300(Q)

coC

Cty Tnnn MTV DVVH Kliang Vift

Vi mach chi c6 tu dien nen dien ap tre pha hon dong dien la n/l:

De tinh t2 ta c6 the d u n g vong tron lugng giac:

B S tr^ kieti thUc V^t II LTDlt tteti k&nh VTV2 t$p 2 - Chu VSn Bi&n

V i du 13: Dat vao hai dau doan mach chi c6 tu dien c6 dien d u n g 0,l/7i (mF)

mot dien ap xoay chieu u = UocoslOOnt (V) Neu tai thai diem ti dien ap la

50 (V) thi cuong do dong dien tai thai diem ti + 0,005 (s) la: i

1) T h a i gian thiet bi hoat dong. p , , (|„.,

M o t thiet bj dien duoc dat d u a i dien ap xoay chieu u = Uocoscot (V) Thiet bi

chi hoat dong k h i dien ap tuc thai c6 gia tri khong nho h o n b Vay thiet bj

chi hoat dong khi u nam ngoai khoang (-b, b) (xem hinh ve)

Thai gian hoat dong trong mot nua chu k i : 2t, = 2 —arccos-—- ,>|' ,|

Thai gian hoat dong trong mot chu k i : t^ = 41, = 4.—arccos— ''''"^

Thoi gian hoat dong trong 1 s: ft^ = f.4.—arccos —

Cty Train M I V U VVH Khang Vlft

V i du 1: Dat dien ap xoay chieu c6 trj hieu dung 120 V tan so'60 H z vao hai

dau mot bong den huynh quang Bie't den chi sang len khi dien ap dat vao

den khong nho hon 60 N/2 V Thoi gian den sang trong moi giay la:

A 0,5 Ian B 2 Ian C ^ Ian D 3 Ian

2) T h a i diem de dong dien hoac dien ap nhan mot gia tri nhat dinh

De xac d i n h cac thoi diem c6 the dung giai phuong trinh luong giac hoac dijng vong tron luong giac

Vi du 1: (DH-2007) Dong dien chay qua mot doan mach c6 bieu thuc i = losinlOOTit Trong khoang thai gian tCf 0 den 0,01 ? cuong do dong dien tiic

thai CO gia tri bang 0,5Io vao nhung thai diem • j

B6 trff kiSn thCrc V^t l i L T B t l trSn kSnh VTV2 t^p 2 - Chu VSn Bien

V i du 2: Dien ap hai dau doan mach c6 bieu thiVc u = 200cos(1 OOTit + 57r/6)

(u do bang von, t do bang giay) Trong i<hoang thoi gian t u 0 den 0,01 s dien

ap tiVc thoi CO gia trj bang 100 V vao n h u n g thoi diem , i v

A 3/200 s va 5/600 s \f|s^,,i;,:, B 1/400 s va 2/400 s

C 1/500 sva 3/500 s ' ' ' ' D 1/200 va 7/600 s

Huong dan Cdch 1: Gidi phumig trinh luong gidc

u = 100=^ cos lOOTTt 57:

=> Chon A (Neu khong cong them 2n

Cdch 2: Dung vdng iron luang gidc

100 V ung voi pha dao dong:

= - - ^ + 2Tt nen thoi gian:

71 „ 5T:

+ 271

-3 6 0) 10071 600

Lan 2 dien ap tuc thoi c6 gia tri bang 100 V ung v o l pha dao dong:

V i du 3: Dien ap giCra hai dau mot doan mach c6 bieu thuc: u = 120sin]007rt

(u do bang von, t do bang giay) Hay xnc djnh cac thai diem ma dien ap

u = 60 V va dang tang (voi k = 0,1, 2, )

Cty Timti nrv DVVH Khang Vipt

Vi du 4: Dien ap giua hai dau mot doan mach ccS bieu thuc u = U()COS(2TTt/T) Tinh t u thai diem t = 0 s, thi thoi diem lan t h u 2014 ma u = 0,5Uo va dang

tang la '• ,-\y-'''' ] r ' '

A 12089.T/6 B 12055.T/6 C 12059.T/6 D 12083.T/6

Huotig dan

Cac thai diem ma u = 0,5Uo va dang tang thi chuyen dong tron deu nam o

nua d u o i vong tron krong giac (moi chu ki chi c6 mot lan)

Vi tri xuat phat ung voi pha dao dong: O,, = 0 Lan 1 ma u = 0,5U(i va dang tang ung voi pha dao dong:

Oj = - ^ + 271 nen thai gian: , , ;

t l =• cl>i - O + 2 7 1- 0

3 _ 5 T

0) 271

T' Lan 2: t2 = t, + T , Lan 2014: 12014 = t i +2013T

5T

2014 + 20131 = 12083T • ChonU

6 6

V i du 5: Dien ap giua hai dau mot doan mach c6 bieu thuc u = Uocos(2Tit/T)

Ti'nh t u thoi diem t = 0 s, thi thoi diem lan t h u 2010 ma u = 0,5U() va dang giam la

V i du 6: Dat vao hai dau doan mach mot dien ap u = UocoslOOrct (V) Trong

chu ki t h u 3 cua dong dien, cac thoi diem dien ap tuc thoi u c6 gia t r i bang dien ap hieu d u n g la

Bidttff USn thiic V^t It LTDH trSn kenh VTV2 t4p 2 - Chu Van Blgn

C h u k i t h u 1: u = • C O S l 0 0 7 t t =

-Chu k i thu- 2: {

It^ = t 2 + T = 0,0375(s) '-^->

'tg = t i + 2 T = 0,0425(s) [ t , = t 2 + 2 T = 0,0575 (s)

Cdch 2: Diing vdng iron luong gidc ' <! '" •

7t „ O j - O g Lan 2 : O , = — + 2 ; : => to =

-Chii y: Ncu khong han chcboi dieu kien dang tang hoac dang gidm thi ung v&i mot

diem tren true ung vai hai diem tren vdng trdn lugng gidc (trit hai vi tri Men)

Do do, trong chu ki dau tien c6 hai thai diem ti vn ti; chu ki thu 2 c6 hai tlwi diem

f.3 = t i + T vd t4 = t i + T; t2i,vi = t i + nT vd t i u ^ i = t i + nT Ta co the rut ra 'meo' Idm

, , So l a n f neu dU 1 => t = nT + t, ,., , „

nhanh: • = n<^ , ,

2 [ n e u d U 2 = > t = nT + t2 -'iiu/ i T l W

V i d u 7: D o n g dien xoay chieu qua mot doan mach co bieu thuc i = Iocos(1007rt

- n/3) (A) (t do bang giay) Thoi diem t h u 2009 c u o n g do d o n g dien tuc thai

I K

Cty Timii PTTV DVVn Kbang VJ^

Chu y: Trong mot chu ki c6 4 tliai diem de /u / =b< Uo Detim thai diem lan thie

n md lul =h ta can luu y:

Lanldenu^ ld:ti

Lan 2 den Id : Lan 3 den u-i Id : Lan 4 den Id : t 4

loo':

Lan 4n +1 den Id: t4„+] = nT + t j

Lan 4n + 2 den W j la : i^^x+Z = nT + t 2

Lan 4n + 3 den la : t 4 , - , + 3 = nT + 1 3 Lan 4n + 4 den la : t 4 n + 4 = nT + t 4

Vi du 8: D o n g dien xoay chieu qua m o t doan mach co bieu thiic i = Iocos(1007it

- n/3) (A) (t do bang giay) T h a i diem t h u 2013 gia t r i tuy?t d o i ciia cuong

dp dong dien tuc t h a i bang cuang do dong dien hi^u d u n g la gt) ^hmr

3) Cac gia tri tuc thoi 6 cac thoi diem

N e u biet gia t r i tuc t h a i 6 thai diem nay t i m gia trj a t h a i d i e m khac ta co the giai p h u a n g t r i n h l u g n g giac hoac d i m g v o n g tron l u g n g giac

Vi du 1: (DH-2010) Tai thai diem t, dien ap u = 200 ^ 2 cos{1007tt - n/2) (trong

do u t i n h bang V, t t i n h bang s) co gia t r i 100 V 2 (V) va dang giam Sau thai

d i e m do 1/300 (s), dien ap nay co gia trj la j 'f j f

B6 trjf kie'n thiic V^t li LTBH tren kcnh VTV2 t^p 2 - Chu VSn Bien

K h i u = 100 V2 (V) va dang giam thi pha dao dong c6 the chon: = -

Sau thai diem do 1/300 (s) (tuang u n g v a i goc quet Acj) = (oAt = 1007t/300 = 7t/3)

thi pha dao dong: O2 = + AO = — f

=>U2 =200V2cosO2 =-100>/2(V)=>ChonC ,,,

V i du 2: Dong dien chay qua mot doan mach c6

bieu thiic i = 4cos(1207it) (A), t do bang giay

Tai thoi diem ti nao do, dong dien c6 cuang

do 2V3 A Deh thai diem t = ti + 1/240 (s), Z

cuang do dong dien bang J- ' •

A 2 (A) hoac - 2 (A) B - V2 (A) hoac 2 (A)

C ->/3 (A) hoac 2 (A) D Vs (A) hoac -2 (A)

Huong dan

V i khong Hen quan den chieu dang tang hoac dang giam nen ta c6 the giai

p h u o n g trinh l u g n g giac de t i m nhanh ket qua

V i d\ 3: D o n g dien xoay chieu chay qua mgt doan mach c6 bieu thiic

i = 2 V2 cos(1007it + (p) (A), t tinh bang giay (s) Vao mot thai d i e m nao do,

1= sfl Ava dang giam thi sau do it nhat la bao lau thi i = + V6 A?

A 3/200 (s) B 5/600 (s) C 2/300 (s) D 1/100 (s)

Huang dan Cdchl: •'^•i^f>fi-"

V i du 4: Vao cung mot thoi diem nao do hai dong dien xoay chieu h = Iocos(cot + cpi

va i2= Incos(cot + 92) CO ciing trj tuc thai 0,5^/3 lo, nhung mot dong dien dang

tang con mot dong dien dang giam Hai dong dien nay lech pha nhau

A 7t/3 B 271/3 C 7t

Huong dan Cdchl: :"'=,'"v;:r

B6 tr^ ki&'n thiic V$t li LTOH Iren kenh VTV2, t$p 2 — Chu VSn BlSn

= — r s i n ( c o t 2 + ( p ) - s i n ( f f ) t i +(p) tt)

V i du 1: D o n g d i e n xoay chieu chay t r o n g day dan c6 bieu i = 2cos(100Kt - 7t/6)

( A ) (t d o b a n g giay) T i n h d i ^ n l u o n g c h u y e n qua tiet d i ^ n t h a n g ciia day

d a n t r o n g l / 3 0 0 { s ) k e t i l - l i i c t = 0 • ^ • • >

A 6,666 m C B 5,513 m C C 6,366 m C D 6,092 m C

Huang dan Cdchl:

Chu y: De tinh dien lugng chuyen qua tiet dien thang cua day dan trong thai gian

At ketit luc dong dien bang 0, ta c6 the lam theo hai each: • | n K : / i

-Cdch 1: Gidi phuang trinh i = 0 detim ra ti

tl+At , I„

sau do tinh tich phan: Q= idt • , ;

'1 O

Cdch 2: Viet lai bieu thuc dong dien duai

dang i = IQ sin cot vd tinh tich phan -i^

vi du 2: M a c day d a n vao n g u o n xoay chieu o n d j n h t h i d o n g d i e n chay qua c6

b i e u t h i i c i = 2cos(1007it - n/3) ( A ) D i f n l u g n g c h u y e n qua tiet d i e n t h a n g

cua day d a n t r o n g t h o i g i a n 1/300 s ke t u liic t = 0 v a ke tie l i i c i = 0 Ian

V i du 3: D o n g d i e n xoay chieu chay t r o n g day d a n c6 tan so goc co D i e n l u g n g

c h u y e n qua tiet d i § n t h a n g cua day d a n t r o n g 1/6 c h u k i d o n g d i e n ke t u liic

d o n g d i e n bang k h o n g la Q i C u o n g do dong dien cue dai la

1) Dong dien den chieu luc no triet tieu i = 0

2) Khodng thai gian hai Idn lien tiep dong dien triet tieu Id T/2 nen dien lugng chuyen

qua tiet dien thang cua day dan trong thai gian do la: f , ; j 0 / i ' , 1 :A *;

V i du 4: C h o d o n g d i e n xoay chieu i = 27csin(1007tt) ( A ) (t d o b a n g giay) qua

mach T i n h d o I o n d i e n l u g n g qua mach t r o n g thoi g i a n 5 p h i i t

Bd trg kie'n thitc V^t It LTDH tr^n kSnh VTV2 t^p 2 - Cha Van Blin

2) The tich khi thoat ra khi dien phan dung dich axit H2SO4

+ Dien l u o n g qua tiet dien thang cua day dan trong 1/2 chu ky: Q1/2 = 2Io/co

+ The tich k h i H 2 va O 2 0 D K T C thoat ra 6 moi di§n cue trong nua chu k i Ian

Q

l u g t l a : = ; ^ n , 2 ( l ) va = - ^ 5 , 6 ( 1 ) 1/2

96500 ' ^ ' ' 96500 + The tich khi H 2 va O 2 6 DKTC thoat ra 6 m o i dien cue trong thoi gian t Ian

T + Tong the tich k h i H 2 va O 2 6 D K T C thoat ra 0 moi dien cue trong thoi gian t

t

l u o t l a : = ^ ^ 1 va

=^^2-la: V = V H 2 + V O 2 = - ( V , + V 2 )

V i du 5: Cho dong dien xoay chieu i = 7:sin(1007it) (A) (t do bang giay) chay qua

binh dien phan chiia d u n g djch H 2 S O 4 voi cac dien cue tro Tinh the tich khi

H 2 6 dieu kien tieu chuan thoat ra trong thoi gian 16 phiit 5 giay 6 m o i dien

V i du 6: Cho dong dien xoay chieu c6 gia tri hieu d u n g 2 A chay qua binh dien

phan chua d u n g djch H2SO4 v o i cac dien cue tro Tinh the tich k h i 0 dieu

kien tieu chuan thoat ra trong thoi gian 16 phut 6 moi dien cue

A 0,168 lit B 0,0235 lit C 0,047 lit D 0,056 lit

^ , U U R U L U C Cuong do hieu d u n g I = — = — = — - = = —- „

Z R Z L Z ( - Zj^^ -ml nid iob gnoriW

Dien ap tren doan mach U ^ N = 12^^ =^ZMN

V i d u 1: Mach dien noi tiep gom dien tro R = 60 (Q), cuon day c6 dien tro thuan

r = 40(Q) CO do t u cam L = 0,4/7i(H) va tu dien c6 dien d u n g C = l/(147t)(mF)

Mac mach vao nguon dien xoay chieu tan so goc IOOTT (rad/s) Tong t r o ciia mach dien la

du 2: Dat m o t di$n ap xoay chieu vao hai dau m o t doan mach mac noi tiep gom t u dien c6 d u n g khang 2 0 0 Q , dien tro thuan 3 0 N / 3 Q va cuon cam c6

dien tro 5 0 ^f3 Q CO cam khang 2 8 0 Q Dien ap giua hai dau doan mach

A som pha h o n cuong do dong dien la n/4

B sdm pha hon cuong do dong dien la Ti/6

C tre pha hon cuong do dong dien la n/4 j ,

D tre pha h o n cuong d o dong dien la 71/6 • >

23

B 6 tr^ hien thiic V^t li LTBH trSn kenh VTV2 t^p 2 - Chu Van Bl&n

Huong dan

_ Z L - Zc _ 280 - 200 _ 1

^ " ^ ^ R + r ~30>/3 + 50>/3 ~ Vs .{p = ^ > 0

=> Dien ap sam pha hon dong dien => Chon B

Vi du 3: Mot mach dien mac noi tiep theo dung thu t u gom dien tro thuan

R = 30 Q, tu dien 1 c6 dien dung = 1/(3TC) (mF) va tu dien 2 c6 dien dung

C2 = I/TT (mF) Dien ap giiia hai dau doan mach la u = 100N/2 coslOOTit ( V ) ,

Cuang do hieu dung trong mach la - ' ' rir: _il,':i n,>i •

Vi du 4: (DH-20n) Dat mot dien ap xoay chieu c6 gia trj hieu dung va tan so

khong doi Ian krot vao hai dau dien tro thuan R, cuon cam thuan c6 do tu

cam L, tu dien co dien dung C thi cuong do dong dien hieu dung qua mach

tuong ung la 0,25A; 0,5A; 0,2Ạ Neu dat dien ap xoay chieu nay vao hai dau

- doan mach gom ba phan t u tren mac noi tiep thi cuong do dong dien hieu

dung qua mach la

V i du 5: Cho mot mach dien mac noi tiep gom mot dien tro R = 40(Q),

cuon cam thuan c6 do t u cam L = 0,8/Tr (H) va mot tu dien c6 dien dung

C = 2.10-V7T (F) Dong dien qua mach c6 bieu thuc la i = 3cos(1007Tt) (A)

Dien ap hieu dung giua hai dau doan mach la i - ' •

V i du 6: Cho mach dien xoay chieu RLC mac nói tiep theo dung t h i i t u gom

cuon thuan cam c6 cam khang 14 (Q), dien tro thuan 8 Q, tu dien c6 dung khang 6 (Q), biet dien ap gifra hai dau mach c6 gia tri hieu dung la 200 (V)

Dien ap hieu dung tren doan RC la Ạ250(V) B lOO(V) C 1 2 5 V 2 ( V ) D 100V2(V)

Huong dan <j/

^ U -rori fir: \ J I R ^ +Zr r- n ,-CI :

URC = I Z R C = ^ Z R C = , , ^ , = 12572 (V) =^ Chon C , , _ „

Vi du 7: Cho mach dien xoay chieu tan so 50 (Hz) noi tiep theo dung thu tu:

di^n tro thuan 50 (Q); cuon day thuan cam c6 do t u cam 0,5/7i (H) va tu di^n

CO dien dung 0,1/?! (mF) Tinh do lech pha giira va u ^ c

-Ạ 71/4 B 7i/2 C 37r/4 D 7i/3

"'' , Huang dan , , ^

Z, =a)L = 50Q,Zc = = 100fi ,, d I Si J f: :

^ ' J,.I>I itoiim.nt}ob }om oxt) 'M tp

tan (PKL = ^ = 1 => (pKL = — -h-nUh i\-íQ-u{ ml J U J ' J ,;?'J i^:.,

tan (PLC = Q - - = ^ = » 9 L C = - ^ :'m.&)t?i

, vf; "'^ (''^''5t'c'L.(i ịdq ^Jit

=> 9RL - ^ L C = — ^- ' ' ^ *^>v OS (b(5i) rxS.O 6j-kj I ' l l

Vi du 8: (DH-2008) Cho doan mach dien xoay chieu gom cuon day mac noi tiep

voi tu dien Do lech pha ctia dien ap giua hai dau cuon day so voi cuong do

dong dien trong mach la 7T/3 Dien ap hieu dung giua hai dau tu dien bang

^y3 Ian dien ap hieu dung giCra hai dau cuon daỵ Do lech pha cua dien ap giua hai dau cuon day so voi dien ap giua hai dau doan mach tren la

tan (p = —^= ~ = -^y3=>(p = - - = > rộj - 9 = — => Chon Ạ

V i du 9: Dat dien ap xoay chieu vao hai dau doan mach AB theo thu t u gom

cuon day thuan cam L c6 cam khang 100 Vs Q, dien tro R = 100 Q va tu dien

C CO dung khang 200^3 Q mac noi tiep, M la diem gii>a L va R, N la diem

giua ciia R va C Ket qua nao sau day khong diing? '

251

Bo trg hiSn thiic V^t li LTDII tren kcnh VTV2, 14p 2 - Cliu Vsin Bien

A D i e n ap giCra hai dau dpan A N £ R C

'' s a m pha h a n d i e n ap g i u a hai A / h y ~ j \~^B

dau d o a n mach A B la 27T/3

B C u o n g do d o n g dien tie pha 7i/3 so v a i dien ap giua hai dau doan mach A B

C D i e n ap g i i i a hai dau doan A N s om pha h o n dien ap g i i i a hai d a u doan

V i d u 10: Cho m o t doan mach R L C k h o n g phan nhanh (cuon day cam thuan)

G o i U R , U L , U C Ian l u g t la dien ap hieu d u n g giiia hai dau d i e n t r a thuan,

hai d a u cuon d a y va hai dau t u dien Bie't U K = U L = 0,5Uc t h i d o n g d i e n qua

mach se:

A tre pha 0,257i (rad) so v o i d i e n ap giiJa hai dau doan mach

B tre pha 0,57T (rad) so v o i dien ap hai giua dau doan mach

C s o m pha 0,25TI (rad) so v o i dien ap giiia hai dau doan mach

D som pha 0,5n (rad) so v o l di en ap giira hai dau doan mach

, tancp = = = ^ ^ ^ ^ - ^ = - 1 = ^ 9 = - - ^ Chen C

V i du 11: D a t dien ap 50 V - 50 H z vao doan mach n o i tiep g o m d ien t r a 40Q

va cuon day t h uan cam thi dien ap hieu d u n g giira hai dau cuon cam la

Ui = 30 V D o t u cam cua cuon day la

V i du 12: Cho mach d ien xoay chieu k h o n g phan nhanh R L C , cuon day thuan

cam va Z i , = 8R/3 = 2Zc D i e n ap hieu d u n g g i i i a hai d a u doan mach la 200

H V Dien ap hi§u dung giiTra hai dau dien tro R la

V i du 13: D o a n mach xoay chieu noi tiep g o m dien t r a t h u a n R, tu dien C va

cuon cam t h u a n L Dat vao hai dau doan mach m o t d i e n ap xoay chieu on

d j n h t h i d i e n ap hieu d u n g tren R, L va C Ian l u g t la 6 0 V , 1 2 0 V va 4 0 V Thay C b o i tu d ie n C t h i d i e n ap hieu d u n g tren tu la 1 0 0 V , k h i do, d i e n ap hieu d u n g tren R la ' '

V i du 14: D o a n mach xoay chieu g o m bien t r o R, tu d i e n C va cuon t h u a n cam

L mac noi tiep K h i dieu chi nh bien t r o 6 gia trj nao d o t h i d i e n ap hieu

d u n g do d u g c tren bien tra, tu dien va cuon cam Ian l u g t la 50V, 90V va 40V D i e u c h i n h de gia trj bien t r o Ion gap d o i so v o i luc d a u t h i dien ap

Bo trg kie'n thitc V^t IILTDH trSn hcnh VTV2 t^p 2 - Chu VSn Blen _ _ _ _ _ _

V i d u 15: M o t m a c i i dien g o m m o t cuon day ccS d i e n t r o t h u a n r he so t u cam L

noi tiep v o i m o t t u d i e n C d u o c mac vao m o t hieu d i e n the xoay chieu

Cu'ong d o hieu d u n g cua d o n g dien qua mach d o d u g c I = 0,2 A H i e u d i e n

the hieu d u n g g i u a hai d a u doan macii, gifra hai dau c u o n day, giira h a i ban

tu dien c6 gia trj Ian l u g t la 120 V , 160 V, 56 V D i e n t r o t h u a n ciia d a y la

V i d u 16: D a t m o t d i e n ap u = 20 ^y2 coslOOrtt ( V ) , (t do bang giay) vao h a i dau

doan mach g o m d i e n t r o R n o i tiep v o i cuon d a y c6 he so t u c a m L = 0,12/7:

(H) va dien t r o t h u a n 9 Q t h i d i § n ap hi?u d u n g tren R la 5 VS V H a y tinh

thi ta se tun dinrc (cot + (p) = i a j ;

chon dau avig hoqc trif dc'sno cho

Khi cho biet cdc gid tri tuc tiioi

Tit do se tiin du'o'c <p ' - u - , ; ' • • •

V i d u 17: M a c h d i e n xoay chieu n o i tiep A B g o m d i e n t r o t h u a n R, cuon cam

t h u a n L va t u d i e n C (R, L , C khac 0 va hCru han) Bien d o cua d i e n ap g i u a

hai d a u d o a n A B va tren L Ian l u g t la Uo va UOL 6 thoi diem t dien ap tuc

98

Cty T/VHH fllTV D VVH Kbang Vl^t

t h o i h a i d a u doan mach A B bang +0,5Uo va dien ap t i i c t h o i tren L bang +UOL/72 Dien ap giua hai dau doan mach

A s o m p h a h o n d o n g dien la 7i/12 B som pha h o n dong dien la 71/6

C t r i p h a h a n d o n g d i e n la 7t/12 D tre pha h a n dong dien la 71/6

Chu }/: Niju cho gid tri tire thai dien dp a hai tlwi diem tin van c6 the tinh duvc cp

V i d u 18: M a c h d i e n xoay chieu n o i tiep A B tan so 50 H z g o m d i e n t r o t h u a n R, cuon c a m t h u a n L v a t u d i e n C (R, L , C khac 0 v a hi>u han) Bien d o ciia

d i e n ap g i u a h a i d a u doan A B va tren L Ian l u g t la Uo v a Uoi, 6 thai diem t i

d i e n ap t u c t h o i g i u a h a i d a u doan mach A B bang +0,5Uo va sau k h o a n g

t h o i g i a n ngan nhat 1/400 s dien ap tuc thoi tren L bang +UQI./72 Dien ap

g i i i a hai d a u d o a n m a c h

A s o m p h a h o n d o n g d i e n la 7t/12 B sam pha h o n dong dien la 7t/6

C tre p h a h o n d o n g d i e n la 7i/12 D tre pha h a n dong dien la 71/6

Bo trp kien thiic V^t liLTDIl tren henh VTV2 t^p 2 - Chu VSn Bien

V i dy 19: Dat di§n ap 200V - 50Hz vao hai dau doan mach A B g o m dien tro

thuan 25^2 mSc noi tie'p v o i doan mach X Cuong do dong dien hieu d u n g

qua doan mach la 2 A Biet 6 thoi diem to, dien ap ti'rc thoi giua hai dau AB

CO gia trj 200V va dang tang; 6 thoi diem to + 1/600 (s), cuong do dong dien

tuc thoi qua doan mach bang 2A va dang giam Tinh do lech pha ciia dien

ap giua hai dau doan mach AB so voi dong dien qua mach va cong sua't tieu

thu dien cua doan mach AB va doan mach X ^

=> (p = - — < 0 : Dien ap U A B tre pha hon i la 7:/3

Cong suat tieu thu dien cua doan mach AB va doan mach X Ian l u g t la: t i

P = Ulcoscp = 200(W) va Px = P - l^R = lOO(W)

V i du 20: ( D H - 2012) Dat dien ap u = 400cosl007tt (u ti'nh bang V, t tinh bang s)

vao hai dau doan mach AB gom dien tro thuan 50 Q mac no'i tie'p v o l doan

mach X C u o n g do dong dien hieu d u n g qua doan mach la 2 A Biet 6

thai diem t, dien ap tuc thoi giua hai dau AB c6 gia t r i 400 V; 6 thai diem

t + 1/400 (s), cuong do dong dien tuc thoi qua doan mach bang khong va

dang giam Cong sua't tieu thu dien cua doan mach X la

7t n

= -=>(p = —

2 4 4-,.i V'V:''

2) Bieu thiic dong di^n va di^n ap

Viet bieu thirc theo phimng phdp truyen thong:

Cty TISHH nrv DVV11 Khang Vi^t

a) Ne'u cho i = Iocos(cj)t + cp;) thi

V i du 1: M o t mach dien xoay chieu mac noi tie'p gom dien tro thuan R = I S Q ,

cuon thuan cam c6 cam khang Z L = 25Q va tu dien c6 d u n g khang Zc = lOQ

Ne'u dong dien qua mach c6 bieu thuc i = 2 V2 cos(1007rt + 7c/4) (A) t h i bieu thuc dien ap hai dau doan mach la , , ' r

R = l=>(p = — > 0 : u sdm hon i Id — 4 'l007rt + ^ + ^ l

4 4J = 2V2.I5V2COS 1007rt + 7C ( V ) :

, .4, Chon A

V i du 2: Mach dien xoay chieu gom dien tro 30 Q, cuon day c6 dien t r o thuan 30Q va CO cam khang 40Q, tu dien c6 d u n g khang lOQ D o n g mgch chinh c6 bieu thuc i = 2cos(1007:t + 7t/6) (A) (t do bang giay) Viet bieu thuc dien ap giiia hai dau doan mach chiVa cuon day va t u d i f n

A ULrC = 60cos(1007it - 71/3) (V) B ULrC = 60cos(1007it + 7l/4) (V)

Bo trp klSn thiic V^t li LTDH trcn henh VTV2, t4p 2 - Chu V0n Blen

Vi du 3: Mot cuon day thuan cam c6 do tu cam 1/n (H) va tu dien c6 dien

dung 2 .10-'/TI (F) ghep noi tie'p, roi no! hai dau doan mach vao nguon c6

dien ap u = 100 V2cos (1007it + Tt/6) (V) Dong dien qua mach la

A i = 2cos(1007it + 71/2) (A) B i = 2cos(100Tit - 7t/2) (A)

C i =2 ^/2 cos(100Ttt - 71/3) (A) D i = 2 V2 cos(1007Tt + 7t/2) (A)

Huong dan

Z, =wL = 100Q;Zc = — = 50Q wC "ri'T,''!' *• ^••••I'rrin'J w o r b w^l/i (cf

- irii (o + }fc)r!',o,.^f,,,,0 ,„>^fU or!'; ir^VI (./

Z, - Z r 7t , , , TT •jV'ub ,h>*v U68

—1^ = +cx )=>(p = — > 0: i i sC/n p/ia /iCw ila— ,

2 2 H'-iii iBfil-'i^r,:* canJ

Vi du 4: Mot doan mach gom cuon day c6 do tu cam 0,6/7i (H) mac no'i tiep vai

mot tu dien c6 dien dung 1/(14?:) (mF) Dat vao hai dau doan mach mot

dien ap xoay chieu c6 bieu thuc: u = 160cos(1007it - 71/12) (V) thi cong suat

tieu thu trong mach la 80 W Bieu thuc cuong do dong dien trong mach la

A i = 2cos(1007it - 7i/6) (A) B i = 72 cos(1007tt + n/6) (A)

C i = V2 cos(1007:t + 7i/4) (A) D i = V2 cos(1007it - 7c/4) (A)

Vi du 5: Dat dien ap xoay chieu u = 10cos(1007it + 7t/4) (V) vao hai dau doan

mach noi tie'p gom mot tu di^n c6 dung khang 30Q, dien trd thuan R = lOQ,

va cuon day c6 di^n tra thuan lOQ c6 cam khang lOQ Viet bieu thiic di^n

ap giiia hai dau cuon day

A ucd = 5cos(1007it + 37C /4) (V) B ucd = 200 ^/2 cos(1007tt + n/6) (V)

C Ucd = 200cos(1007tt + Tc/6) (V) D Ucd = 5cos(1007it + 7t/4) (V)

Dodo: u,a =U(,cdCos 4 2 = 5cos 1007lt + 371 (V)=^Chon A

Vi du 6: (DH-2009) Dat dien ap xoay chieu vao hai dau doan mach c6 R, L, C

mSc noi tie'p Bic't R = 10 Q, cuon cam thuan c6 L = 0,1/71 (H), tu dien c6

C = 0,5/7t (mF) va dien ap giita hai dau cuon cam thuan la ^ ^

ui = 20 V2 cos(l 007it + 71/2) (V) Bieu thuc dien ap giira hai dau doan mach la

A u = 40cos(l OOTtt + 7t/4) (V) B u = 40cos(1007ct - 7t/4) (V)

C u = 40 N/2 cos(l 007it + 71/4) (V) D u = 40-Jl cos(1007it - 7:/4) (V)

Vi du 7: Doan mach xoay chieu khong phan nhanh gom cac phan tu theo dung

thu tu: dien trd thuan 30 (Q), cuon day thuan cam c6 do tu cam 0,6/7c (H) va

tu dien CO dien dung IOO/TI ().iF) Dien ap giiia tren doan mach chi gom cuon

cam va tu dien c6 bieu thuc ULC = 160cos(1007rt - 7t/3) (V) (t do bang giay)

Bieu thuc dong dien qua mach la

A i = 4V2 cos(1007tt + 7t/6) (A) B i = 4cos(1007tt + 7t/3) (A)

C i = 4cos(1007tt - Ti/6) (A) D i = 4cos(1007tt + n/6) (A) : ih : '

Hudtigdan '-.} /

ZL =wL = 60Q;Zc = = 100Q; ZLC = ^ 0 - ^ C ) = 40<^

tancpL^; = hon)

Z, - Z • (PLC = - — < 0 : ULC tre P^a hon i la 7i/2 (i som pha

33

B S trp klih thiic V^t It LTDtl tr&n k6nh VTV2 t$p 2 - Chu VHn Bien

= > 1 = 1 0 0 K t - - - ( p L C = 4cos lOOrtt- (A)=>Chon D

V i du 8: (DH-2010) Dat dien ap u = Uocoscot vao hai dau doan mach gom dien

tro thuan R, cuon cam thuan c6 do t u cam L va tu dien c6 dien dung C mac

noi tiep Goi i la cuong do dong dien tuc thoi trong doan mach; u , , U 2 va

U 3 Ian lugt la dien ap tuc thoi giira hai dau dien tro, giua hai dau cuon cam

va giCra hai dau tu dien He thuc dung la ^ ^

A i =

-R2 + coL - \ • I ' i (>,f'i/ ;.j';Hn

D i = (oL

Huang dan

Chi Ui Cling pha vdiineni- — ^ Chon C

•;'ir-: Chu y: Neu eho biet bieu thuc u, i thi ta se tinh duge trakhdng

V i du 9: Mot doan mach gom cuon day c6 dien tro thuan 100 Vs Q, c6 do tu

' „ cam L noi tiep voi tu dien c6 dien dung 0,00005/7t (F) Dat vao hai dau doan

• mach mot dien ap xoay chieu u = Uocos(1007rt - Tt/4) (V) thi bieu thuc cuong

do dong dien tuc thoi qua mach i = V2 cos(1007tt - 7c/12) (A) Xac djnh L

V i d u 10: Dat dien ap xoay chieu u = U V2 coslOOnt (V) vao hai dau doan mach

noi tiep gom dien tro R = 50 Q, cuon cam thuan L va tu dien C thi dong dien

•'V; i ' qua mach c6 bieu thuc i = 2 V2 cos(1007rt + 7t/4) (A) Goi U L va Ian luot

, la dien ap hieu dung tren L va tren C He thuc diing la

va cam khang cua cuon cam la

mach s6m pha hon dien ap u la c|)i va dien

ap hieu dung giira hai dau cuon day.la 30 V

Neu thay C i = 3C thi dong dien cham pha hon u goc c|)2 = 90" - c|)i va dien ap hieu dung

giua hai dau cuon day la 90 V Tim Uo

; I2 ^ = 3 1 , ; i j som pha hon u; 12 tre pha hon u; I , 112 Hinh

chieu cua 0 tren I la 0,^

U2LC = U 2 L - U 2 C = U l R z O 3 Z L - ZC = R (1)

UILC = U I C - U H = U2K r : i> Z c - Z l , = 3R (2)

Tu (1) va (2) => Z L = 2 R ; Zc = 5 R Ban dau

tUi trp kiSn thiic V$t IILTBH trSn henJt VTV2 t4tp 2 - Chu VSn Blen

Z M N = A / I ^ M N + ( Z L M N " Z C M N ) Z M N = I ^ M N + ' ( Z L M N ~ ^ C M N )

Zi = Z, i , Z e = -Z(_i ( v o l i la so a o )

+ B A M M O D E !_ ( D e cai dat t i n h toan v d i so p h u c )

( D e cai dat h i e n thi so p h t i c d a n g A Z 9 )

B6 trg klS'n thiic V$t li LTOH tren henh VTV2 tap 2 - Chu VSn Bien

[5^R[ENGl0plOOlR^[)]R| SHIFT I ^ ^ R CMPLX R Math

12 ( A )

V i d u 2 : Dat dien ap xoay chieu u = 220^/2 cos(1007it + n/3) (V) vao hai dau

"doan mach theo diing thii t u gom dien tro thuan R = 50Q, tu dien c6 dien

dung C = 100/7i()j,F) va cuon cam thuan c6 do t u cam L = 0,5/7r(H) mac noi tie'p

1) Tinh tong tro ciia mach Dien ap giiia hai dau doan mach som hay tre

pha hon dong dien trong mach bao nhieu?

2) Viet bieu thiic cua cuong do dong dien tiic thoi qua doan mach

3) Viet bieu thuc dien ap 6 hai dau chua R va C v

4) Viet bieu thiic dien ap 6 hai dau chua C va L " ' t

v i d u 3: M o t mach dien xoay chieu mac noi tie'p gom dien tro thuan R = 15Q,

cuon thuan cam c6 cam khang Z L = 25r} va tu dien c6 dung khang ZQ =

lOO Neu dong dien qua mach c6 bieu thuc 1 = 2 V2 cos(100Tit + 7t/6) (A) thi

bleu thuc dien ap gii>a hai dau doan mach la

A u = 60cos(l OOKt + 571/12) (V) B u = 30 V2 cos(1007it + 7i/4) (V)

C u = 60cos(1007rt - 7i/4) (V) D u = 30 N/2 cos(1007rt - 57r/12) (V)

Bam ISHIFTI [(+)J R se dUdc UQ = 60 Bam |SHIFT| 9 se dMc cp^, = 75

V i d u 4: M o t doan mach dien xoay chieu noi tie'p theo d i i n g t h u t u gom cuon cam thuan L c6 cam khang 30Q, dien tro R = 30Q va tu dien C c6 dung

khang 60Q Dong qua mach c6 bieu thuc 1 = V2 cos(1007it + nl6) (A) Viet

bieu thuc dien ap glQ-a hai dau doan mach chiia LR

Bo trg kicn thiic V^t IILTDII trcn Renh %rrV2 t^p 2 - Chu VSn Bl£a

Bam I SHIFT I [(+)| [=] se duac C/,„ ^ = 60 Bam [SHIFT | y se (fu^tfc cp^^ =75

Vi du 5: Dat dien ap xoay chieu u = 220 ^/2 coslOOTit (V) vao hai dau doan mach

gom dien tro thuan R = 55Q mac noi tiep voi tu dien thi cong sua't tieu thu

tren doan mach la 440 W Bieu thuc cuong do dong dien qua doan mach la

A i = 4cos(1007tt-7t/4) (A) B i = 2 V2 cos(100Trt + 7i/4) (A)

C i = 4cos(1007rt + K / 4 ) ( A ) D i = 2 N/2 cos(1007tt - 7i/4) (A)

y-'- Huang dan :

,•••/'<-p = r R = U-R

22072

•440 = 220\55 55^ + Zc Z e = 5 5 ( Q )

u

" Z " 55+1(0-55) = 4Z —T: <=> i = 4cos 4 1007lt + -4, ( A ) i ^ C h o n C

Vi d u 6: M o t doan mach gom cuon day c6 dien tro thuan 100N/3 Q , C6 do t u

cam l/n (H) noi tiep voi tu dien c6 dien dung 50/TC ().iF) Dat vao hai dau

doan mach dien ap: u = 200N/2 cos(]007it - TC/4) ( V ) Bieu thiic dien ap tiic

thoi tren cuon day la

A u,d = 200 ^/2 cos(1007rt + 7t/12) (V) B u ^ = 100>/2 cos(1007it + 7r/6) (V)

ti C u^d = 200 N/2 cos(1007tt + n/6) (V) D u ^ = 100 ^/2 cos(1007ct + 7:/12) (V),

•g/vju Huang dan

Vi du 7: Cho doan mach xoay chieu noi tiep theo d u n g t h u t u gom cuon cam

thuan 1 CO do t u cam Li = 0,1/?: (H), dien tro thuan 40 Q va cuon cam thuan

2 CO do t u cam L2 = 0,3/71 (H)

/in

Cty TnmnnrvDVVHKltang y/ft

Dien ap 6 hai dau doan mach u = 160 V2 coslOOTit (V) Viet bleu thuc dong

dien qua mach va tinh dien ap hieu dung tren doan mach chua RL2

A i = 2N/2cos(1007it + 7 t / 6 ) ( A ) v a U i^^^ = WO (V)

B i = 2N/2 cos(]OOTit + n/4) (A) va URL2 = 6 0 (V) .,.j;f^ [ ;

C i = 4.cos(1007tt - 71/6) (A) va URLJ = (V)

UKL2 = I-ZRL2 = 2V2.5O = 100V2 ( V ) ^ Chon D

Vi d u 8: Cho mach dien xoay chieu gom dien tro thuan R, cuon day thuan cam

L va tu dien C = 1/n mF mac noi tiep Neu bieu thuc ciia dien ap giCra hai

ban tu dien la Uc = 50%/2 cos(1007Tt - 37T/4) ( V ) thi bieu thiic ciia cuong do

dong dien trong mach la ^ ' i ^ ^ ' ^ ' - ' ^ " ^ f-^-'

A i = 5 V2 cos(1007rt + 37r/4) (A) B i = 5 x/2 cos(1007:t) (A),

C i = 5N/2cos(1007rt-7r/4)(A) D i = 5cos(100Trt - 37i/4) (A)

i = 5V2i cos lOOTlt (A)=>ChonC

Vi du 9: M o t doan mach xoay chieu noi tiep AB gom dien tro lOOQ, cuon cam

thuan CO cam khang lOOQ va tu dien c6 dung khang 200Q Biet dien ap tuc thoi gii>a hai dau cuon cam c6 bieu thiic ui = 100cos(1007Tt - 7T/6) (V) (t do bang giay) Bieu thuc dien ap hai dau doan mach AB la

Bo trffhicn thiic V^t li LTDH tren k&nh VTV2, t^p 2 - Chu VHn Bien

u = 100N/2COS lOOnt- TTTT

1 2 ) ( V ) = > C h o n A

V I d u 10: M o t doan mach xoay chieu no'i tiep A B theo d u n g thu" tir gom dien

t r o R = 25N/3 il, cuon cam thuan L c6 cam i<hang 75Q va tu dien C c6 d u n g

Ichang lOOQ Diet dien ap tuc thoi tren doan mach chiia RL c6 bieu thuc

URi, = 90cos(1007Tt + 7T/6) (V) (t do bang giay) Viet bieu thiic dien ap giira hai

dau doan mach ; » i , 0

A u = 30 cos(l OOKt - 71/3) (V) B u = 30 V2 cos(1007it - 7r/3) ( V ) , '

C u = 30 V3 cos{l OOrtt + TI/6) (V) D u = 30 V2 cos(l OOrtt + 7r/6) (V)

2 ) IJng d u n g de t i m hop k i n k h i cho biet b i e u thiic d o n g d i e n hoac d i e n ap

+ B A M ^ 0 D E [ § ] (De cai dat t i n h toan v o i so phiic) M y i f :

* Neu cho bieu thCrc dong dienva dien ap giita hai dau doan mach

U = U() cos ( O t + Cp^i ) i, : , ;

i = I() COs(0)t + cpi ) i - : ' ' ' ' JX

u

thi CO the t i m tro khang: Z = R + i ( Z L 2 \ " _ U Q ^ ^ U

Vi d u 1: M o t doan mach xoay chieu no'i tiep gom cuon cam thuan c6 do t u cam

0,6/K (H), dien tra thuan R va tu dien c6 dien d u n g C Biet bieu thiic dien ap

gii>a hai dau doan mcich va dong dien trong mach Ian l u g t la:

Cty TiyHHMTVDVVnKhang VIft

V i d u 2: M o t doan mach xoay chieu gom dien tra thuan R mac noi tiep hop kin

X H o p kin X hoac la tu dien hoac cuon cam thuan hoac dien tra thuan Biet bieu thiVc dien ap giua hai dau doan mach va dong dien trong mach Ian luot la: u = 100 72 coslOOnt (V) va i = 4cos(100Tit - TI/4) (A) H o p kin X la

A dien tra thuan 50 Q

B cam thuan voi cam khang Zi, = 25 Q '

C tu dien voi d u n g khang Zc = 50 Q

D cam thuan voi cam khang Zi = 50 Q

v i d u 3: M o t doan mach chiVa hai trong ba phan t u : tu dien, dien tro thuan,

cuon cam thuan mac no'i tiep Biet dien ap giua hai dau doan mach va cuong do dong dien qua no Ian lugt c6 bieu thuc: u = 60cos(1007tt - 7t/2) (V),

i = 2sin(100Kt + 7r/6) (A) H o i trong doan mach c6 cac phan t u nao? Ti'nh

d u n g khang, cam khang hoac dien tro tuong ung v a i m o i phan t u do Tinh cong suat tieu thu ciia doan mach , •>

V i d u 4 : Dat vao 2 dau hop k i n X (chi gom cac phan t u mac noi tiep) m o t dien

ap x o a y chieu u = 1 0 0 c o s ( 1 0 0 K t + TI/6) (V) t h i cuong d o dong dien qua mach

i = 2 c o s ( 1 0 0 7 i t + 271/3) ( A ) N e u thay dien ap tren bang dien ap khac c6 b i e u

t h u c u = 400-72 cos(2007rt + 7i/3) (V) t h i cuong d g dong dien:

i = 5 72 c o s ( 2 0 0 7 r t - 7i/6) ( A ) X c6 t h e c h i i a

A R = 2 5 ( Q ) , L = 2 , 5 / 7 i ( H ) , C = 10-*/7t ( F )

B L = 0,7/71 ( H ) , C = 10-3/(1271) ( F )

' 4 3

Bo trp hien tiluc V^l li L TP 11 tren kcnh VTV2 t4p2-Chu V0n Blin

V i d y 5: Dien ap a 2 dau cuon day c6 dang u = lOOcoslOOTit (V) va cirong do

d o n g dien qua mach c6 dang i = 2cos(100Trt - 7r/3) (A) Dien t r o thuan cua

cuon day la:

Chu y: Mach dien dp xony chicu A B gom hai doan mach AM (dd bict) va MB (chua

biet) mac noi dep Dexdc dink MB ta dim vdo: Z ^ B = = x Z ^ M

-i " A M

V i d u 6: M a c h dien ap xoay chieu A B g o m hai doan mach A M va M B mac noi

tiep Doan A M g o m dien t r o thuan R = 50 Q mac n o i tiep v o i tu dien c6

d u n g k h a n g 50 Q, doan M B la cuon day c6 dien tro thuan r va c6 d p tir cam

L Biet bieu thiVc dien ap tren doan A M va tren doan M B Ian l u g t la:

UAM = SOcoslOOTit (V) va UMD = 200 72 cos(1007Tt + 77T/12) (V) Gia tri cua r va

cam k h a n g Z L Ian lu-gt la

U K = 120cosl007rt (V) va u^^ = 120cos(100Tct + K/3) (V)

K e U u a n nao khong dung? , •,;>;.v/i^v

A C u o n day CO dien tro r khac 0

B Dien ap giua hai dau doan mcich A B tre pha TI:/6 SO voi dien ap giija hai dau cuon day. j>,^ ,,•,;3 " : • ' v : ,

C D i ^ n ap h i ^ u d u n g giCta hai dau doan mach A B la 60 7 3 ^ ^

mac noi tiep Doan A M gom dien tro thuan 50 il mac noi tiep v o i tu dien c6

d u n g khang 50 Q Biet bieu thuc diC^n ap tren doan A M va tren doan M B Ian lugt la: UAM = 80cos(100nt - n/4) (V) va u.vm = 200 72 cos(1007it + TT/4) (V)

Tinh tong tro cua doan M B va do lech pha cua dien ap tren M B so v o i dong

neu bam p h i m '=' t h i duoc ket qua 176,77669 + 176,77669i, con neu bam

'shift 2 3 = ' thi dixgc ket qua 250) A V , ,

45

Bd trphJSn thitc V$t IILTDH tren henli VTV2. t^p 2 - Chu Van Bien

V i d u 9: Dat vao hai dau AB mot dien ap xony chicu co gia trj hieu d u n g va tan

so khong doi Doan mach AB gom doan mach A M noi tiep voi doan mach

MB Doan mach A M gom cuon cam thuan co cam khang 50 (Q) va dien tro

thuan Ri = 50 (Q) mac noi tiep Doan mach NB gom tu dien co dien d u n g C

va dien tra thuan R2 mac noi tiep Dien ap tuc thoi 6 hai dau doan mach

A M va M B Ian lugt la UA.\ = 200cos(100Tit + TI/6) (V) va UMH = 100cos(1007Tt

-57T/12) ( V ) H o i tren AB tong cam khang nhieu hon hay it hon tong dung

khang bao nhieu? Tinh tong tra cua doan mach AB Tinh do lech pha cua

dien ap tren AB so voi dong dien Tinh he so cong suat cua mach AB

(50 + 50i)

Sau khi nhap vao may tinh so'lieu n h u tren:

Nell bam p h i m '=' ta duoc ki^'t qua: 67,68 + 19,381

Tir ket qua nay ta suy ra: R A B = 67,68Q va Z , ( ^ B ) " Z C ( A B ) = 19,38Q (tong

cam khang nhieu hon tong d u n g khang la 19,38 Q)

Neu bam p h i m 'shift 2 3 =' ta duoc ket qua: 70,4Z0,279

T u ket qua nay ta suy ra: Z ^ B = 70,4Q va cpAi? = 0,279 rad (Dien ap UAB som

pha h o n i la 0,279 rad)

He so cong suat cua mach AB: coscpAu = cos0,279 = 0,96 '"'

Co the tinh true tiep coscpAis bang may tinh casio fx570es t u ket qua:

1 + 12

200Z

^-6 (50 + 50i)

Bam p h i m '='

Bam 'shift 21=' (de lay goc cpAis)

Bam 'cos =' se duoc ket qua 0,96 (tuc la cos(pAB= 0,96)

V i du 10: (DH-2011) Doan mach AB gom hai doan mach A M va M B mac noi

tiep Doan mach A M gom dien tro thuan Ri = 40 Q mac noi tiep voi tu dien

CO dien d u n g C = 0,25/:: mF, doan mach M B gom dien tro thuan R2 mac noi

tiep voi cuon cam thuan Dat vao A, B dien ap xoay chieu co gia tri hieu

d u n g va tan so khong doi thi dien ap tuc thoi 6 hai dau doan mach A M va

• M B Ian l u o t la : UAM = 50 V2 COS(1 OOnt - 7Tr/l 2) V va UMB = ISOcoslOOnt (V)

He so cong suat cua doan mach AB la

- A M

-7K 12' J

Thuc hien cac thao tac bam may tinh [=] bllilil dJ EE 0,84 nghia la coscp « 0,84 => Chon B

cos

x ( 4 0 - 4 0 i )

duoc ket qua

V i du 11: Cuon day thuan cam co he so t u cam L = 2/71 (H) mac noi tiep voi doan mach X Dat vao 2 dau mach mot dien ap u = 120N/2 cosl007:t (V) thi cuong do dong dien qua cuon day la i = 0,6 V2 cos(1007:t - 71/6) (A) T i m hieu dien ap hieu d u n g giua 2 dau doan mach X

A.240 V B.120N/3V C.60^/2V D 1 2 0 V

Huong dim

ux = u - U L = u - I Z L = 120>y2 - (0,6V2Z ~ 30)200i = 120^y2Z - 60 r:>Ux = 1 2 0 ( V ) = ^ C h o n D

VA DIEU KlfN LECH PHA

tan cp = 0 =>(p = 0 ne n u = U R , i : cung pha :

V i du 1: Cho doan mach RLC noi tiep co gia t r i cac phan t u co d i n h Dat vao hai dau doan mach nay mot hieu dien the xoay chieu co tan so thay doi K h i tan so goc cua dong dien bang COQ thi cam khang va d u n g khang co gia tri 20

Q va 80 Q De trong mach xay ra cong huong, phai thay doi tan so goc cua dong dien den gia t r i CO bang

A 2 COg B. 0,25 COQ C 0,5 C O Q D 4coo

trphtSn thUc V$t It LTDII Ht'ni hcnh VTV2, t^p 2 - Chu VMii isk-ri

V i d u 2: M o t cuon day c6 dien tro thuan 100 (Q) va c6 do t u cam l/n (H), noi

tiep voi tu dien c6 dien d u n g SOO/TI ().iF) Dat vao hai dau doan mach mot

dien ap xoay chieu tan so 50 (Hz) De dong dien trong mach cung pha v o i

dien ap ta phai ghep noi tiep voi tu C mot tu C i c6 dien d u n g la bao nhieu?

A 500/K (|,iF) B 250/Tt (laF) C 125/7t (^iF) D 50/7t (^iF)

De (p = 0 thi Zc + , = Z, => — + = coL => C, = —(i-iF) => Chon C

V i d u 3: Cho doan mach dien xoay chieu gom cuon day thuan cam L, tu dien C

va bien tro R mac noi tiep Khi dat vao hai dau mach mot dien ap xoay

chieu on d j n h c6 tan so'f thi thay An^i'^hC = 1 K h i thay doi R thi

A dien ap hieu d u n g gii>a hai dau bien tro thay doi ,

B tong tro cua mach van khong doi

C cong suat tieu thu tren mach thay doi ^, ,

D he so cong suat tren mach thay doi :i , , , ,

Hu6iig dan

Tir dieu kien 4TI^FLC = 1 suy ra Z L =ZQ, tuc la trong mach xay ra cong

'U,^ = U = khong doi VR

hirang va liic nay :

cos(p = —• = 1 = khong doi VR

V i d\ 4: Doan mach xoay chieu RLC mac noi tiep, dien tro thuan cua mach

R = 50Q K h i xay ra cong huong d tan so'fi thi cuong do dong d i f n bang 1 A

Chi tang tan so cua mach dien len gap doi thi cuong do hieu d u n g trong

mach la 0,8 A Cam khang cua cuon day khi con 6 tan so fi la

hay V - - • • • 0,8

V i du 5: ^^9* doan mach AB gom hai doan mach A M va M B mac noi tiep Doan mach A M gom dien tro thuan Ri mac noi tiep voi tu dien c6 dien d u n g C , doan mach M B gom dien tro thuan R2 mac no'i tiep v o i cuon cam thuan c6 do

tu cam L Dat dien ap xoay chieu u = Uocoscat (Uo va co khong doi) vao hai dau doan mach A B thi cong sua't tieu thu cua doan mach AB la 85 W K h i do LCCO^ = 1 va do lech pha giira UAM va UMB la 90" Neu dat dien ap tren vao hai

dau doan mach M B thi doan mach nay tieu thu cong sua't bang: ^n^,

Dat dien ap vao AB :

Dat dien ap vao M B :

Chu y: Neii cho bicii thuc u, ui hoac uc ta dnh dime do lech pha cua u vai UL hoac

uc Mat khdc ui sani han i la KI2 va uc tre han i la TT/I ; tie do suy ra (p

V i d u 6: M o t mach dien xoay chieu gom mot tu dien C noi tiep v o i m o t cuon day Dat vao hai dau doan mach mot dien ap u = U V2 coscot (V) thi dien ap hai dau tu dien C la u ^ = U N/2 cos(a)t - 7t/3) (V) Ty so gii>a d u n g khang va cam khang bang - •

A 1/3 B 1/2 C 1 D.2 x^^^^m

Huang dan

V i I luon luon som han la n/2 va theo bai ra U som han UQ la n/3 nen

^ tre pha han I la 71/6, tuc la (p = - —

6 tri? Men thitc V$t li LTDH tren htinli Vli2 l.,p J - Chu VSn BlSa

i du 7: Mot doan mach xoay chieu noi tiep AB gom dien tro thuan R, cupn

cam thuan L va tu dien c6 dien dung C Dien ap giiia hai dau doan AB la:

u = Uo>/2 coscot (V) thi dien ap tren L la U L = Uo N/2 cos(cot + 7t/3) (V) Muon

mach xay ra cong huang thi dien dung ciia tu bang

' Huang dan

Vi 7 luon luon tre pha han f/, la n/2 va theo bai ra U tre pha han U^^ la n/3

nen U som pha hon / la TC/6, tiic la cp = —

3 ^ — = i — C = - C => Chen B (oC 3coC 4

i du 8: Mot doan mach noi tiep gom cuon cam thuan, tu dien va dien tro R

Dat vao hai dau doan mach dien ap xoay chieu c6 gia tri hieu dung 120V thi

cam khang cuon cam la 25Q va dung khang cua tu la lOOQ Ne'u chi tang

tan so dong dien len hai Ian thi dien ap hieu dung giiia hai dau dien tro R la

Xay ra cong hudng => UR = U = 120(V) => Chon B

du 9: Mot doan mach noi tiep gom cuon cam thuan, tu dien va dien tro R

Dat vao hai dau doan mach dien ap xoay chieu c6 gia tri hieu dung U thi

dung khang gap bon Ian cam khang Neu chi tang tan so'dong dien k Ian thi

dien ap hieu dung giiJa hai dau dien tro R la U Gia tri k bang

CM y: Neu cho Met = nL/C thi = nZj^Zc vd Ua' = H U L U C •

V i dv 10: Mot doan mach AB mac noi tiep gom: dien tro thuan R, tu dien c6 dien dung C va cuon cam thuan c6 do tu cam L thay doi dugc Dat vao hai dau doan mach AB dien ap xoay chieu 100 V - 50 Hz Dieu chinh L de

R 2 = 6,25L/C va dien ap 6 hai dau cuon cam lech pha so voi dien ap o hai

dau doan mach AB goc n/2 Dien ap hieu dung a hai dau cuon cam la

dau cuon cam hang 200 (V) Khi do hieu dien the hieu dung giCra 2 ban hi la

A. 100 V3 (V) B. 200 (V) C. 100 (V). D. 100 V2 (V)

Humgdan

' T 2 T , 2 / T T I T \ T T T T ^ ''^ M Ji'A LV^iH %St^i ii ' J • '

U, =Ur = + ( U L - U c f ^ UR = U = 100

Uld = + => 200^ = 100^ + =^ Uc = lOoVs (V) => Chon A

V i du 12: Doan mach xoay chieu noi tiep gom dien tra thuan R, hi dien C va

cuon cam Lr Dat vao hai dau doan mach mot dien ap xoay chieu 120V - 50Hz thi dien ap giira hai dau doan R-C va dien ap giira dau doan C-Lr va co

Dien ap hieu dung gifra hai dau tu dien la

A 3 0 > ^ V B 6 0 V 2 V C 3 0 V 3 V D.30V

C/iii y; Tin' y; tn CQn<g hiani^ t h i hmn, Pimu, URIWIX Dcxdc dinh xu the tang ginin, ta

can cit vao phqm vi him thicn: cang gan vi tri cong huang thi I, P, UR cang Ian;

cang xa vi tri cong huang thi cdc dqi lugng do cang he • • ^ '' •

V i du 13: Dat dien ap xoay chieu u = 220cosl007i:t (V) vao hai dau doan mach

gom dien tro thuan 100 Q, cuon day thuan cam c6 do t u cam 1/K ( H ) va tu

dien c6 dien d u n g C thay doi, mac no'i tiep Neu thay doi dien d u n g C tu

200/7: (|iF) den SO/T: (|.iF) thi cuong do dong dien hieu d u n g qua mach

A giam B tang

C cue dai tai C = C2 j„ - D tang roi giam

* 1 ] 100

K h i mach cong huong: wL = — =>€„= — - = (f.iF)

Vi — ( 1 1 F ) > C„ > — ( M F ) nen I tang roi giam => Chon D

7t 71

^ Chuy:_ : : , „ ' ; • 1 , ,

Khi mach R^LiCj xay ra cong huang ta c6: w^L,C, = 1

Fo>' Khi mach R2L2C2 xdy ra cong huang ta c6: w j L j C j = 1 '•

V<o?C, « 2 C 2 J CO C, C,

Srt;( khi tun dinrc lien he cdc co ta suy ra lien hecdcfhoqc cdc T

V i dy 14: H a i doan mach no] tiep RLC khac nhau: mach 1 va mach 2, cong

h u o n g v o i d o n g dien xoay chieu c6 tan so goc Ian l u g t la coo va 2coo Biet do

t u cam cua mach 2 gap ba do t u cam ciia mach 1 Neu mac noi tiep hai doan

mach dcS vc7i nhau thanh mpt mach thi no se cong h u o n g voi dong di^n

xoay chieu CO tan so gocla ,„ ^ , ^ ,^ ^ , , , ^

A cooN/3 B l,5coo C coo7l3 D 0,5coo

CO^I.2C2 = 1

C,

1 C- = co^L2

V i dy 15: Mach xoay chieu R | , L [ , C | mac noi tiep c6 tan so'cong h u o n g f,

Mach R 2 , L 2 , C 2 mac noi tiep ccS tan so cong h u o n g k Biet C] = 2 C 2 va

= 2f| Mac ncYi tiep hai mach do voi nhau thi tan so cong hucrng la

coCj C0C2 • CO ^to?C] 2co?Ci

Botrpkien thitc V^t li LTDH tren henli VTV2 t^p 2 - Chu Van Bien

2) Dieu ki#n I^ch pha

* Tren doan mach khong phan nhanh chi chua cac phan t u R, L va C Gia sir

M , N , P va Q la cac diem tren doan mach do Do lech pha ciia \Xy^^, upg so

v6i dong dien Ian l u g t la: tancp^^fj = ^^^^ va tancppQ = ^'"^

* U M N U p Q k h i va chi k h i tancpMN tancppQ = - 1 ^ PQ ^ _^

V i du 1 : (DH-2010) M o t doan mach AB gom hai doan mach A M va M B mac

noi tiep Doan mach A M c6 dien tro thuan 50 Q mac noi tiep v a i cuon cam

thuan CO do t u cam I / K ( H ) , doan mach M B chi c6 tu dien v o i dien d u n g

thay doi duoc Dat dien ap u = UocoslOOrct (V) vao hai dau doan mach AB

Dieu chinh dien d u n g ciia tu dien den gia trj Cj sao cho dien ap giua hai

dau doan mach A B lech pha 7i/2 so v o i dien ap giira hai dau doan mach

A M Gia t r i ciia Ci bang

A 40/71 (laF) B.80/7r(nF) C 20/7i (^F) D 10/7i(^F)

=>Zc =125(Q)=>C = ^ — = -.10"^(F)=>ChonB i ,H iofi i-^f/

V i du 2: Cho doan mach xoay chieu mac no'i tiep theo diing t h u t u gom cuon

cam thuan c6 do t u cam L = 4/K ( H ) , dien tro thuan R va tu dien c6 dien

dung C = 0,l/(7r) (mF) Ne'u dien ap hai dau doan chua RL vuong pha vai

dien ap hai dau doan chua RC thi R bang

A 30 Q , B 200 Q C 300 Q D 120 Q

Huong dan

tan (PRI tan (PRC = - 1 => • — ^ = - 1 => R = J — = 200 (Q) => Chon B

Chu y: Ncu 92 - cp, = A(p thi tan ((p2 -^>^) = = tan ^^P

1 + tancpj tan(pi

V i du 3; Dat dien ap xoay chieu vao hai dau doan mach AB gom hai doan

mach A M va M B mac noi tiep Doan A M gom dien tro thuan R = 100>y3 Q

mac noi tiep v o i cuon cam thuan c6 cam khang Zi., doan M B chi c6 tu dien

CO d u n g khang 200Q Biet dien ap giCra hai dau doan mach A M va dien ap

giij-a hai dau doan mach AB lech pha nhau 7c/6 Gia trj Zi bang

Vi dien ap giira hai d a u doan m a c h A M v a dien ap giiia hai d a u doan m a c h

AB lech p h a nhau 71/6 nen suy ra cp^^ - cp^H = - >1v|.;i!:;M'J:>»TS.':t';yrii tancpAM -tantpAB _ • ''^ 200.100N/3 1

Buoc 1: V o i Z L = 1 0 0 Q thi cpAM = 7t/4 va cpMB = -7t/4 => khong d u n g

55

Bd trp kiSn tbiic V$t It LTOHtri ,i h<nli 1 11 J I.ip J ( Ini VMn Bten

Bu-oc 2: V a i Zi, = 100 Q thi c p A M = 7t/3 va cp.viB = -7r/12 => diing

, Buoc 3: V o i Zi = 300 Q thi khong hop ly

Buoc 4: Ke't luan chon A

V i d u 5: Dat dien ap xoay chieu on djnh vao hai dau doan mach mac no'i tiep

g o m cuon day co dien tro thuan R, co cam khang 150 Q va tu dien co dien

d u n g C thay doi dugc K h i d u n g khang Zc = 100 Q va Zc = 200 Q thi dong

dien trong mach co pha ban dau hon kem nhau TC/3 Dien tro R bang

V i d u 6: Su d u n g m o t dien ap xoay chieu on d i n h va 3 d u n g cu gom dien tro R,

tu dien C, cuon cam thuan L K h i mac Ian l u g t hai doan mach noi tiep RC

? hoac RL vao dien ap noi tren thi cuong do dong dien tiic thoi trong hai

t r u o n g hop lech pha nhau 27t/3 va co cijng gia t n hieu d u n g 2 A K h i mac

, doan mach noi tiep RLC vao di^n ap noi tren thi gia trj cuong do dong dien

hieu d u n g trong mach la ' \

V i d u 7: Doan mach xoay chieu gom cuon thuan cam L , noi tiep voi dien tro R

Dien ap xoay chieu hai dau mach chi tan so goc co thay d(>i ducjc Ta thay co

2 gia trj ciia co la co^ va CO2 thi do lech pha cua hieu dien thegiCra hai dau doan mach v o i dong dien Ian lugt la (pi va (p2 Cho biet cpi + 92 = n/4 Chon he

Ami-11^^-=> (o), + CO2 ) L R = R~ - coiUjLr => Chon A , •„ .,,

V i d u 8: Cho mach gc^m tlien trci thuan R, tu dien C va cuon day thuan cam L mac no'i tiep VtVi cac gia t r i ban dau thi cuong do hieu d u n g trong mach

dang CO gia trj I va dong dien / som pha n/3 so v o i dien ap ;( dat vao mach

Neu ta tang L va R len hai Ian, giam C d i hai Ian thi I va dc) lech pha giua

va se bien doi thenao? ,5.) 1-">IS^;

A I khong doi, do lech pha khong doi , yUuA^i rod? imt mli WM) ^ n l n '

-B I giam V 2 Ian, do lech pha khong doi dsSm i-^tfe : I '

C I giam 2 Ian, do lech pha khong dcii ,:Q,-fC>r*>

D I va do lech pha deu giam ;n oSv

Bo trfi kicn thiic V^t li LTDH tren hcnh VTV2, t^p 2 - Chu VSn BiBn

I , M , li J , i.1 I >U : ,>) t 'I ' >i

Huang dan r

Z, I - 3R tan = < 0

1) Mach R L C noi vdi nguon xoay chieu

Cong suat toa nhiet: P = I^R = U^R

R

He so'cong suat: cos(p = — =

R^ + ( Z , -Zcf ,

Z , / R ^ + ( Z L - Z ^ ) ^ „;il OLM.-.,

Dien nang tieu thu sau thoi gian t: A = Pt • • ^'

V i d u 1 : M o t mach A B noi tiep gom t u dien c6 dien d u n g C = 0,l/(87t) mF, dien

tro R = 100 Q, cuon day c6 do t y cam L = l/ii H va c6 dien tra r = 200 Q Mac

AB vao mang dien xoay chieu c6 dien ap 220 V, tan so 50 H z

1) Tinh he so cong suat cua cuon day va cua mach AB

2) T i n h cong suat cua cuon day va cua mach A B T i n h dien nang ma mach

A B tieu thu trong mot phiit

£)ien nang ma doan mach A B tieu thu trong mot phiit

CO dien tra r va do t y cam L va doan NB chi c6 tu dien c6 dien d u n g C

Cong suat tieu thu trung binh 6 doan j

Vi du 3: Dat dien ap u = 400cos(100Ttt + TC/3) (V) vao hai dau doan mach RLC

no'i tiep c6 R = 200 Q, tha'y dong dien va hieu dien t h e o hai dau doan mach lech pha nhau 60" T i m cong suat tieu thu ciia doan mach?

Vi du 4: Cho doan mcich RLC, dat vao doan mach dien ap xoay chieu

u = U>/2 coslOOnt (V) Khi U = 100 V thi cuang do dong dien trong mach tre pha hon dien ap la 7T/3 va cong suat toa nhiet cua doan mach la 50 W

Khi U = 100 V3 V, de cuang do dong dien hieu dung van n h u cu thi can ghep

noi tiep v d i doan mach tren dien tra Ro c6 gia trj

~Bo tr^kien tlsiic Vat li L mil l,<^n kenh VTVZ t$p 2 - Chu VMn Bien

7(R + R o r + ( Z L - Z c ) ' V ' ^ + ( Z i - Z c )

=> Chon B

V i d u 5: Dat dien ap u = 200cosl007it (V) vao doan macii noi tie'p g o m dien tro

R = 100 Q, tu dien co dien d u n g C = 15,9 |.iF va cuon day tliuan cam c6 d o tu

cam L thay doi dugc Biet cong suat tieu thu cua mach la 100 W va cuong

do dong dien trong mach som pha so v6i hieu dien the'gii>a hai dau mgch

Gia trj L i cua cuon cam va bieu thuc cuong d o dong dien qua mach dirge

V i d\ 6: Doan mach xoay chieu gom dien tro thuan R, cugn day thuan cam L

va tu dien co dien d u n g C thay doi dugc Dien ap dat vao hai dau mach c6

tan so 50 H z Ban dau do lech pha giira dien ap giCra hai dau mach va dong

dien la 60" thi cong suat tieu thu trong mach la 50 W Thay doi C de dien ap

giira hai dau mach cung pha vai i thi mach tieu thu cong sua't la

A lOOW B 200W C 5 0 W • D 1 2 0 W

U'»i(b./t Hitoitg dan if;tb , D ' j ^ i •

P = UI cos CP = —cos^ ^ > = ^ ^ = ^ P2 = P, = 200 (W) Chon B

R P| cos (pj >•• • <.•'• cos" IP|

Chiiy: «

cos" (p Kcl hap vai dicu kicn (p^±(p.,=a hi tiiili duvc cik dqi limn<^ khdc

cos- ^1

V i d u 7: Dat dien ap xoay chieu on djnh vao hai dau doan mach gom cugn day

noi tie'p v o i tu dien c6 dien d u n g C thay doi K h i C = C i dong dien trong

mcich la i) va cong sua't tieu thu cua mach la P, K h i C = C2 > C i thi dong

di^n trong mgch la i j va cong sua't tieu thy la P2 • ^^'^^ ^2 3Pi va i , vuong

60

Cty Timn MTV D vvniihang Vtft

pha voi i2 • Xac djnh goc l§ch pha cpi va <p2 giCra dien ap hai dau doan mach

i, va i2 !C : vm ):y.i<\.> iJ'^: '^^'•^ ' ' 'p'

A (pi = 71/6 va (p2 = - 7 T / 3 A I g n s j b ti^- B (pi =-7r/6 va (p2 = 7i/3 r

C (pi = -7t /3 va (p2 = n/6 •fi^iikf.U> v.<l\ (pi = -n/4 va (p2 = n/4 ui u

yj3 COS c/>| cos ^,

V i d u 9: Cho mach xoay chieu gom cugn day khong thuan cam co do t u cam L, dien tro r mac noi tie'p v o i tu dien ccS dien d u n g C thay d o i Dien ap 6 2 dau doan mach u = U V2 cosl007rt V K h i C = C i thi cong suat mach co gia trj la

240 W va i = I V 2 sin(1007rt + 7t/3) A K h i C = C2 thi cong sua't cua mach cue

dai Xac dinh cong sua't cue dai do? '

A 3 0 0 W B 320W C 960 W D 480W

Huaitgdan

2 ^

P = _ c o s 2 <p = P,^,„^, ha.mg cos^ ^>=>240 = P,,„g ha<.ng ^

•Pc6„gha(,nK=320(W)=>ChonB final} i=fy.^ i J i ' i f

61

B S trp kiSn thitc V^t It LTDtl tren kenh VTV2 t^p 2 - Chu Vitn Blen

V i d u 10: Trong mot mach dien xoay chieu gom mot dien tro thuan mac noi

tiep voi mot tu dien Dien ap hieu dung dat vao doan mach la 150 V, dong

dien chay trong mach c6 gia tri hieu dung 2 A D i ^ n ap h i ^ u d u n g giiia hai

ban tu dien la 90 V Cong suat tieu thu ciia doan mach la ' ^ HV7:)

A 200W B 180W C 240W D 270 W

Huang dan ,

U = U K + U c =>150 = U R + 9 0 ^ UR = 1 2 0 ( V ) H

P = I^R = I.UK = 240 (W) =^ Chon C

V i d u 11: Dat mot dien ap u = 100 V2 coslOOnt (V), (t do bang giay) vao hai dau

doan mach gom tu C noi tiep voi cuon day thi dien ap hieu dung tren tu la

100 V S V va tren cuon day la 200 V Dien tra thuan ciia cuon day la 50Q

Cong suat tieu thu dien ciia doan mach la: ' ' ' "

d u 12: Dat mot hieu dien the xoay chieu u = 120>/2 cos(1007rt - n/6) V v i

dau doan mach RLC no! tiep cuon day thuan cam c6 L = 0,l/7t H thi tli

dien ap hieu d u n g tren tu va tren cuon day bang nhau va bang 1/4 dien > ^

hieu d u n g tren R Cong suat tieu thu tren mach la

A 3 6 0 W B 180W C 1440W D 120W

- Huong dan • Z'^^^i^J

M = U ,

R = 4Z| =4coL = 40(Q) Mach cong hUdng => I = —

p = I^R = — = 360(W) => Chon A ' * ^ '

du 13: M o t doan mach gom cuon day no'i tiep v o i tu dien c6 dien dung

C = 0,1/K (mF) Dat vao doan mach dien ap xoay chieu u = 100 V2 cosSOnt (V)

thi thay dien ap giiia hai dau cuon day sam pha hon dong dien trong mach

la 7t/6, dong thai dien ap hieu dung tren cuon day gap doi tren tu dien

Cong suat tieu thu ciia doan mach la

V i d u 14: M o t mach dien xoay chieu noi tiep gom tu dien c6 d i ^ n dung C, dien

tro thuan R va cuon cam thuan c6 cam khang 80 Q Do Ion he so cong suat

ciia doan mach RC bang he so cong suat ciia ca mach va bang 0,6 Dien tro thuan R CO gia trj

R = 30(Q)=:>Chon B (ri'ri'jib i<:

V i d u 15: Mcich dien xoay chieu gom cuon day mac noi tiep v a i tu dien Cac dien ap hieu d u n g 6 hai dau doan mach 120 V, a hai dau cuon day 120 V va

a hai dau tu dien 120 V He so cong suat ciia mach la

V i d u 17: Doan mach dien xoay chieu mac no'i tiep gom tu ctien, dien tra thuan

va cuon cam thuan Dien ap hieu dung 6 hai dau doan mach va tren cuon

cam Ian ktot la 360 V va 212 V He so cong sua't cua toan mach coscp = 0,6

Dien ap hieu d u n g tren tu la

A 500(V) ^ B 200 (V) C 320 (V) D 400 (V) ,,5,^

! , , , , , , A , , r.: r^:' m -O' ^ " ' ^ - " S , , , „

cos(p = ^ = 0,6=^U|, =0,6U = 2 I 6 ( V ) >,n,'r*^nit\ (bi ill

U- = Uf, +(U| - U^.)^ => 360- = 216- +(212- U(.)- ^ =500(V)

Chon A

V i d u 18: Doan mach dien xoay chieu mac no! tiep gom tu dien, dien tro thuan

va cuon cam thuan co cam khang 80 Q Dien ap hieu d u n g a hai dau doan

mach va tren tu Ian luot la 300 V va 140 V Dong dien trong mach tre pha so

voi dien ap hai dau doan mach va he so cong sua't cua mach coscp = 0,8

C u o n g do hieu d u n g dong qua mach la

A 1 (A) B 2 (A) C 3,2 (A) D 4 (A)

Humtgdan

Z, >Z^-=>U| >Uc;coscp = - ^ = 0,8 =i.U|, =0,8U = 240(V) " ' ' t '

U- = Uf^ +(U| - Ue)" ^ 300- =240- + { U , -140)- =>U| =320(V)

^ = 4 ( A ) ^ Chon A ^'5'"

Zi

Chil y: NCni hict cCm;^ siid't tiC'u thu trcii toan mach de tinh dien tnr Iioac cos(p ta

dim vao con;^ thu'c: P = l~R = •

R ^ + ( Z , Z J

-V i d u 19: Dat vao hai dau ctoan mach A B mot dien ap xoay chieu:

u = 400cos(1007rt) ( V ) Mach AB gom cuon day co dien tro thuan R co do t u

cam 0,2/7: (H) mac noi tiep voi tu dien co dien d u n g 100/K (HF) Neu cong

sua't tieu t h u R la 400 W t h i R bang :

R = 160(Q)

V i d u 20: Dat vao hai dau doan mach mot dien ap xoay chieu co gia t r i hieu

dung 200 V Doan mach g o m cuon day co dien tro thuan R co cam khang

140 Q mac noi tiep v o i tu dien co dung khang 200 Q Biet cong sua't tieu thu

tren mach la 320 W He so'cong sua't ciia mach la

V i d u 21: Dat vao hai dau doan mach mot dien ap xoay chieu 100 V - 50 H z Doan mach mac noi tiep g o m dien tro thuan R, cuon cam co do t y cam L =

I/TI (H) va tu dien co d u n g khang Zc Biet cong sua't tieu t h u tren mach la

100 W va khong thay d o i neu mac vao hai dau L m o t ampe-ke co dien tro khong dang ke Gia trj R va Zc Ian luc^t la

r Z c = 5 0 ( Q )

R = 50(Q)

100^ R R^+Z^

> Chon B

U ^Jl'nwtl Mach dien liic dau

Mach dien sau

65

Bo tip hien thiic Vpl li LTDH tren hSnh VTV2, t^p 2 - Chu Van Bien

V i du 22: Dat vao hai dau doan mach AB mot dien ap xoay chieu 100 V - 50

Hz Mach AB gom cuon day c6 dien tro thuan 20 Q c6 cam khang 60 Q mSc

noi tie'p voi tu dien c6 dung khang 20 Q roi mac noi tiep voi dien tro R Ne'u

cong suat tieu thu R la 40 W tiVi R bang

V i du 23: Mot mach gom co dien tro R, cuon cam thuan L va tu dien C mac noi

tie'p, dien ap giua hai dau doan mach u = 50 \/2 coslOOnt ( V ) Dien ap hieu

dung 6 hai dau cuon cam va hai dau tii dien Ian lugt la U L = 30 V va Uc = 60

V Bie't cong suat tieu thu trong mach la 20 W Gia tri R bang

V i du 24: Mot mach dien xoay chieu gom dien tro R noi tiilp voi cuon day c6

dien tro 1 0 Q Dat vao hai dau doan mach dien ap u = 40 ^/6 coslOOTtt ( V ) , (t

do bang giay) thi cuong do dong dien cham pha hon dien ap giua hai dau

doan mach la Tt/6 va cong suat toa nhiet tren R la 50 W Cuang do hieu

dung trong mach la: '-i";*') ' •

A 1 A hoac 5 A B 5 A hoac 3 A C 2 A hoac 5 A D 2 A hoac 4 A

\'d V Huong diin

' I = 1(A)' UIcoscp = PR + I^r ^ 40V3.1.— = 50 + I^.IO Chon A

I = 5 ( A )

V i du 25: Mach dien gom cuon day c6 dien tro thuan 10 mac no'i tie'p voi mot

bong den 120 V - 60 W Noi hai dau mach dien voi nguon dien xoay chieu

220 V - 50 Hz, thi den sang binh thuong Do t u cam cuon day la:

A 1,19 H ~r::::Z B 1,15H C 0,639H D 0,636H

Htiatig dan

Khi den sang binh thirang thi cuong do dong dien chay qua va dien tro

thuan cua den:

Vi du 26: Dat dien ap u = 120sin(1007Tt + TT/3) (V) vao hai dau mot doan mach

thi dong dien trong mach c6 bieu thuc i = 4cos(100TTt + nib) (A) Cong sua't

tieu thu cua doan mach la A.240>y'3W B.120W C 240 W D 120>/3 W

-sau do ba'm 0 dugcketqua 120-207,851 , , • :

Vi du 27: Doan mach AB g5m hai doan A D va DB ghep noi tie'p Dien ap tiic thoi tren cac doan mach va dong dien qua chung Ian lugt c6 bieu thuc:

UAD = 100 V2 cos(100nt + nil) (V); um = 100 76 cos(1007it + 2TI/3) (V)

va i = V2 cos(100r!:t + 7T/3) (A) Cong sua't tieu thu cua doan mach AB la

Bd trp hien thiic V$t IIL TO I I trcn k&nh VTV2 t^p 2 - Chu Via BlSn

2) Mach R L mic vao nguon mgt chieu roi mic vao nguon xoay chieu

* Mach no'i tiep chua tu cho dong xoay ^ i '

chieu d i qua n h u n g khong cho dong , | | < ^ ^ ^ ^ •

mot chieu d i qua

* Mach noi hep RL vua cho dong xoay chieu di vua cho dong mot chieu di

qua N h u n g L chi can tro dong xoay chieu con khong c6 tac d u n g can tro

dong m o t chieu ' ' ' - •\r':)'}')n{.:\j\\

Nguon 1 chieu : I , =—;R = IfR = , • • • >(

U U^R • Nguon xoay chieu : I , = , ;P; = \iR = — - ; Z , = wL

^'!v^^V'\•J-V i d u 1 : ( D H - 2012) K h i dat vao hai dau mot cuon day c6 do t u cam 0,4/7i (H)

mot hieu dien the mot chieu 12 (V) thi cuong do dong dien qua cuon day la

0,4 (A) Sau do, thay hieu dien the nay bang mot dien ap xoay chieu c6 tan

so 50 (Hz) va gia tri hi^u d u n g 12 (V) thi cuong do dopg dien hieu d u n g qua

cuon day bang : v i ; :

V30-+40-V i d u 2: Dat vao hai dau cuon day co do t u cam L = 0,35/7i (H) mot dien ap

khong doi 12 V thi cong suat toa nhiet tren cuon day la 28,8 (W) Neu dat

vao hai dau cuon day do dien ap xoay chieu c6 tan so 50 H z va gia tri hieu

•' d u n g la 25 V thi cong suat toa nhiet tren cuon day bang bao nhieu?

R-+Zl 5^+35^

Vi du 3: Dat vao hai dau ong day mot dien ap mot chieu 12V thi cuong do

dong dien trong ong day la 0,24A Dat vao hai dau ong day mpt dien ap

xoay chieu c6 tan so 50 H z va gia tri hieu dung 100 V thi cuong do dong

Cty TimnniV UWJrKnang r j p i

-dien hieu d u n g trong ong day la l A Mac mach -dien gom ong day noi hep voi tu dien ccS dien d u n g C = 87|aF vao mach dien xoay chieu noi tren Cong suat tieu thu tren mach la:

A i = 5N/2cos(120Tit-7t/4)(A) B i = 5cos(1207tt + 7i/4) (A)

C 1 = 5^/2 cos(1207it + 7t/4) (A) D i = 5cos(1207rt- 71/4) (A)

Mac vao nguon 1 chieu : R = y = 30 ( f i )

Mfic vao nguon xoay Chieu :

B d t r a kle'n thurc V^it If LTDlt t r e n kenh VTV2 t^p 2 - Chu VSn B i c n

J ,2

Nguon mot chieu ; P' = I^K = —^

=*P' = 2P =>ChonB

Chu y:

1) Khi mac dong thai nguon mot chicu va xoay cliicu f u = a + bV2 cos((ot + (p)) vao

mach noi tiep chi'm tu thi chi ddng dien xoay diicii di qua: I^^ = , ^

2) Khi mac dong thai nguon mot cliicu vi) xoay chieu (u = a + b^/2 cos(wt + cp)) vijo

mach not tiep khong chi'ra tu thi cd dong dien xoay chieu va dong mot chieu deu di

qua: = —j= ^ = , 1,^,= — Do do, dong liicu dun<^ qua mach:

V i du 6: Mach gom dien tro R = 100 Q mac noi tiep v o i cuon day thuan cam

L = l/7i(H) Dien ap dat vao hai dau doan mach co dang u = 400cos2507rt (V)

•'' C u o n g do dong dien hieu d y n g qua mach c6 gia trj bang

+100-=> I = + Ixc = N /5 (A) => Chon D

V i du 7: Dat m o t dien ap c6 bieu thiVt u = 200N/2 cos2(1007rt) (V) vao hai dau

doan mach AB gom dien tro R = lOOQ va cuon cam thuan c6 do t y cam

0,25/7t (H) mac noi tiep Cong suat toa nhiet tren dien tro la

Vi d u 8: Dat vao 2 dau mach dien c6 2 phan tir C va R voi dien tro R = Zc = lOOQ

mot nguon dien tong hop c6 bieu thirc u = [100cos(100Trt + 7r/4) + 100] V

Tinh cong suat toa nhiet tren dien tro

BAI TOAN LIEN QUAN DEN GIAN DO VECra

Da so hoc sinh thuong d u n g p h u o n g phap dai so'de giai cac bai toan dien con p h u o n g phap gian do vecto thi hoc sinh rat ngai d i i n g Dieu do la rat dang tiec v i p h u o n g phap gian do vecto d u n g giai cac bai toan rat hay va ngan gon dac biet la cac bai toan lien quan den nhieu dien ap hieu dung, lien quan den nhieu do lech pha Co nhieu bai toan k h i giai bang p h u o n g phap dai so rat dai dong va phuc tap con khi giai bang p h u o n g phap gian

do vec to thi to ra ra't hieu qua

Trong cac tai lieu hien co, cac tac gia hay de cap den hai p h u o n g phap,

p h u o n g phap vec to buoc (vec to chung go'c) va p h u o n g phap vec to trugt (vec to noi duoi) H a i p h u o n g phap do la ket qua cua vl§c van d u n g hai quy tac cong vec to trong h i n h hoc: quy tac hinh binh hanh va quy tac tam giac Theo chiing toi, mot trong n h u n g van de trong tam ciia viec giai bai toan bang gian do vec to la cong cac vec to (» j imdv/j v , -

1) Cac q u y t3c cpng vec to Trong toan hoc de cong hai vec to a va b , SGK h i n h hoc, gioi thieu hai quy tac: quy tac tam giac va quy tac hinh binh hanh

H i n h a

71

Bo trg hicn thiic V^t li LTDII tren kenh VTV2 t$p 2- Chu VSn Bl€n

a) Quy tac tarn gidc

N o i dung cua quy tac tarn giac la: Tir diem A tuy y ta ve vec to A B = a, roi

t u diem B ta ve vec ta B C = b Khi do vec to A C duoc goi la tong cua hai

vec to a v a b (Xem hinh a)

b) Quy tac hinh binh hanh d'> vi^ox }>noh A > if!-i n y.n>nf-f(,J >••'•('( , r r.pr.f

N o i dung ciia quy tac hinh binh hanh la: T u diem O tuy y ta ve hai vec to

O B = a va O D = b , sau do dung diem C sao cho OBCD la hinh binh hanh thi

vec to O C la tong ciia hai vec to a va b (Xem hinh b) Ta thay khi dung

quy tac hinh binh hanh cac vec to deu c6 chung mot goc O nen goi la cac

vec tobuoc .,

Goc hop boi hai vec t o a va b la goc B O D (nho hon 180°)

Van dung quy tac hinh binh hanh de cong cac vec to trong bai toan dien

i xoay chieu ta c6 phuong phap vec to buoc, con neu van dung quy tac tarn

giac thi ta c6 phuong phap vec to trugt ("cac vec t o noi duoi nhau")

2) C a so vat li ciia phirong phap gian do vec to ' ""^

Xet mach dien Dat vao 2 dau doan AB mot dien ap xoay chieu Tai mot thoi

^ diem bat k i , cuong do dong dien 6 moi cho tren mach dien la n h u nhau

Neu cuong do dong dien do c6 bieu thiic la: i = IQ coswt ( A ) thi bieu thuc

^^y; dien ap giiia hai diem A M , M N va NB Ian lugt lac , ( ^ j , ; i

u^^l = U L V 2 cosf Q t + - 1 ( V ) ^.i^.uuA - n

2

U M N = U K V 2 c o s w t ( V )

" N B = U c \ / 2 c o s ( D t - - ( V )

+ Do do, dien ap hai dau; A, B la: u^g = u + U ^ N + " N B •

+ Cac dai luong bien thien dieu hoa ciing tan so' nen chiing c6 the bieu dien

bang cac vec to Frexnel: U ^ B = U L + U R + U C (trong do do Ion ciia cac vec to

bieu thi dien ap hieu dung ciia no)

+ De thuc hien cong cac vec to tren ta phai van dung mot trong hai quy tac

cong vec to

3) V e gian do vec to bang each van dung quy tac hinh binh hanh - Phuong

phap vec to bupc (vec to chung goc)

Ve gian do vec ta theo phuong phap vec to buoc gom cac hu&c nhu sau:

•Bieu dien cac so Ueu len gian do

•Dua vao cac he tliijc lutmg trong tam giac de tim cac dien ap hoac goc chuabiet

Mot so'diem can heu y: ; ,5> , •

Cac dien ap tren cac phan tu* dugc bieu dien boi cac vec to ma chieu dai ti le voi dien ap hieu dung ciia no

Do lech pha giiia cac dien ap la goc hop boi gii>a cac vec to tuong ling bieu

d i i n chiing Do lech pha gii>a dien ap va cuong do dong dien la goc hop boi vec to bieu dien no voi true I Vec to "nam tren" (huong len tren) se nhanh pha hon vec to "nam d u o i " (huong xuong duoi)

Viec giai cac bai toan la nham xac djnh do Ion cac canh va cac goc ciia cac tam giac hoac t i i giac, nha cac he thiic lugng trong tam giac vuong, cac he thuc lugng giac, cac djnh li ham so sin, ham so cos va cac cong thiic toan hgc

• ,,M A 'y] tiff J ^rit

—•— — • T

•:.d

Trong toan hgc mot tam giac se giai dugc neu biet truoc 3 (hai canh mot goc hoac hai goc mot canh hoac ba canh) trong so 6 yeu to' (ba goc trong va ba canh)

73

B o t r g k i e n t h ^ c Viit l i L mil l i c n henh VTV2 t^p 2 - Chu VSn B i e n

T i m tren gian do vecto tam giac biet triioc ba yeu to (hai canh mot goc, hai

goc mot canh), sau dcS giai tam giac do de tim cac yeu to c h u a biet, c u tiep

tuc nhu vay cho cac tam giac con lai

D o dai canh cua tam giac tren gian do bieu thi dien ap hieu dung, do Ion

goc bieu thj do lech pha

Mot so he thii'c l u o n g trong tam giac vuong: i ,

a' -~ b' + c

• H T

h- b- />- = a.b'

c-Mot so he thi'rc hrong trong tam giac thuong:

a' = b' + c - 26ccos A

a b c

^ sin A sill B sin C

R C

Phu'ong phdp vec ta bugc chi hicu qua v6i cac bai

todn CO R nhm giua dong thai lien qua den dien

dpbatclieo O ^ N ' ^ M B

-V i d u 1: Tren doan mach xoay chieu khong phan nhanh c6 bon diem theo

dung t h u t u A, M , N va B Giua hai diem A va M chi c6 cuon cam thuan,

giua hai diem M va N chi c6 dien tro thuan, giOa hai diem N va B chi c6 tu

dien Dien ap hieu dung giua hai diem A va N la 400 (V) va dien ap hif u

dung hai diem M va B la 300 (V) Dien ap tuc thoi tren doan A N va tren

doan M B lech pha nhau 90° Dien ap hi^u dung tren R la

A 2 4 0 ( V ) B 120(V) C 500 (V) D 180 (V)

' Huong dan

Vi lien quan den U ^ N -L ^ M B " ^ n ta tong hgp theo quy tac hinh binh hanh

cac vec ta dien ap do: 0 = UR + U , , U^n = OR + Uc

B6 lis> hicn lliiic yjt li LIOll litin hcitli VTV2 t^p 2 — Chu V^n Bien

Chu y: Neii cho bict = L/C tht sm/ ra:

Chu y: Ne'u dung phwcmg phdp vec to huge thi khong nen ve vec ta tongl Chi nen

ve cdc dien dp bat cheo de tinh cdc dien dp thdnh phan UR, UL, UC roi dp dung he

thitc: = + ( U L - U c )^• tan cp = ; cos cp = HJL

B S trgkiSn thiic V$t IILTOH ttenkSnh VTV2 l./)> van Blen

• " C/tu I/; Nn/ da) /;/^? R = tin LIR., = (ii + DW ' '

V i du 7: Tien doan mach xoay chieu khong phan nhanh c6 bon diem theo

d u n g thiV tu A, N , M va B Giun hai diem A va N chi c6 dien tro thuan R,

giiia hai diem N va M chi co cuon day (c6 dien tra thuan r = R), giua 2 diem

M va B chi c6 tii dien Dat vao hai dau doan mach mot dien ap U - 50 Hz thi

dien ap hieu d u n g tren doan A M bang tren doan NB va b3ng 30^5 (V)

Dien ap tiVc thoi tren doan A M vuong pha voi dien ap tren doa.i NB Gia trj

i giua hai diem M va N chi c6 cuon day,

; giua hai diem N va B chi c6 tu dien

Cuon day dien tro thuan r = 0,5R Dien ,

ap hieu d u n g tren doan A N la U 73 va tren doan M B ia U Dien ap tuc thoi tren doan A N va tren doan M B lech

pha nhau 90" Dien ap tuc thoi UA.\m

pha hon dong dien la {

Kinh nghieni: Plnmng phdp vix hr buoe khd hieu qua v&i bai loan c6 R 6' gii'ra dong

thd'i lien quan den dien dp bat eheo Phuvng phdp ndi/ thwang lien quan den ede

doan mach sau:

Ve gian do vec to theo

p h u o n g phap vec to trugt gom cac buoc nhu sau:

+ Chon true ngang la true dong dien, diem dau mach lam goc (do la diem A )

79