BotroKienthucLuyenthiDaihocTrenkenhVTV2VatlyPhan2DienxoayChieu p2

~Bo tr^kien

tlsiic Vat li L mil l,<^n kenh

VTVZ

t$p 2 - Chu VMn

Bien
Cty

T.

lOOVS

T

100

7(R + R o r + ( Z L - Z c ) '
=> Chon B.

^,

,

i, va i2.

V i d u 5: D a t dien ap u = 200cosl007it (V) vao doan macii noi tie'p g o m dien t r o
R = 100 Q, t u dien co dien d u n g C = 15,9 |.iF va cuon day tliuan cam c6 d o tu

!C : vm ):y.i<\.> iJ'^:

A. (pi = 71/6 va (p2 = - 7 T / 3 .

do d o n g dien t r o n g mach som pha so v 6 i hieu dien the'gii>a hai d a u mgch.

B. L i = 1/71 ( H ) va i = V2 cos(100Kt + 7r/4) ( A ) .

,^

-

= Ul

c o s cp =

''"'^ ' A

; / -*f*;

^- '

C. L i = 3/71 ( H ) va i = cos(l OOTrt - 7r/4) ( A ) .
C. L i = l / 7 t ( H ) v a i = V2cos(1007it-7T/4)(A).
Huang
„
P =

2
(p=>100

CDS

100-.2
=

t....

dan

.

R

- cos

(p :

•-


'••'MA-'

7T
„

.73 =

cos(p2 _

COS(P|

.3 = - ^ =

COS^

(P2

COS

COS^

(P|

cos(p|

-sin(pi

' (pj =

COS(pi

(P2

^

r-

^

4 =^i = V 2 c o s

=>L = - H => Chon B.

1007rt + - -

(A)

'

,

. ^ « p ,(,ji

tan so 50 H z . Ban dau d o lech pha giira dien ap giCra hai dau mach va d o n g
dien la 60" t h i cong suat tieu t h u trong mach la 50 W . Thay d o i C de dien ap
giira hai d a u mach c u n g pha v a i i thi mach tieu thu cong sua't la
U'»i(b./t
2

P = UI cos CP = — c o s ^ ^ > = ^ ^ =
R

P|

C. 5 0 W .
Hitoitg dan
'
'

•

D. 120W.

•,,U.l>l' -

ri J i}i f T O ^ ri'>i>m 'fia'".,

song v o i t u d i e n C i thi d o n g dien trong mach la i2 va cong suat tieu t h u la
P2. Biet P I = 3P2 va ii v u o n g pha v o i i : . Xac d j n h goc lech pha cpi va (p2 giua

^ P2 = P,

cos (pj >•• • <.•'•

cos"

= 200 (W)

,,,,

U
P = U I cos(p = — cos^ (p

_ c o s ^ , _ -siiif/?!

Chon B.

IP|

. «

COS c/>|

cos ^,

P,
p2

• o = —

G2 = C i + C ' = 5C, : ^ Z c 2 =
1

1 ' , i * ^'

B. ( p i = - 7 t / 6 v a ( p 2 = Tr/3.

'•901 •

=

. ^„|

dan

cos^ (pi
^..2
C O S (p2

,5 ] "
COS(p2

1

tos(p,

V3

—
n
>^1 =

=> Chon B.

V i d u 9: Cho mach xoay chieu g o m cugn day k h o n g t h u a n cam co d o t u cam L,
dien tro r mac n o i tie'p v o i t u dien ccS dien d u n g C thay d o i . D i e n 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 t h i cong sua't cua mach cue

cos" (p
vai dicu kicn (p^±(p.,=a

hi tiiili duvc cik dqi limn<^ khdc.

cos- ^1

dai. Xac d i n h cong sua't cue dai do?
A.300W.

V i d u 7: D a t dien ap xoay chieu o n d j n h vao hai dau doan mach g o m cugn day

B. 3 2 0 W .

'
C. 960 W .

mcich la i) va cong sua't tieu t h u cua mach la P,. K h i C = C2 > C i t h i d o n g
di^n t r o n g mgch la i j va cong sua't tieu thy la P2 • ^^'^^ ^2

3 P i va i , v u o n g

D. 480W.

Huaitgdan

noi tie'p v o i t u dien c6 dien d u n g C thay d o i . K h i C = C i d o n g dien trong

60

' ' ! ' ( ' . •

D . (pi = -7r/4 va (p2 = 7t/4.

Huang

yj3

if;tb , D ' j ^ i •

2

Chiiy:
Kcl hap

}(••

noi tie'p v o i tu dien co dien d u n g C i . K h i d o d o n g dien t r o n g mach la i i va

C. (pi = 7i/4 va (p2 = - 7 i / 4 .

va t u d i e n co dien d u n g C thay d o i dugc. D i e n ap d a t vao hai dau mach c6

B. 2 0 0 W .

I • y-i"

V i d u 8: Dat dion ap xoay chieu on d j n h vao hai dau doan mach g o m cugn day

dien ap hai dau doan mach v o i ii va i2.

V i d\ 6: Doan mach xoay chieu g o m dien tro thuan R, cugn day t h u a n cam L

A. l O O W .

= V3

71

=> Chon C.

A. tpi = 7 t / 6 va (p2 = - 7 i / 3 .

tan cp =

ui u

cong sua't tieu t h u cua mach la Pi. Lay mc)t tu dien khac C = 4Ci mac song

cos"(p=>(n = —

R
too
P = I - R ^ 1 0 0 = I-'.100=?>I= l A

M -

-''^ '

' ' 'p'

.'iK/I

C o > C i = > Z c 2 < Z c i =>(p2 - 'PI = T = = ^ ^ 2 = 9 l +
^

Vtft

r.

Huang dan

.Vv

Gia t r j L i cua cuon cam va bieu thuc c u o n g d o d o n g dien qua mach dirge
xac d i n h

'^^'•^

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

C. (pi = -7t/3 va (p2 = n/6. •fi^iikf.U> v.
cam L thay d o i d u g c . Biet cong suat tieu thu cua mach la 100 W va cuong

'' '

MTV D vvniihang

pha v o i i2 • Xac d j n h goc l§ch pha cpi va
V'^ +(Zi.-Zc)

A. L I = 3/7r ( H ) va i = N/2 cos(1007tt + 7i/4) ( A ) .

Timn

P = _ c o s 2

=>240 = P,,„g ha<.ng
•Pc6„gha(,nK=320(W)=>ChonB.

2

.. .final} i=fy.^

^

^

iJi'if

61


Cty
B S trp kiSn

thitc

V^t It LTDtl

tren

kenh

VTV2.

t^p 2 - Chu Vitn

Blen

Huang

V i d u 10: T r o n g m o t mach dien xoay chieu g o m m o t d i e n t r o t h u a n mac noi
tiep v o i m o t tu dien. D i e n ap hieu d u n g dat vao doan mach la 150 V, d o n g
dien chay t r o n g mach c6 gia t r i hieu d u n g 2 A . D i ^ n ap h i ^ u d u n g g i i i a hai
ban tu d i e n la 90 V. Cong suat tieu t h u ciia doan mach la
A. 200W.

B. 1 8 0 W .

C. 2 4 0 W .

= U K + U c =>150

=UR+90^

^ HV7:)

D . 270 W .

Huang dan
U

'

doan mach g o m tu C n o i tiep v o i cuon day t h i dien ap hieu d u n g tren t u la
100 V S V va tren cuon day la 200 V. D i e n t r a t h u a n ciia cuon day la 50Q.
C o n g suat tieu t h u d i e n ciia doan mach la:

' ''

"

C. 120 W .
Huang

tancp =

DVVH

Khang

Vipt

dan

= 200(Q) ;

U

= tan - => Uj =
6

Uc = U , = H ( V )

U ' = U?+(U| -Ue)^ = 1 0 0 '

V i d u 11: Dat m o t d i e n ap u = 100 V2 coslOOnt (V), (t d o bang giay) vao hai dau

'

coC

MTV

U,=100(V)

H

UR =120(V)

B. 100 W .

=

,

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

A. 150 W . = ' ;;

Zr

Tisnn

I =

Zc

2V3

1

P = l'r =

•t)

^ r = ^ = 200^/3 (Q)
1

= -V(A)

.200V3 * 28,9(W) => Clion B.

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

D . 200 W .

tro t h u a n R va cuon cam t h u a n c6 cam khang 80 Q. D o Ion he so cong suat

dan

ciia doan mach RC bang he so cong suat ciia ca m a c h va b a n g 0,6. D i e n t r o
t h u a n R CO gia t r j
B.30(Q).

A . 50 (Q).
=> 100^ = 200^ + 3.100^ - 200V3.UL
U, =100V3
[ U , =100

,
=>P = I r = — ^ = 200{W)=>ChonB.
r

"

^''

d a u doan mach RLC no! tiep cuon day thuan cam c6 L = 0,l/7t H t h i tli
d i e n ap hieu d u n g tren t u va tren cuon day bang nhau va bang 1/4 d i e n > ^
hieu d u n g tren R. C o n g suat tieu t h u tren mach la
B. 1 8 0 W .
-

R
COSCPKC =

: = 0,6
Zc =0,5ZL =40(Q)
R = 30(Q)=:>Chon B.

= 0,6

=U,

D. 120W.

• Z'^^^i^J

a hai dau t u d i e n 120 V. H e so cong suat ciia mach la

A. 0,125.

B. 0,87.

C. 0,5.
Huang dan

U2=U^+(UL--UC)'_

Mach cong hUdng => I = —

p = I^R = — = 360(W) => Chon A.
R

•

' *

^

'

C = 0,1/K (mF). Dat vao doan mach dien ap xoay chieu u = 100 V2 cosSOnt (V)
thi thay d i e n ap g i i i a hai dau cuon day sam pha h o n d o n g d i e n t r o n g mach
la 7t/6, d o n g t h a i d i e n ap hieu d u n g tren cuon day gap d o i tren t u dien.
Cong suat tieu t h u ciia doan mach la
B.28,9W.

C. 240 W .

^c=^la=^l+^i
coscp =

/f

d u 13: M o t doan mach g o m cuon day no'i tiep v o i t u d i e n c6 d i e n d u n g

A.200W.

( r i ' r i ' j i b i<:

V i d u 15: Mcich dien xoay chieu gom cuon day mac noi tiep v a i t u d i e n . Cac

R = 4Z| =4coL = 40(Q)
M

dan

dien ap hieu d u n g 6 hai dau doan mach 120 V, a hai dau cuon day 120 V va

C. 1440W.
Huong dan

R

coscp =

^ R 2 + ( Z L - Z C )

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

A.360W.

Huang

if!>

D . 100 (Q).

C.67(Q).'

D.57,7W.

U

U

'I'lOr i . : '1 , t j - ,JS +

jl202=u|+(UL-120f
ll202=U|+u2
;

= 0,87^
'

D . 0,75. '

Chon B.

'

M i , , ,

. .viLi'

|UL=60.1:?
U K = 6OV3

«'lU f!;,Ue

,<,.-i:„,,

. „

,

,r,,j.-.

^--.^^•5!•M,.=•'I •viuVVv'^(;'')!\

V i d u 16: M o t d o a n mach dien xoay chieu RLC k h o n g p h a n n h a n h , cuon day
c6 d i e n t r o t h u a n . D i e n ap hieu d u n g g i i i a hai dau doan mach, tren d i e n tro
R, tren cuon day va tren tu Ian l u g t la 75 (V), 25 (V), 25 (V) va 75 (V). H e so
cong suat ciia toan mach la
A . 1/7.

B. 0,6.

'

C. 7/25.

W'tKH

D . 1/25.

i-

63


B o t r pk i c n thiic

V^t l i LTDH

t r e n kenh

VTV2.

t a p 2 - Chu

Huong

U- = (UK +

+ ( U , - U^.f =

Vdn

CtyTNHHMlTVDVVtlKhang

Bicn

dan

A. 5 a.

B. 10 n hoac 200 Q.

C. 15 Q hoac lOO Q.

D . 40 0 hoac 160 O.
•;,d ii hh V/ Oi.«,) >; «!•(•' r'^•.f

Z, =coL = 2 0 ( n ) ; Z e = — = 100(Q)
wC
7 3 - = 2 5 ^ + 25-+ 2 . 2 5 . U , - 2 U , .75 + 75f U , =20(V)

Up + U

[ U , - 15{V)

,,i

^ \
•

U

'

•

•

( ^iJ

,1

P = 1'^R =

"

*•

»

,

,

-R =

R = 40(D)

- 200R + 6400 = 0 :

200r2R
R^ +(20-100)^

400 =

R^+(Z,-Zc)^

R = 160(Q)

V i d u 17: D o a n mach dien xoay chieu mac no'i tiep g o m tu ctien, dien t r a t h u a n

Chon D.

^

>iH

va cuon cam t h u a n . D i e n ap hieu d u n g 6 hai dau doan mach va tren cuon

V i d u 20: D a t vao hai dau doan mach m o t dien ap xoay chieu co gia t r i hieu

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

d u n g 200 V . D o a n mach g o m cuon day co dien t r o t h u a n R co cam khang

D i e n ap hieu d u n g tren tu la
A. 500(V).
! , , . , , . , , A , , r.:

^
.r^:' m

cos(p = ^

B. 200 (V).
-O'

.

^

C. 320 (V).
"

'

^

= 0,6=^U|, =0,6U = 2 I 6 ( V )

-

"

S

,

D. 400 (V).
,

,

,,5,^

„

140 Q. mac n o i tiep v o i tu dien co d u n g k h a n g 200 Q. Biet cong sua't tieu t h u
tren mach la 320 W . H e so'cong sua't ciia mach la
B. 0,6 hoac 0,8.

A. 0,4.

Huang

ill

>,n,'r*^nit\ (bi

U - = Uf, + ( U | - U^.)^ => 360- = 216- + ( 2 1 2 - U(.)- ^

Z, =a)L = 140(Q);Zc =
P = 1^R = - ^ R =

V i d u 18: Doan mach dien xoay chieu mac no! tiep g o m tu dien, dien t r o thuan
mach va tren tu Ian l u o t la 300 V va 140 V. D o n g 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. 3,2 ( A ) .

D. 4 (A).

Humtgdan

U- = Uf^ + ( U | - U e ) " ^ 300- =240- + { U , -140)- =>U|
= 4 ( A ) ^ Chon A.

R

"''t'.

=320(V)

^'5'"

.

.

= 0,8
•ChonB.

!r:,M

V i d u 21: D a t vao h a i dau doan mach m o t dien ap xoay chieu 100 V - 50 H z .
I/TI ( H ) va tu dien co d u n g k h a n g Zc. Biet cong sua't tieu t h u tren mach la
100 W va k h o n g thay d o i neu mac vao hai dau L m o t ampe-ke co dien t r o
k h o n g d a n g ke. Gia t r j R va Zc Ian luc^t la
A.40i^va30Q.

B. 5 0 Q v a 5 0 Q .

u = 400cos(1007rt) ( V ) . M a c h AB g o m cuon day co dien t r o t h u a n R co d o t u
cam 0,2/7: ( H ) mac noi tiep v o i tu dien co dien d u n g 100/K (HF). N e u cong

: ..

U^R

100^ R

p
R'^ + Z,c
rZc=50(Q)
R = 50(Q)

C. 3 0 Q v a 3 0 a

R^+Z^.

D . 20 Q va 50 Q.

dan

100-R

'""""R^ + (Z,,-ZC)^

.

V i d u 19: Dat vao hai dau ctoan mach A B m o t dien ap xoay chieu:

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

- 125R + 3600 = 0

= 0,6

Huong

•
R ^ + ( Z , - Z J -

•

+ (140 - 200)^

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^ +(140-200)^

D o a n mach mac n o i tiep g o m dien t r o t h u a n R, cuon cam co d o t y cam L =

Z, >Z^-=>U| >Uc;coscp = - ^ = 0,8 =i.U|, = 0 , 8 U = 240(V)

^
Zi

D . 0,75.

;7t iJfi? v/.ni I f i u a ^/.no'j t'>::ci

2001R

=> 320 =

R^+(Z,-Ze)^

R = 45(Q)=> coscp =

C u o n g do hieu d u n g d o n g qua mach la
B. 2 ( A ) .

dan

R
R
R = 80(Q)=> coscp = — =
Z
yJR^ +(140-200)

va cuon cam t h u a n co cam k h a n g 80 Q. Dien ap hieu d u n g a hai d a u doan

A. 1 (A).

C. 0,45 hoac 0,65.

^ = 200(Q)

coC
U-R

=500(V)

Chon A.

64

i,v.:io!:

Huong dan

+ Uf ) + Uf, + 2U„U, - 2U, Ue + U^^

Vift

= 100

R2+(100-ZJ^

= 100

U ^Jl'nwtl

Mach dien liic dau

> Chon B.
M a c h dien .sau

65


Bo tip hien thiic

Vpl li LTDH

Cty

VTV2, t^p 2 - Chu Van

tren hSnh

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
A. 5 Q .
B. 10Qhoac200Q.
'
;i;:,-OfJL.

C. 15^2 hoac 1 0 0 Q.

• i^'iU
T2T,
PR

U^O

r.^; : .

D. 20Q.

• Huong dan

,\)--->\s

U^R

=r R = — R =

=> 40 =

(R + r)2+(Z, - Z c f

R2 -210R + 2000 = 0=>

J- s ..,

5

(R +20)2+(60-20)2

R = 10(Q)

,:,vyb

=> Chon B.
R = 200(Q)

. . ^ = - ^ = 0,5(A)
^'^ U j
120

-<x>2 ^ — = * / ( R d + r)^ +(1007rL)2 = —

tie'p, dien ap giua hai dau doan mach u = 50 \/2 coslOOnt ( V ) . Dien ap hieu
V . Bie't cong suat tieu thu trong mach la 20 W. Gia tri R bang

,
= U | + ( U L - UC)^

p = I2R = 2K-.R

C. 15Q.
Huong dan

^

D. 2 0 Q .

- ,X

tieu thu cua doan mach la
A.240>y'3W.
Cdchl:

C. 240 W.

u = 120sin 1007rt + - j = 120cos lOOnt-V

D. 120>/3 W.
•

3;

6,

(V)

i = 4cos 100TUt + - ( A )
6)
3

UR

= 40(V)

\

Cdch 2: Goi i* la so phuc lien hop cua i thi cong suat phuc: P = - i u
= 120 - 207,85i => P = 120(W) ^ Chon B.

4Z-

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

6J

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

(Phan thuc cua cong suat phuc la cong suat tieu thu con phan ao la cong

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

suat phan khang).

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

Thao tac ba'm may tinh: sau khi nhap -

'-i";*')

dung trong mach la:
A. 1 A hoac 5 A.
\'d

B. 5 A hoac 3 A.
V.

sau do ba'm 0 dugcketqua 120-207,851.

' I = 1(A)'
I = 5(A)

mac no'i tie'p voi mot

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
A. 173,2 W.

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:

?in-: i i

iiK

220 V - 50 Hz, thi den sang binh thuong. Do t u cam cuon day la:
B. 1,15H.

,, • :

thoi tren cac doan mach va dong dien qua chung Ian lugt c6 bieu thuc:
Chon A.

bong den 120 V - 60 W. Noi hai dau mach dien voi nguon dien xoay chieu
~r::::Z

7:

120Z--

Vi du 27: Doan mach AB g5m hai doan A D va DB ghep noi tie'p. Dien ap tiic

Huong diin

V i du 25: Mach dien gom cuon day c6 dien tro thuan 10

A . 1,19 H .

ba'm IshiftlfUfzll^

' •

C. 2 A hoac 5 A. D. 2 A hoac 4 A.

UIcoscp = PR + I^r ^ 40V3.1.— = 50 + I^.IO

66

B.120W.
•

20 = — =^ R = 80(Q) =^ Chon A.
R
V /
.

R2

'

P = UIcoscp = 60N/2.2>/2 C O S — = 120(W) =:> Chon B.

\

^ 50^ = U ^ + (30 - 60)^

Chon B.

thi dong dien trong mach c6 bieu thuc i = 4cos(100TTt + nib) (A). Cong sua't

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

L «1,15(H)

Huang dan

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

A. 80Q.

yj^

Khang

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

lOO^R
J

TISnn MTV own

Bien

B. 242 W.
- )i ,

C. 186,6 W.

D. 250 W. '

Huong dan

E^ien ap tong: u = L I ^ D + " D B
Cong sua't phuc:

,'•'1

1

u = ^^72Z-1
flO072Z- + 100V6Z—1 = 173,2 + 2001
2
3; I
2
3,J
^
=>P = 173,2(W)=>ChoiiA.
• "
1 = -1

2

, /

. . . . . . . . . . u:, , '.. xHtK^:

- : v : a.

67


Cty
Bd

trp

hien

thiic

V$t

IIL

TO I I trcn

k&nh

VTV2.

t^p

2 - Chu

Via

M a c h no'i tiep chua tu cho d o n g xoay

^

chieu d i qua n h u n g k h o n g cho d o n g

,

|

i
|

voi

'

<^^^^

50W.

''

-

Nguon 1 chieu : I , =—;R

= IfR =

Nguon xoay chieu : I , =

,

U

C. 120W.

•\r':)'}')n{.:\j\\
,

U^R

U

Nguon xoay chieu (RL): L =

• • • >(

;P; = \iR = —

- ; Z , = wL

D . lOOW.

U
= — ^ 50 (Q)

U
Nguon 1 chieu (RL) •.1^= — ^^

qua. N h u n g L chi can t r o d o n g xoay chieu con k h o n g c6 tac d u n g can tro
'

B, 200W.

Huangdan

M a c h noi hep RL v u a cho d o n g xoay chieu d i vua cho d o n g m o t chieu di
d o n g m o t chieu.

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:

•

m o t chieu d i qua.
*

• ^'!v^^V'\•J-

P3=1^R =

m o t hieu dien the m o t chieu 12 (V) thi c u o n g do d o n g dien qua cuon day la

100

•=>1 =

- Z L =50%/3(Q)

+Z

Nguon xoay chieu (RLC): Zc =

V i d u 1 : ( D H - 2012) K h i dat vao hai dau m o t cuon day c6 do t u cam 0,4/7i (H)

(oC

= 36,6(Q)

U^R

100^50

R2+(Z|-ZC)^

50^+(50V3-36,6)

aOO(W)=^ChonD.

0,4 ( A ) . Sau do, thay hieu dien the nay bang m o t dien ap xoay chieu c6 tan

Vi dii 4: (DH-2009) K h i dat dien ap k h o n g d o i 30V vao hai dau doan m?ch g o m

so 50 (Hz) va gia t r i h i ^ u d u n g 12 (V) thi c u o n g d o d o p g d i e n hieu d u n g qua

dien t r o thuan mSc noi tiep v o i cuon cam thuan c6 do t u cam 0,25/Tt (H) t h i

cuon day bang

:

d o n g dien t r o n g doan mach la d o n g dien m o t chieu c6 c u o n g d p 1 A . Neu

A. 0,30 A .

B. 0,40 A .
.i^

.

v

. i ; :

;

" u

C. 0,24 A . ' - • ' D . 0,17 A .
Huangdan

dat vao hai d a u doan mach nay dien ap u = 150 V2 cosl207rt (V) t h i bieu

'

thuc ciia c u o n g do d o n g dien trong doan mach la

•
.
,v«t nail ' j u d q

" u

N g u o n l c h i e u : ! , = — = > R = — = 30(Q)

'

'

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 ) .
i'

Huong dan
Nguon xoay cliieu :

Vi

:UV-

,

h = •I
R-+Zf

=

12
,
^ = 0,24(A)z=>ClionC.
V30-+40-

Mac vao nguon 1 chieu : R = y = 30 ( f i )

d u 2: Dat vao hai dau cuon day co do t u cam L = 0,35/7i ( H ) m o t dien ap

Z L =coL = 30(Q)

k h o n g d o i 12 V t h i cong suat toa nhiet tren cuon day la 28,8 (W). N e u dat

Mfic vao nguon xoay Chieu : Z =

vao hai dau cuon day do dien ap xoay chieu c6 tan so 50 H z va gia t r i hieu
•' d u n g la 25 V thi cong suat toa nhiet tren cuon day bang bao nhieu?
• A . 14,4 (W).

B.5,0(W).

C.2,5(W).

Nguon 1 chieu : Pi = — => R = — = 5(Q)

•
:.

• V -Silt •

Nguon xoay chieu:

'

'Z| =a)L = 35(Q)
P, =

U^R
=
R-+Zl

5^+35^

= 2 , 5 ( W ) =^ Chon C.

du 3: Dat vao hai dau ong day m o t dien ap m o t chieu 12V thi c u o n g do
d o n g d i e n t r o n g o n g day la 0,24A. Dat vao hai dau ong day m p t dien ap
xoay chieu c6 tan so 50 H z va gia t r i hieu d u n g 100 V thi c u o n g do d o n g

R

'

•••SI/

= 30V2 ( Q )

!(, =

= 5(A)

= !=:>« = — > 0 : u sdm pha hdn i la —
4

i = 5cos 1207rt - - ( A ) => Chon D.
4
V i d u 5: Dat dien ap xoay chieu c6 gia trj cue dai Uo vao hai dau m o t dien tro
thuan R t h i cong suat tieu t h u la P. K h i dat vao hai dau dien t r a do m o t hieu

.
S

+ zl

tancp =

D . 28,8 (W).

Huattg dan

Vi

r j p i -

UWJrKnang

dien hieu d u n g trong ong day la l A . Mac mach dien g o m ong day noi hep

2) Mach R L mic vao nguon mgt chieu roi mic vao nguon xoay chieu
*

TimnniV

BlSn

I

dien the k h o n g doi c6 gia t r i Ug t h i cong suat tieu t h y tren R la ^
A. P.

B.2P.

C.PV2.
^ Huang dan

Nguon xoay chieu .• P = I R =

R

D.4P.
_

'i,; ;

2R

69


B d t r a kle'n

thurc

V^it If LTDlt

t r e n kenh

VTV2.

t^p

2 - Chu

VSn

Cty

Bicn

J ,2

DVVHKhang

VIft

m o t n g u o n d i e n tong h o p c6 bieu thirc u = [100cos(100Trt + 7r/4) + 100] V.

=*P' = 2P =>ChonB.

T i n h cong .suat toa nhiet tren dien t r o

Chu y:

A. SOW.

B. 2 0 0 W .

mach noi tiep chi'm tu thi chi ddng dien xoay diicii di qua: I^^. =

,

^

.

mach not tiep khong chi'ra tu thi cd dong dien xoay chieu va dong mot chieu deu di
^

1,^,= — . Do do, dong liicu dun<^ qua mach:

= ,

'

D. ISOW.

dan

D o n g 1 chieu i
p = rR = 2) Khi mac dong thai nguon mot cliicu vi) xoay chieu (u = a + b^/2 cos(wt + cp)) vijo

C.25W.
Huong

1) Khi mac dong thai nguon mot chicu va xoay cliicu f u = a + bV2 cos((ot + (p)) vao

= —j=

NTV

Vi d u 8: Dat vao 2 dau mach dien c6 2 phan tir C va R v o i d i e n t r o R = Zc = lOOQ

Nguon mot chieu ; P' = I^K = —^

qua:

TlStlH

Zl

= 25(W)=i-ChonC.

BAI TOAN LIEN QUAN DEN GIAN DO VECra
Da so hoc sinh t h u o n g 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 t h i hoc sinh rat ngai d i i n g . D i e u d o la rat

V i du 6: M a c h g o m d i e n t r o R = 100 Q mac noi tiep v o i cuon day thuan cam

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

L = l / 7 i ( H ) . D i e n ap dat vao hai dau doan mach co d a n g u = 400cos2507rt (V).

ngan gon dac biet la cac bai toan lien quan den nhieu d i e n ap hieu d u n g ,
lien quan den nhieu d o lech pha. Co nhieu bai toan k h i giai bang p h u o n g

•'' C u o n g d o d o n g d i e n hieu d y n g qua mach c6 gia trj bang
^•^A-

B. 3,26 A.

•"'^
' ^^^^^^^^^^^

C.(2H-V2)A.

D . Vs

A.

Ap d u n g cong thuc ha bac viet lai: u = 400cos- (507ct)= 200 + 200cos(]007rt)(V)
U 1c

Dong 1 chieu: I , ^ =

200,

do vec to t h i to ra ra't hieu qua.
T r o n g 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 p h a p vec to buoc (vec to chung go'c) va p h u o n g p h a p vec to t r u g t
(vec to n o i d u o i ) . H a i p h u o n g phap d o la ket qua cua vl§c v a n d u n g hai q u y

= 2(A)

/ R ^ + Z , \-

tac cong vec to t r o n g h i n h hoc: q u y tac h i n h b i n h hanh va q u y tac t a m giac.
100^/2

Dong xoay chieu : 1^^ = •

VlOO- +100-

•JR^ + Zl
=> I =

phap dai so rat dai d o n g va phuc tap con k h i giai bang p h u o n g p h a p gian

i

I'

• = ](A)

Theo c h i i n g t o i , m o t t r o n g n h u n g v a n de t r o n g t a m ciia viec giai bai toan
bang gian d o vec to la cong cac vec to.

(» j imdv/j

v , .. -

1) Cac q u y t3c cpng vec t o

+ Ixc = N/5 (A) => Chon D.

V i du 7: Dat m o t d i e n ap c6 bieu thiVt u = 200N/2 cos2(1007rt) (V) vao hai dau
d o a n mach AB g o m d i e n t r o R = lOOQ va cuon cam t h u a n c6 d o t y cam

T r o n g toan hoc de cong hai vec to a va b , SGK h i n h hoc, g i o i thieu hai quy
tac: quy tac t a m giac va quy tac h i n h b i n h hanh.

0,25/7t ( H ) mac n o i tiep. Cong suat toa nhiet tren d i e n t r o la
, A.280W.

B. SOW.

C. 3 2 0 W .

D . SOW.

Humgdan
^ Ap d u n g cong t h i i c ha bac vie't l a i : u = lOO-Jl + 100N/2cos2007tt ( V )
Z L = 2007t.L - 50 ( Q ) ; P = I^^R + I^^R =

[ R
P =

10012

100^100

100

1002+502

R +-

U^R

= 2 8 0 ( W ) r > C h o n A.
Hinh a
71


Bo trg hicn

thiic

V^t li LTDII

tren kenh

VTV2.

Cty T/SHff MTV DVt^H KHang

t$p 2- Chu VSn Bl€n

Vlft

a) Quy tac tarn gidc
N o i d u n g cua q u y tac tarn giac la: Tir d i e m A t u y y ta ve vec t o A B = a, roi
t u d i e m B ta ve vec t a B C = b . K h i do vec t o A C d u o c goi la tong cua hai
vec t o a v a b (Xem h i n h a).
b) Quy tac hinh binh hanh

d'> vi^ox }>noh A > if!-i . n y . n > n f - f ( , J >••'•('( , .r r . p r . f

N o i d u n g ciia q u y tac h i n h b i n h hanh la: T u d i e m O t u y y ta ve hai vec to

o

O B = a va O D = b , sau do d u n g diem C sao cho O B C D la h i n h b i n h hanh thi
vec t o O C la tong ciia hai vec t o a va b (Xem h i n h b) . Ta thay k h i d u n g
q u y tac h i n h b i n h hanh cac vec t o deu c6 chung m o t goc O nen goi la cac
vec t o b u o c .

.,

Goc h o p b o i hai vec t o a va b la goc B O D (nho h o n 180°).
V a n d u n g q u y tac h i n h b i n h hanh de cong cac vec t o t r o n g bai toan dien
i xoay chieu ta c6 p h u o n g phap vec t o buoc, con neu van d u n g q u y tac tarn
giac t h i ta c6 p h u o n g phap vec t o t r u g t ("cac vec t o n o i d u o i nhau")..
2) C a so vat l i ciia phirong phap gian do vec to

' ""^

*Chgn ngang la true dong dien, diem O lam
goc.
*Ve ISii luol cac vec-to" bieu dien cac di^n ap,
cung chung goc O theo nguyen tac:
ji: ' ik
+ L - len.
+ C - xuSng.
+ R - ngang.
Do dai cac vec-to' ti le vol cac gia tri liieu
dung tuolig ling.
*Chi t6ng hffp cac vec-to" dien ap c6 lien quan
den du kien cua bai toan.
^
-.,
•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* d u g c bieu dien b o i cac vec to ma chieu dai t i le
v o i dien ap hieu d u n g ciia no.
D o lech pha g i i i a cac dien ap la goc h o p boi gii>a cac vec t o t u o n g l i n g bieu

Xet mach d i e n . D a t vao 2 d a u doan A B m o t dien ap xoay chieu. Tai m o t thoi

d i i n chiing. D o lech pha gii>a dien ap va c u o n g do d o n g dien la goc h o p boi

^ d i e m bat k i , c u o n g d o d o n g dien 6 m o i cho tren mach dien la n h u nhau.

vec t o bieu dien no v o i true I . Vec t o " n a m t r e n " ( h u o n g len tren) se nhanh

N e u c u o n g d o d o n g dien d o c6 bieu thiic la: i = IQ coswt ( A ) t h i bieu thuc
^^y; dien ap g i i i a hai d i e m A M , M N va N B Ian l u g t lac , ( ^ j
u^^l = U L V 2 cosf Q t + - 1 ( V )
2
UMN

, ; i

^.i^.uuA - n .

pha h o n vec t o " n a m d u o i " ( h u o n g xuong d u o i ) .
Viec giai cac bai toan la nham xac d j n h do Ion cac canh va cac goc ciia cac tam
giac hoac t i i giac, nha cac he thiic l u g n g trong tam giac v u o n g , cac he thuc
l u g n g giac, cac d j n h l i ham so sin, ham so cos va cac cong thiic toan hgc.
• , , M . A ' y ] t i f f J ^rit..

=UKV2coswt(V)

" N B = Uc\/2cos

( D t - -

(V)

+

D o do, dien ap hai. dau; A , B la: u^g = u

+ U^N +"NB•

+

Cac dai l u o n g bien thien dieu hoa ciing tan so' nen c h i i n g c6 the bieu dien
b a n g cac vec t o Frexnel: U ^ B = U L + U R + U C (trong do do I o n ciia cac vec to
bieu t h i dien ap hieu d u n g ciia no).

+

—•—

D e thuc h i e n cong cac vec to tren ta phai van d u n g m o t t r o n g h a i quy tac
cong vec to.

Ve. gian do vec ta theo phuong phap vec to buoc gom cac hu&c nhu sau:

a'- •

•

T

•:.d

3) V e gian do vec to bang each van dung quy tac h i n h binh h a n h - Phuong
phap vec to bupc (vec to chung goc)

— •

T r o n g toan hgc m o t tam giac se giai dugc neu biet t r u o c 3 (hai canh m o t goc
hoac hai goc m o t canh hoac ba canh) trong so 6 yeu to' (ba goc t r o n g va ba
canh).
73


Cty
Bo trg kien

t h ^ c Viit

l i L mil

l i c n henh

VTV2.

t^p

2 - Chu

T/VHH nrv

T i m tren g i a n d o vecto tam giac biet triioc ba y e u to (hai c a n h mot goc,

Khang

Vipt

hai

goc mot c a n h ) , sau dcS giai tam giac do de tim cac y e u to c h u a biet, c u tiep

u,

tuc n h u v a y c h o cac tam giac con lai.
D o dai c a n h c u a tam giac tren g i a n do bieu thi d i e n ap h i e u d u n g , d o Ion

400,/

/•I

/

goc bieu thj d o lech p h a .
M o t so he thii'c l u o n g trong tam giac v u o n g :

i

a' -~ b' + c
1

1

h-

DVVn

VSn B i e n

b-

• H

O

,

o
I

306'^

1

I
11,

Chii y: Khi sit dung gian do vec ta ta tinli duyc dien ap hieu dung va do lech pha.

T

c-

u,

/>- = a.b'

R

Tie do CO th(;'tinh dwgc dong dien, cong sud't:

P = l-'R

M o t so he thi'rc h r o n g trong t a m giac t h u o n g :

V i d u 2: Tren doan mach xoay chieu k h o n g phan nhanh c6 b o n d i e m theo
d i i n g t h i i t u A , M , N va B. G i i i a hai d i e m A va M chi c6 cuon cam thuan,

a'

= b' + c

giOa hai d i e m M va N chi c6 dien tro thuan, giCia 2 d i e m N va B chi c6 tu

- 26ccos A

a

b

c

^ sin A

sill B

sin C

Phu'ong phdp vec ta bugc chi hicu qua v6i cac bai
todn CO R nhm giua dong thai lien qua den dien

dien. D i e n ap hieu d u n g giCta hai d i e m A va M la 150 (V) va dien ap hieu
d u n g g i u a hai d i e m N va B la 200/3 (V). D i e n ap tiVc t h a i tren d o ^ n A N va
tren doan M B lech pha nhau 90". D i e n ap hieu d u n g tren R la '
R

C

dpbatclieo O ^ N ' ^ M B V i d u 1 : Tren doan mach xoay chieu k h o n g phan nhanh c6 bon d i e m theo
d u n g t h u t u A , M , N va B. Giua hai d i e m A va M chi c6 cuon cam thuan,
giua hai d i e m M va N chi c6 dien tro thuan, giOa hai d i e m N va B chi c6 tu

A . lOO(V).

'

200
L

D . 180 (V)

He thiic ktcing : -

=h =

be

1
b"

R

-KJ

,B

300.400

h
r
150
/

be
'b^+c^

7300^+400^

74

A/f

UR + U , , U^n = OR + U c .

1

= 2 4 0 ( V ) = > C h o n A.

i

.150 = 1 0 0 ( V ) = > C h o n A.

UT

V i lien quan den U ^ N -L ^ M B " ^ n ta tong h g p theo q u y tac h i n h b i n h hanh
=

•

HethiJtcIildng:h^ =b'.c'

Huong dan

cac vec ta dien ap do: 0

*

cac vec t o dien ap do: U ^ N = UR + U| , 0^415 = OR + U c .

doan M B lech pha nhau 90°. D i e n ap h i ^ u d u n g tren R la
C. 500 (V)

'

D. 180(V).

V i lien quan den 0^^^ 1 U^^u nen ta tong hap theo q u y tac h i n h b i n h hanh

d u n g hai d i e m M va B la 300 (V). D i e n ap tuc t h o i tren doan A N va tren
B. 120(V)

C.90(V).

Huong dan

dien. Dien ap hieu d u n g giua hai d i e m A va N la 400 (V) va dien ap h i f u

A.240(V)

B. 120(V).

O
Uc

o

150'

?
\ 2 0 0 / 3 ,
200/3

!

I

1

7

\

\

A

1

1

= a J b '
75


B6

lis> hicn

lliiic

yjt

li LIOll

litin

Chu y: Neii cho bict
«

^

coC
tanip,^,

VTV2.

t^p

2 — Chu

V^n

Bien

cty Timn MTV p vvn m^ng vi^t

= L/C tht sm/ ra:

R 2 = , , L . — = Z,Zc

»

hcitli

^

R

tancpRc = -1 «

= - l
R

0^,

•

-

• ;
_L

Y i d v 5: T r e n d o a n m a c h x o a y c h i e u k h o n g p h a n n h a n h c 6 b o n d i e m t h e o
Vi c
d u n g t h u t u A , B, C v a D . G i u a h a i d i e m A v a B c h i co t u d i e n , g i u a h a i
d
d i e m B v a C c h i c 6 d i e n t r o t h u a n , giCra 2 d i e m C v a D c h i c 6 c u o n

t :•./

t h u a n c a m . D i e n a p h i e u d u n g g i i r a h a i d i e m A v a D l a 100

0^^

V i d u 3: M a c h d i e n x o a y c h i e u n o i t i e p A B t h e o d u n g t h u t u g o m c u o n Cam
t h u a n L, d i e n

t r o t h u a n R va

URC = 0,75UKL v a
A . 0,8.

tu dien

C.

Cho

biet dien

ap

hieu

dung

R- = — = ZLZC

do hieu d u n g chay qua m a c h la 1 (A). D i e n ap tire t h o i tren d o a n A C va tren
ctoan B D l e c h p h a n h a u 6 0 " n h u n g g i a t r i h i e u d u n g t h i b a n g n h a u . D u n g

A.40Q.

B.lOOa

dan

•'

C.^>/3:Q,

Huong,

<^

, !>, i j i V H '-ntiCi j r ' i s h '^^ncvv

s i n a = 0,6

'' •

ac d e u n e n

R

\}Q = 0,75a sin a = 0,45a => COS (p = —

,r[ & u i O . , S fr/ lA ,,M

'''''

: 0,864 = > C h o n B .

t u d i e n C.

Cho

biet dien

ap

hieu

dung

= L/C. T i n h h e s o ' c o n g s u a t c i i a d o a n m a c h A B .

A . V2/7.

C. 43J7

B. ^/3/5.
Huong

= C

,2
= Z,Zc =>UR

.

D.

I

• = 1 0 0 ( Q ) !> C h o n B .

d i e m M v a B l a 40 ^/3

^

doan

AN

va

tren

doan

MB

lech

pha

n h a u 90", d i e n a p t u c

tren
pha

u,,

= J-r^ChonC.

ha

phwcmg

phdp vec to huge thi khong

+ ( U L - U c )^• tan cp =
U]3

-

m"-^

theo

(V).

NB

nhau

va

hieu

C
N

M
UT

1,0,

o

— ^ .

AN

lech

30"

do

R

va
dung

>

0.

,<-''M"
v
-»

UR

?

:Ul!+r .

t r o n g m a c h la N/3 ( A ) .

ve cdc dien dp bat cheo de tinh cdc dien dp thdnh phan
=

doan

cuong

Vuf,+(U,-Ucr

y: Ne'u dung

Uc

D i e n ap t u c t h o i tren

U L = a>/3 cos a = 1,5a

Z

Uc

d u n g t h u t u A , M , N v a B. G i u a h a i d i e m A v a M c h i co c u o n d a y , g i i i a h a i

thoi tren d o a n M B

- 7 =

I

6: T r e n d o a n m a c h x o a y c h i e u k h o n g p h a n n h a n h co b o n d i e m

\]Q = a s i n a = 0,5a

R
• COS(p = — =

thitc:

V i du

Uc

IUR

100 V3

a p h i e u d u n g g i u a h a i d i e m A v a N la 60 ( V ) v a d i e n a p h i ^ u d y n g giCra h a i

dan

=U[Uc

U R = a c o s a = 0,5a^/3

UR

d i e m M v a N c h i co d i e n t r o t h u a n , giCra 2 d i e m N v a B c h i co t u d i e n . D i e n

72/5.

A O U R C U R L v u o n g t a i 0 =:i> a = 3 0 "

Chu

4i

=>Zc =

t r o t h u a n R va

UKL = V3 URC v a

UB

o

V ==l O100,0( (VV))

U

V i d u 4: M a c h d i e n x o a y c h i e u n o i t i e p A B t h e o d u n g t h u t u g o m c u o n c a m
L, d i e n

'"-^

D u a v a o g i a n d o vec t o t i n h d u o c :

M+i^L-^cf
thuan

*

•D

UK = U = 100N/3(V)

U L = a c o s a = 0,8a
cos tp = •

4i

= U,- = ^

C

T i r d o s u y ra m a c h c o n g h u o n g :

Uf, = 0,75a c o s a = 0,6a

U,,

u,

B

-^H

IJ
cos a = 0,8

D . 20 Q.

dan:

T a r n g i a c c a n co m o t g o c 60° la t a r n

U R = ULU(_. => A v u o n g t a i 0

t a n a = 0,75:

(V) va c u o n g

k h a n g c i i a t u d i e n la

= L/C. T i n h h e so c o n g sua't c i i a d o a n m a c h A B .
D . 0,867.
B. 0,864.
C. 0,5.
Huong

cam

• •

nen ve vec ta tongl

Chi

UR, UL, UC roi dp dung

; cos cp = HJL .
,
U

nen
he

Dien

tro

thuan

cua

\

Ail

c u o n d a y la
A. 4 0 Q .

B. l O Q .

C. 5 0 Q .

D. 20Q.

\

\

Un

\
77


B S trgkiSn

thiic

V$t IILTOH

ttenkSnh

VTV2.

l./)>

Huong
ih

van

Cty

Blen

dan

i du 8: Tren

AOUKUMM : UK = 40>/3.sin30" = 20V3 ( V )

v ; .(

:y;

) Ji

uf

j>iit,

'

' • I I I ' ; , v , : r ;
tin LIR., = (ii + DW

' '

d u n g thiV tu A, N , M va B. Giun hai diem A va N chi c6 dien t r o thuan R,

giiia hai d i e m N va M chi co cuon day (c6 dien tra t h u a n r = R), giua 2 d i e m
M va B chi c6 tii dien. Dat vao hai dau doan mach m o t dien ap U - 50 H z thi
dien ap hieu d u n g tren doan A M bang tren doan N B va b3ng 30^5

(V).

Dien ap tiVc thoi tren doan A M v u o n g pha v o i dien ap tren doa.i N B . Gia trj
U bang
B. 90 V.

.

' ::

C. 60 ^/2 V.

Huang dan

AOU^Ufjij : sin a =

30^5

A/~vi I I I
^K+r
2U
AOU,..U,,:cosa = ^ . - ^

U,^,^ =30V5.cosa = 60
U,,e=30V5.cosu = 60
[fill B(iX}:i':gm:':

A

R

t-'.'

=> tan a =

- •;

D . I 20 V.
• * -

k h o n g phan nhanh c6 bon d i e m theo

sin a =

sin a

1
=—
cosa 2

i giua hai diem M va N chi c6 cuon day,

c^.

cosa = .

••
; Si

^*

Cuon day dien tro thuan r = 0,5R. D i e n
ap hieu d u n g tren doan A N la U 73

1

2

;U,.

,

va

tren doan M B ia U . Dien ap tuc thoi
tren doan A N va tren doan M B lech
pha nhau 90". D i e n ap tuc thoi UA.\m
pha hon d o n g d i e n la
A. 60".

B. 45".
if

{

{

• •

D . 15".

C. 30".

^

Huang

dan:

•u/^'«"- >

AOU^UMI, : s i n a = U

< " ' ' f . ; ; <

3U.

tan a =

A O U , , , U , , . . . . . - ^ ^ _ - ^ ^

cosa

• a = 30" => Chon C.

s

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

—

^

L.r

C

VV'J'.'V

?;1

r..!\i.
I'vV

';::^\
30 VS,-

-mm

o

4) V e gian do vec to bang each van dung

quy tac tarn giac - phuong phap

vec to trugt (vec to noi duoi)
\30V5:

\

\

Ve

-

!

i

gian

phuong

do

vec

to

theo

phap

vec

to

trugt

g o m cac buoc n h u sau:

u,.
u-

ede

doan mach sau:

=> U = J U r , , , + Ufc = 6 0 V 2 ( V ) = > C h o n C .
^
V /
.

UAM

o

Vlft

chieu

; giua hai d i e m N va B chi c6 tu dien.

V i du 7: T i e n doan mach xoay chieu khong phan nhanh c6 bon d i e m theo

, ,

Khang

d i e m A va M chi c6 dien tro thuan R, , ^

U
r = — i - = 10(Q)=>ChonB.

A. 30 V.

mach xoay

nrvDVVH

d u n g thu tir A , M , N va B. Giua hai

- ' ' i ' A O U , . ^ , U , ^ N : U|^,, =60.sin60" = 3 0 V 3 ( V ) = J . U , =10>/3(V)

• " C/tu I/; Nn/ da) /;/^? R =

doan

TNtlH

.

1. >,.•!.

1

.

R

A.
M

N

C

(in,

N
11

,

i)

+ Chon true ngang la true d o n g
dien, d i e m dau mach lam goc

UL

(do la d i e m A ) .

* '1 ': \;

1 \

Cliil J/; Mrti xkh
78

quan trong trong bai loan tren la xac dinh goc

a.
79


BS tr^

kiSa

thUc

V$t If LTD I I tt0n

kenh

VTV2,

t^p

2 - Chu

cty
Van

+ Ve Ian lu-gt cac vec to dien ap tu dau mach den cuoi mach

A M , M N , NB

"noi duoi nhau" theo nguyen tac: L - di len, R - di ngang, C - di xuo'ng.

A A M B can

^ I= ^

dien dien ap U A \ vec ta MB bieu dien dien ap UNH.
Mot so'dictn cmi Iwii y:

* Neu cuon day khong thuan cam (tren doan A M c6 ca L va r (Xem hinh a
duoi day)) thi 0^^,, = 0, + 0^ + U,^ + 0^ ta ve L truoc nhu sau: L - di len, r di ngang, R - di ngang va C - di xuong (Xem hinh a) hoac ve r truoc nhu
sau: r - di ngang, L - di len, R - di ngang va C - di xuong (Xem hinh b). ; ^
Ui

M

M

= 4 ( A ) => C h o n C .

,

,

,

vi^t

Vi du 2: (GIAN DO R-rL) Doan mach dien xoay
" ^ ^ ' ' ^ ', ^
.p
chieu AB gom dien tro thuan R mac no'i tiep
M
vai cuon day. Dien ap hieu dung 6 hai dau
,,
.-:^B
dien tro, cuon day va hai dau doan mach Ian '* '
luot la 70 V, 150 V va 200 V. He so cong sua't
-''iso/
ciiacuondayla
'
/
UL
B.0,9.
D.0,6.

= -0,6

cosMcd = 0,6

^"^-A
M

=> Chon D.

/

•

200^ = 70^ +150^ + 2.70.150.cos(p,-d

'ri-.,., ^

^

..^ '

Ta dugc: AB^ = A M " + MB^ + ZAM.MB.coscp^^

gian nhu phuong phap da neu.

"

• •

Cach 2: Binh phuong v6 huong hai ve: AB = A M + MB

Hinhb

Hinh a

'

«jw>';'.Fi

2.70.150

Neu mach dien c6 nhieu phan t u thi ta cQng ve dugc gian do mot each don

'•'). vv "*

coscp^j = 0,6

•<

f

. r •, ,

Vi du 3: (GIAN DO R-rL) Doan mach di^n xoay chieu gom dien tro thuan R
M

N

Ci
E"F

17,^ = MB = 120( V )

cos A M B =

(GiQa A va M c6 ca UL va Uj)

D

M ^

A . - " '
'1^
V> - Huang dan
Cach 1: A p dung dinh ly ham so cos cho tam giac AMB:

* Qioii tmc ngang la true dCng difen.
* Qion di^m iin mach A lam g6c.
* Ve lin luot tir A laiig B tlieo nguyen tac
ndidudinliau:
,o f
L-Diten.
,
R-Dinsans.
.
C - Di xudng.

A

tai

A 0,5.
C.0,6.

N

M

loiang

Huattg dan

+ Noi A voi B thi vec to AB bieu dien dien ap UAH. Tuong tu, vec to A N bieu

L,r

D vvn

Timn nrv

BiSn

mac noi tiep voi cuon day. Dien ap hieu dung 6 hai dau dien tro, cupn day
va hai dau doan mach Ian luot la 35 V, 85 V va 75 N/2 V. Cuon day tieu thu

O

M

N

B

UL2

Ur

cong sua't 40 W. Tong dien tro thuan ciia toan mach la

UT

A.

*0»

50 (Q). ^

B.

35 (Q).

C. 40 (Q).
Humgdan

-••I

• - cm-

352+(7572f-85^
2.35.75V2

\inM 'of 'A'i <)!>

V i du 1: ( G I A N DO R-rL) Doan mach dien
xoay chieu gom di$n tro thuan 30 (Q) mac

R

noi tiep voi cuon day. Dien ap hieu dung 6
hai dau cuon day la 120 V. Dong di^n

1

' ) ) -J';;'

r, L

A.

C. 4 (A).

D. ^

(A).

,

2

•

..-;lB
x''

•

/

pL

I
=>r + R = i ^

= 75(Q)r^ChonD.

Uj^

M

^' dy 4: (GIAN DO L-R-C) Dat mot dien ap xoay chieu c6 gia tri hi#u dung

ap hai dau cuon day. Cuong do hi^u dung
B. 3 (A).

A - - C Z > - ^ « - ^ B

Pr=I^r = I.U, = ^ I = - ! J ^ = 1 ( A )

B

ctau doan mach va lech pha 7i/3 so voi dien

A. 3 V3 (A).

rL

M

trong mach lech pha 7r/6 so voi dien ap hai

dong dien qua mach bang

R

/2

=^UK+r = A E = ABcos(p = 7 5 ( V ) = ^ U , =45(V)

D. 75 (Q).

120,V

200(V) vao hai dau doan mach A B gom cupn cam thuan c6 dg t u cam L,

/ \"

di?n tro thuan R va tu dien c6 dien dung C mac no'i tiep theo t h u t u tren.
^i?n ap hieu dung tren L la 200 V2 (V) va tren doan chua RC la 200(V). Di?n
hieu dung giiia hai dau tu dien la

' '
81


a' tr(» hien thitc

V^t 11LTBH

trgn kSnh

VMn Bt&n

72 (V).

D. 100 V3 (V). ' '

Ve gian do vec to truot.

M

AMB = 45

tai B

nen
N

=^Uc = ^^ = 100V2(V)r^ChpnC.

: .

giac

U 'R
200V

vuong

can

Vt^t

,

N
Uc

200 V2V

A.

=>NMB = 45"=> ANMB la
tai

tam

—f45"

Vi A B I M B nen B pliai nam tren. AAMB
giac vuong can

Huang dan
= U = 200(V) => Chon B.

AAMB Id tam giac deu

Huong dan

la tam

Cty Tiy/ltl MTV D VVtl Khang

B. 60 (V).

A. 80 (V).

C 100

VTV2. t^p 2 - Chu

200V

I

A

n du 5: (GIAN DO L-R-C) Dat dien ap u = 120 V2 coslOOnt (V) vao hai dau
doan mach AB gom hai doan mach A M va MB mac noi tiep. Doan A M gom
cuon cam thuan L mac noi tiep voi dien tro thuan R, doan MB chi c6 tu dien
C. Biet di?n ap giira hai dau doan mach A M va dien ap giiia hai dau doan
mach MB lech pha nhau 2n/3. Di|n ap h i f u dung tren A M bang mot nira
tren MB. Dien ap hieu dung giira hai dau doan mach A M bang
A. 40

V3 V.

B. 220/

73 V.

C. 120 V.. ,

D. 40 V.

Huang dan
1i "

120^ = AM^ + 4.AM^ - 2.AM.2.AM.0,5

tiep voi tu dien. Do lech pha giira cuang dp dong di?n trong mach va dien
ap hai dau mach la 7i/3. Dien ap hi?u dung giira hai dau tu bang Vs Ian
dien ap hai dau cuon day. D Q ]|ch pha ciia di?n ap giira hai dau cupn day
so voi cuong do dong dien trong mach la
A. 71/3.

B. 7t/2.

AM = 40^3 (V)

] Ap dung djnh l i ham so sin cho AAMB:

^

R

L

C. 7i/4.

D . 7i/6.

Ur

sin(60°+9,d)

sin 30°

Chon A.
sin(60"+Vcd^

^

I .

Huang dan:

Ap dung djnh ly ham so cos cho AAMB:
AB^ = AM^ + MB^ - 2.AM.MB.COS60''

i du 7: (GIAN DO Lr-C) Mot doan mach xoay chieu gom cuon day mac noi

M

L,r M

• ^0° +

= 120° =^

= 60°

Chon A.

.B

I
•1^
J

f

B

t:fr:i

Vi du 6: (GIAN D 6 Lr-C) Mach dien gom cuon day mac noi tiep voi tu dien C
Dat vao hai dau doan mach dien ap xoay chieu 200 V - 50 Hz thi di?n ap ha'
dau cuon day va hai dau tu d i f n c6 cung gia tri hi?u dung nhung lech pb^
nhau 120". Dien ap hi?u dung tren tu la
A. lOOV.
B.200V.
, C.300V.
6:

D . 400 V.

du 8: (GIAN DO Lr-C) Dat dien ap 100 V - 25 Hz vao hai dau doan mach
mac noi tiep gom cuon day c6 dif n tro thuan r, c6 do t y cam L va tu dien c6
dien dung C = 0,l/7i (mF). Biet di^n ap hai dau cuon day som pha han dong

i trp kUfn thUc V$t It LTDH tr&n k&nh VTV2. t^p 2 - Chu V^n Biin

dien trong mach la K/6, dong thoi dien ap hieii d u n g hai dau cuon day gap
doi tren tu dien. Cong sua't tieu thu cua toan mach la
A.lOOVaW.
B.50/V3W.
C.200W.
D.120W.

, ^ - Huong dan

Z e = 4 r = 50Tt.^10 = 200(Q)
AAMB vuong nen ME = U,,, sin 30" = — =
U(^- = UK tan30"
100P=
R m)S

A

CV a n t ' !

S

E = B Mach cgng hudng

ChonB. '

,

Vi du 10: (DH - 2012) (GIAN D O C-L-R) Dat dien ap u = Uocosojt (Uo va co
khong doi) vao hai dau doan mgch AB theo thu tu gom mot tu di^n, mot
cuon cam thuan va mot dien tro thuan mSc noi tiep. Goi M la diem noi giua
tu dien va cuon cam. Bie't dien ap hieu dung giua hai dau A M bang dien ap
hieu d u n g giua hai dau MB va cuong do dong dien trong doan mach lech
pha 7r/12 so voi dien ap giua hai dau doan mach. He so cong sua't cua doan
mach MB la
A. 0,5 Vs.
B.0,26.
C.0,50.
D.0,5V2./ '
AAMB can tai M nen 15" +

VMl!

Huong dan

= 75"

9MI3

= 60" => COS ipi^i, = 0,5 => Chon C.
7

15"

.

A

i^i

B

M

15

P;.3 /

JO
/i d^ 9: (GIAN D O C-L-R) Dat di$n ap
u = Udcoscot (Uo va co khong doi) vao
hai dau doan mach AB theo thii tu
gom mot tu dien, mot cuon cam
thuan va mot dien tro thuan mac
noi tiep. Goi M la diem noi giua tu
dien va cuon cam. Bie't dien ap hieu
d u n g giiJa hai dau MB gap N/3 Ian .4
dien ap hieu d u n g giiia hai dau AM
va cuong d o dong dien trong doan
mach lech pha n/6 so vol dien ap
giiia hai dau doan mach. H e so cong
sua't cua doan mach MB la
A. 0,5 7 3 .

C. 0,50.

B. 0 , 5 > / 2 . - V 5 ^

D. 1.

Huong dan

AAMB can tai A nen AMB = 30"
=^ ^p^g = 60" ^ cos VMB = 0,5 => Chgn C.

M

Vi du 11: (DH - 2012) (GIAN D O R-L-C) Dat dien ap u = UocoslOOnt (V) vao hai
dau doan mach AB gom hai doan mijch AM va MB mac noi tiep. Doan
mach A M gom dien tro thuan 100 Vs Q m^c noi tiep voi cuon cam thuan co
dp tu cam L. Doan mach MB chi co tu dien co dien d u n g 10-4/(2TC) (F). Bie't
dien ap gii>a hai dau doan mach AM lech pha 7i/3 so voi dier. ap giua hai
dau doan mach AB. Gia tri cua L bSng
A. 2/71 (H).
.
^
^
__ c•
M
B. 1/TC (H).
d:Miion5ofc iiril) ififi
^,C.V2/71(H). V
•6-¥.&a.D
.V U)l ,f
M
D. 3/71 (H).
• J ^,

/
/

/

1

c.\ts

Huong dan

1 = 200(0).
uC
Tarn^ 1 . giac AMB deu:
-^ = -(H)
=>Z,
=100=>L='^
0)
71
=:> Ch9n B,

'

_

j

, (viob^

Z,. =200

85


Irct lileif^liiltc V^t II LTDtl tren Keitn VTfm;~T^~i - L H U van

men-

d u 12: ( G I A N D O R-L-C) Dat di?n ap xoay chieu tan so 50 H z vao hai dau

du 14: ( G I A N D O C-rL) M o t doan mach g o m

doan mach A B g o m hai doan mach A M va M B mMc no'i tie'p. Doan A M g o m

^^^ dien mac noi tie'p v o i m o t cuon day. Dien

dien t r o t h u a n 100 N/S Q m3c n o i tie'p v o i cuon cam t h u a n c6 do t u cam L ,

ap g'"'^

doan M B chi c6 t u dien c6 di#n d u n g 0,05/K (mF). Biet d i e n ap giiia hai dau

cuong do d o n g dien va lech pha n/2 so v o i

doan mach M B va d i e n ap giij-a hai dau doan mach A B lech pha nhau 7r/3.

di?n

Gia t r i L bang

d u n g giiia hai dau doan mach bang 100 V,

A . 2/71 ( H ) .

,„j,

B. l/7t ( H ) .
Huang

C. V3 In ( H ) .
dan:

D . 31% ( H ) .

JJ'

ay lech pha n/3 so v o i

I

^^^^'^ mach. Biet dien ap hieu

100 V

|
B

Uc

U,

cd

A. 60Vva60V3 V .

B. 200V va 100 x/3 V.

C.60V3Vval00V.

D . 100 ^/3 V va 200V.

^ V i

. Chon B.

L.r

A

cuon day Ian k r g t la

Zc = — = 200(Q) ; AAEB : BE = AE.cotnn- = lOO(O)
wC
3
• Z L = Z C - B E = 100(Q)=^L =

'^^^ cuon'

M

A.

Huang

Ui

30"

M

dan

CO

M

tan 30'
100

Xet A A M B :

=>ChonB.
= 200(V)

sin 30'
.B

V i d u 15: ( G I A N D O C-rL) M o t doan mach dien xoay chieu g o m m o t tu dien

Ur

CO d u n g khang 200 Q va m g t cuon day m^c noi tie'p. K h i dat vao hai dau

Ui

A.

- I

doan

Ur

hieu d u n g la 120 va som pha 7i/2 so v o i dicMi ap dat vao mach. Cong suat

mach

tren

mot

dien

ap

xoay

chieu

luon

c6

bieu

thuc

u =

120Ny5cos(1007tt + 7i/3) (V) thi tha'y dien ap giua hai dau cuon day c6 gia trj
tieu thu cua cuon day la

B

A. 7 2 W .

B . 2 4 0 W . ,?,t

C. 120VV.

Huong
i d u 13: ( G I A N D O R-L-C) Dat dien ap xoay chieu tan so 300 V - 50 H z vao
hai dau doan mach A B g o m hai doan mach A M va M B mac noi tie'p. Doan

D. 144 W .

dan
C

A A M B la can tai B:

M

L,r

A.

„ 1 ,^

•B

f

Uc = V M B ^ T A B ^ = ^20^/2 ( V )

•\

I

A M g o m d i e n t r o t h u a n mac noi tie'p v o i cuon cam thuan, doan M B chi c6
tu d i f n . Biet d i e n ap hieu d u n g giii'a hai dau doan mach M B la 140 V va
d o n g d i e n t r o n g mach tre pha h a n dien ap hai dau doan mach A B la cp sao

V

I = - ^ = 0,672 (A)

B. 200 V .

C. 500 V . •

Huang

A E = 300cos(p = 240(V)

D . 400 V .

A A M B la can tai B :

=

60V2 ( V )

B
120V
\

M

t : Wall.,

N

^ ' du 16: ( G I A N D O R-C-L) Tren doan mach xoay chieu k h o n g p h a n nhanh c6

• E M = EB + B M = 320

bon d i e m theo d u n g t h u t u A, M , N va B. GiiJa hai d i e m A va M chi c6 dien

A M = 7AE^ + E M ^
1H)

.

=

=>Pr =!'r = i.U, =72(W)

«

Chon A .

=:>ChonD.

^

!,

dan

BE = 300sintp = 300Vl-cos (p =180

= ^240^ +320- = 400 ( V )

120V

1

cho coscp = 0,8. D i e n ap hieu d u n g giija hai dau doan mach A M la
A . 300 V .

f

thuan, giua hai d i e m M va N chi c6 tu dien, giua hai d i e m N va B chi c6
^Uon cam thuan. Dat vao A B m o t dien ap xoay chieu 120 V - 50 H z thi dien
tuc thoi tren doan A N va tren doan A B lech pha nhau 60", dien ap tiic
87


io trf> hicn

thuc

Vat li LTBtl

tren

henh

VTV2,

lii/i

( liu

J

Vein

Bien

t h o i tren d o a n A B va tren doan N B lech pha nhau 60". D i e n ap hieu dung

H i n h thoi c6 goc 60

giCra hai dau tu d i e n la
A . 120 (V).

B. 6 0 ( V ) .

C. 6OV2 ( V ) .

D . 100 (V).
' '

A A N B deu

1

U AN

' •

' Humtgdan
,},!•

nen:

NB = A B = 1 2 0 ( V )

< n i : yiiijo

tUi.rn

iiSioh

r Y '

nov

'

A^60«

= 60(V)

M

2

u,.

= 60N/3(V)
COS a

V i du 18: ( G I A N D O R-C-rL) Tren doan mach xoay chieu k h o n g phan nhanh
CO bon d i e m theo d u n g thiV t u A , M , N va B. Giua hai d i e m A va M chi c6

M

Up

f

dien t r o thuan, giua hai d i e m M va N chi c6 tu dien, giua hai d i e m N va B

C

chi CO cuon cam. Dat vao hai dau doan mach m o t dien ap xoay chieu 240V 50 H z t h i UMii va UAM lech pha nhau 7x/3, UAIS va UMH lech pha n h a u 7t/6. D i e n

,Vt)(

=> C h o n B . J

N

CM

• a = 30"

Binh luan: Cdch gidi2 phdi ve nhieii dieang net phicc tapl ' .'WMH •'*>

• ''

NB
=>Ur = M N =

Cdch 2: D u n g p h u o n g phap vec to buoc:

y: Doi vai mach c6 4 phan tu tra len ma khong lien quart den dien ap bat chco

heme R a giila thi nen diing phivang phdp vec ta tnegt.

ap hieu d u n g tren R la
A . 80 (V).

B. 60 (V).

C.80>/3 (V).

D. 6 O V 3

B

A A N B can tai M :

dien t r o thuan R, giira hai d i e m M va N chi c6 tu dien, giua hai d i e m N va B

fyz A B M = 60" - 3 0 " = 3 0 " )

chi CO cuon cam. D a t vao hai dau doan mach m o t dien ap 90 V3 V - 50Hz thi

Theo d i n h ly h a m so'sin:

d i e n ap hieu d u n g tren R va tren doan M B deu la 90 ( V ) . D i e n ap tuc thoi

UR

AB

hai d a u doan mach A N va M B lech pha nhau nil. D i e n ap hieu d u n g tren

sin 30"

sin 120"

'^'^^^

D . 6OV3 ( V ) .

C.IOOV2 ( V ) .
Huang

dan

'30""^
R

Ur
A

R

•-cz:

M

N

L,r

f

•

^

N

=> C h o n C.

c u o n g do hieu d u n g qua mach la 0,5 A . Doan A M g o m d i e n t r o thuan R

• £1 -

u

UMB
••••••

*
/:

90/

:

mac noi tiep v o i t u dien C, doan M B g o m cuon cam. Biet d i e n ap g i u a hai
dau doan mach M B va dien ap giija hai dau doan mach A B lech pha nhau
7i/2. D i e n ap hieu d u n g tren R bang m o t nua dien ap h i e u d u n g tren doan

90>-'''

A M . C o n g suat tieu t h y cua mach la
I

A. 60(W).

B.90(W).

C.90V3(W).

D.60V3(W).

III

Huang
A A M N :sin(p =

Ur

''''' "'^'^

AN
AM

AN

• coscp = yjl - sin^ (p =

M

s

^'''

P = U I coscp = 120V3.0,5.— = 9 0 ( W )
UAN = - ^

cos a
58

„ cIA ±

hai dau doan mach A B g o m hai doan mach A M va M B mSc n o i tiep thi
m't.

A A M B can goc a day 30" => a = 30"

B

V i du 19: ( G I A N D O R-C-rL) Dat dien ap xoay chieu u =120 V6 coscot (V) vao

u,,t

Zdch 1: D i i n g p h u o n g phap vec to trugt:

120V

A .

„

=> U R = 8 O V 3 ( V )
B.60(V).

%

UT

CO bon d i e m theo d u n g thir t y A , M , N va B. Gifra hai d i e m A va M chi c6

A.80(V).

.d

Huong dan

/ i du 17: ( G I A N D O R-C-rL) Tren doan mach xoay chieu k h o n g phan nhanh

doan A N la

.-n

(V).

= 6OV3(V)
• Chon B.

dan

Bo

t r p k i e n thiic

V^t l i LTOH

tren henli

VTV2.

t a p 2 - Chu VHn B i e n

W\u 20: ( G I A N D O Lr-R-C) Tren doan mach xoay chieu tchong phan n h a n h

yf dV 22: ( G I A N D O Lr-R-C) Tren doan mach xoay chieu k h o n g phan nhanh

CO bon d i e m theo d u n g t h u tir A , M , N va B. G i u a hai d i e m A va M chi c6

CO bon d i e m theo d u n g thu' t y A , M , N va B. Giua hai d i e m A va M chi c6

cuon day, giua hai d i e m M va N chi co dien t r o thuan R = 60 Q, gifra 2 d i e m

cuon day, giua hai d i e m M va N chi c6 dien t r o thuan R, giua 2 d i e m N va B

N va B chi c6 tu dien. D i e n ap hieu d u n g giua hai d i e m A va N la 120 (V) va

CO tu dien. D i e n ap hieu d u n g tren A B , A N va M N thoa m a n he t h i i c

d i e n ap h i ^ u d u n g hai d i e m M va B la 80A/3 ( V ) . D i e n ap tiVc t h o i tren doan

0,^15 = U A N = U M \ N/3 = 120N/3 ( V ) . D o n g hieu d u n g t r o n g mach la 2 N/2 ( A ) .

A N va tren doan M B lech pha nhau 90", dien ap tiic t h a i tren M B va tren N B

Dien ap tiic t h o i tren A N va tren doan A B lech pha nhau m o t goc d u n g

lech pha nhau 30". D i e n trcV thuan cua cuon day la

bang goc lech pha giua d i e n ap tiVc thoi tren A M va d o n g dien. T i n h cam

A. 40Q.

B. 6 0 Q .

C. 30 Q .
Hu6iig

' »
D . 20 Q .

khang cua cuon day.
A.60N/3Q.

dan
N

U«

A M N B i M N = UK =MB.sin30" = 4 0 V 3 ( V )

B.1576Q.

C. 3 0 V 3 Q .

Huong

D. 30-./2Q.

dan

A A N B can tai A ma M A I = N A B
>

A

^mms'^

UL

120'

A A E N ^ E N = AN.COS30" =60N/3(V)

=>

/

Uc

• •

N

g

L,T

SOVJV

«y

120

N

= E N - M N = 20^/3
30"

=^- = ^ = -=>r
R
UR

=> A A M N can tai M vd a = 30"

= - = 30in)=> ChonC.

B 4

Vi du 21: ( G I A N D O Lr-R-C) Dat dien ap xoay chieu u = 120>y6 coscot (V) vao

U L = ^ 2 0 ^ / 3 s i ^ a = 60^/3
=^ZL

=^

/

= 15V6(Q)

hai dau doan mach A B g o m hai doan mach A M va M B mac no'i tiep. D o a n
A M la cuon day c6 dien t r o thuan r va c6 do tir cam L, doan M B g o m dien

=> Chon B .

t r a thuan R mac noi tiep v a i tu dien C. D i e n ap hieu d u n g tren doan M B
gap d o i d i e n ap hieu d u n g tren R va c u o n g do hieu d u n g cua d o n g d i e n
t r o n g mach la 0,5 A . D i e n ap tren doan M B lech pha so v a i dien ap hai dau
doan mach la n/2. C o n g sua't tieu thu toan mach la

A. 150W.
m^iruhi

B.20W.

.M-).of8A f , i r : f . . '".i/ri:-

A M F B : sincp =

C.90W.
Huvngdan

D . 100 W .

-

Vi du 23: ( G I A N D O C-R-rL) M o t mach dien xoay chieu n o i tiep g o m tu dien
CO d i e n d u n g C, dien t r a thuan R va cuon day c6 d o tir cam L c6 dien tro
thuan r. Diang v o n k e c o dien tro rat Ian Ian l u g t do hai dau dien tro, hai

U,,

= 0,5 =:i> cp = •

dau cuon day va hai dau doan mach t h i so chi Ian l u g t la 50 V, 30V2 V va

u Mti
P = UI COS (p = 120 V3.0,5 cos - = 90 ( W )

6
• Chon C.

80 V . Bie't d i e n ap tuc t h a i tren cuon day som pha h o n d o n g d i e n la 7i/4.
Dien ap hieu d u n g tren tu la

B. 30V2V.

A . 30 V.

C. 60 V.

D.20V.

Hu6itg dan
A

M

R

^AMB

=^ Tii gidc AMNB

= MN + NE = 80V = AB

=*-ChonA.

1 •d

>

Id hmh ch a nhat

= > U c = A M = EB = 3 0 ( V )
Kinh nghicm: Khi cho bie't do lech pha bang nhau thi tren gidn dovec ta c6 the c6
tamgidccdn!
/
; i • ,5-.:

• 1 , 1 ' ,i

Id tarn gidc uuong can tai E

=>NE = EB = 30V^ME

>

*
,
: •

'

91


ISO TTp Rfen

thiTc

vpt

n L m n

tn

->
I

B

A

c

R

M

L,

N

r

.B

Cty

A A E B :

A B -

=

TISnn

MTV o w n Khang

3200 = (25 + x ) ' + [ 6 0 - V 6 2 5 - X -

A E ^ + EB^

Vlft

N

= 15
P
30V

P=IUcoscp = I.AE=>I = — =
=>ChonB.

M

40

U

-

= ] ( A ) ^ r = Y-

= 15(Q)

^^^^

.

30V

V i d u 24: ( G I A N D O C-R-rL) M o t mach dien xoay chieu noi tiep A B g o m : doan
A N chiVa tu dien C noi tiep v o i dien tro thuan R va doan N B chi c6 cuon
day CO d o t u cam L ccS dien tro thuan r. Dien ap hieu d u n g tren cac doan
A N , N B va A B Ian l u p t la 8 0 V, 1 7 0 V va 1 5 0 V. C u o n g d o hieu d u n g qua

Co thedimg may Huh Casio 570cs

mach la 1 A . H e so cong sua't cua doan A N la 0 , 8 . T o n g dien t r o thuan cua

degiai phieong trinh va bam uhir saii:

toan mach la

i

A. 1 3 8 Q .

B. 3 0 N / 2 Q .

Huattg
i

Bam

C. 60 Q.

D . 9 0 Q.

ANPm

Gidi phiidng tr i nh:

dan

B

Nkap xong bajn \SHIFT\CALC\

•i •

R

N

r

=

Ur

(^dc CO canh tiCdiig ling vuong goc)

M

A F = ABsincpAN = 9 0 ( V )
U K + U ,

AF

I

I

=

Z

\

A

U

R+r

N

cuon day c6 cam khang 100 n c6 dien t r o r = 0,5R, giiJa 2 d i e m N va B chi c6
tu dien c6 d u n g k h a n g 200 Q. Dien ap hieu d u n g tren d o a n A N la 200 (V).
D i e n ap tuc t h o i tren doan M N va A B lech pha n h a u n/2. N e u bieu thuc

tro t h u a n r va tu dien C t h i cong sua't tieu t h u cua mach la 40 W . Bie't dien

d o n g dien t r o n g mach la i = IV2 cos(1007tt + (pi) A t h i gia t r j cua I va cpi Ian
l u p t la

A. 1

A

va K / 3 .

B.

Cdch 1: Pliu'ongplidpdqiso':

«"iW,,

--^m, ,?5^Vi 4 - V i W \ 7\M., X-^. 'AM',

Z,

ni'c D.3on.

92

: N E =

X / M N '

- M E '

=

sjeiS-x^

E B = 60 -

A

^b25-y}

,

.jfv n o d r >

s,

va K/3.

U

C.

+ Z

A

va 7r/4.

^y'
Z, - Z r

D . 1 A va 7i/4.

| ,y

v
= -l=>r =

IOON/S)^

100

(O)
( i HA

200

AN

V2

Humgddn

R+r

Huong Mn
A M N E

V2

.

ap h i ^ u d u n g tren dien tro, tren cupn cam va tren ty d i ? n Ian l u p t la 25V,
C.20Q.

V vao hai

G i i i a hai d i e m A va M chi c6 dien tro thuan R, giu-a hai d i e m M va N chi c6

Ur

( <i>AH

dau doan mach noi tiep g o m di$n tro R, cuon cam c6 d p t u cam L , c6 dien

B. IS n .

^ ,v

dau doan mach A B . Doan A B c6 bon die'm theo d u n g t h u t u A , M , N va B .

V i d u 25: ( G I A N D O R-rL-C) Dat dien ap xoay chieu u = SOcoscot (V) vao hai

A. s o n .

_

^

V i d u 26: ( G I A N D O R - r L - C ) Dat dicfn ap u = U ^ / 2 cos(100Tct + n/6)

\80V

90(Q)=>ChonD.

25V va 60 V. Gia t r j r bSng

{AI^IPHA^

ta se t i m d u o c he so cons sua't va cong sua't:

UT

i7oy/

=> A B F = A N M =

=:>R + r =

/
f->

A N H A B ^

Bmn

Doi v o i loai bai toan nay mat xich quan t r p n g la t i m U r . Sau k h i t i m d u p e Ur

.B

A A N B la tarn gidc ywong tai A v\:
NB^

+(60--j625-

xf

Bam liNPHiQ

=0'6
M

CALC

3200 = (25 +

Tarn gidc uuong A A M N : COS9AN = 0 , 8
COS 9 A N

f

= 1(A)
+100^

93


Bo" t r p h f S n

fan cp =

thurc

V^t I I L T D H

tren kenh

VTV2.

t^p 2 - Chu

R + r^ " " ^ " ^ " ^ " " f

V^n

BIcn

C/y

^""^ P'''^ h o n d o n g dien la 7t/6

iiay d o n g dien sam piia hon dien ap la Tt/6.
=> i = l72cos 1007rt + - + - l = 72 COS
6 6

T/VHHMTV

DVVHKhang

Vift

V i d u 27: Tren doan mach xoay chieu k h o n g phan nhanh c6 bo'n d i e m theo
f-diing t h u t u A , M , N va B. Giua hai d i e m A va M chi c6 dien t r o R, giua hai
i; d i e m M va N chi c6 cuon cam ma dien t r a thuan r = 0,5R va d o t u cam L =

1007tt +

-

' 1/n H , g i i i a 2 d i e m N va B chi c6 t u dien c6 dien d u n g C = SO/TT ^ F . D i e n ap

( A ) = > C h o n A.

hieu d u n g tren doan A N la 200 V. D i ^ n ap tren doan M N lech pha v a i dien
ap tren A B la Tr/2. Bieu thuc dien ap tren A B la UAH = Uocos(1007it + TT/12) V.

7:V

Bieu t h u c dien ap tren N B la
MN

A. UNB = 2 0 0 V 2 c o s ( 1 0 0 T T t + 5Ti/12)V.

B. UNB = 200N/2 cos(1007Tt - 7i/4)V.

C. UNB = 200cos(1007Tt + Ti/4)V.

o

I

D . UNB = 200 V2 cos(100rt + 7n/12)V.
Huong

G

- I

dan

Z, = u L = 100(Q);Z^-= — = 200(Q) = 2Z, : A M la duang trung tuyen
cuC

cua

A A N B . Suy ra, M la t r o n g tarn cua A A N B . M a t khac M cung la true tam nen
id

•,v;i(;r

N B = 200V
> U

AD

A A N B la t a m giac d e u .

U|vjB =

200\/2

COS

tri hdn U ^ g la —

a = — => U ^ i B

(V)

lOOTltH-

12

Chon B .

3)

T o n g h o p cac vec to d i ^ n ap theo quy tac h i n h b i n h :
iiS',:' Sir

Xet AOEF ( U A N = 2 0 0 V, H la t r u n g d i e m EF, O G = G H ) d i e m G v u a la
tarn vira la true tarn nen tarn giac nay la tarn giac deu. - :

.

Uc = 2 0 0 V = > I = H c

>i = V I COS

1007Ct +

- + -

6
dch 3: Phuvng phdp gidn do vcc ta tnivt:

M vira la t r o n g tarn v u a la
true

tarn

cua

tarn

^

^

M

A A M B nen tarn giac nay la
tarn giac d e u .

T u do suy ra:

r

L

nzHD-^—O^Wfff^

.

giac

6)

N'l

B

N

N

nguai ta dd "sang tdc" ra cac "hai todn la",

; • . , ilpkil^M ^ i -

,,

U C = U A N =200(V)

_

/ u!
•M

va I s o m p h a h a n D^^g la7t/6.
D o do: i = V2cos
6

67

'i d u 28: D o a n mach xoay chieu A B g o m hai doan A M no'i tiep v a i M B . Doan

„

M

Kinh nghicm: Ne'u tavi guic ANB deu thi Zc. = Zt. vd R = 2r. Dim vcio y twang nay

A M g o m dien t r a t h u a n R noi tiep v a i cuon cam c6 dien t r a r va doan M B
chi CO tvi dien. D i e n ap tren doan A M va A B c6 cung gia t r i hieu d u n g
n h u n g lech pha nhau 60". D i f n ap tren cupn .cam v u o n g pha v o i d i ^ n ap
tren A B . T i so r/R la

(A):

A . as.

- ''^
B.2.

'
C.l.'ryr.,.,^^lf,^

D.

0,87.

B

9S

Cty

Hudng dan

c

r,L

R

D

II.
60

A

B

M

-0,

(J

I

60 \

. G

0.

60

? 60 \

u.

0.

D

\
60

V

Vift

B

^

TL

M

M

3

A

it,<: Tarn giac A M B la tarn giac deu vi c6 A M = A B va goc MAB = 6 0 " . Do do, G
J vCra la true tam vua la trong tarn => UR = U r => R = 2r => Chon A .

TNilHMTVDVVnKhang

0,

B

B

Clu'i y: Voi mot bai todn cu the c6 the dimg hoqc phicang phdp dqi so hoqc phitang

/»««: Voi bai todn nay thl pitirong phdp vec ta trugt hay han phuang phdp vec
ta bugc. Nliung trong vi du tie'p theo thl ngugc Iqi.

phdp gidn dovcc ta biioc lioqc phiivng phdp gidn dovec ta trwgi. Trong ba cdch gidi

Vi du 30: Mach dien xoay chieu noi tie'p c6 bon diem theo dung thu t u A, M , N

do vffi mot dang cu the tin se c6 mot cdch gidi nhnnh vd ngdn ggn nhd't.

va B. Giua hai diem A va M chi c6 tu dien, giua hai diem M va N chi c6

V i du 29: Dat dien ap xoay chieu 60 V - 50 Hz vao hai dau doan mach AB gom

hai doan mach A D va DB mac noi tie'p. Doan A D gom dien tro thuan noi
tie'p cuon cam thuan, doan DB chi c6 tu dien. Dien ap hieu dung tren A D va
tren DB deu la 60 V. Hoi dong dien trong mach som hay tre pha hon dien

dien tro R, giua 2 diem N va B chi c6 cuon cam thuan. Dien ap hieu dung
tren doan A N va tren MB la 120 V2 V va 200 V. Dien ap tuc thai tren doan
A N va MB lech pha nhau 98,13". Tinh dien ap hieu dung tren R.
A. 120 V.

B. lOOV.

ap hai dau doan mach AB?

Huong dan

A. tre pha hon 60".
C. som pha hon 30".

^rt^-

B. som pha hon 60".

' ' '"^^<;',

jl

L

D. tre pha hon 30".

...

" • '•

Huang dan

= U?^ +
U?<+(UL-UC;

60^

602

i •'•

•

D. 160 V.
1 .

Cdchl: Phuang phdp vec ta trugt.

v ,
m

"^v ^w'

N E - = A E " + AN^ -2AN.AEcos98,13" => NE w 280
AN
NE

.
situT"" sin98 13" ^ ^'"'^ ^ ^ ' ^

Cdch 1: Phwang phdp dai so

U' =

C.250V.

" MB.sina

120(V) => Chon A.

- 2UL U C

+
602

UL

60

=30

U R = 30>/3

on
60^

tan ^ =

-—^ => ip = - — => Chon C.
S
6

R

Cdch 2;

n..i

''fil'''''

Phuang phdp vcc to bugc. T u A O U U A D deu =^ 9 = - .^

Chon C.
h'iv- Jijiq

Cdch 3;
Phuang phdp vec ta trugt. T u A A D B deu =^ 9 = — =^ Chon C.
'
6
MS)

.0

^dch 2: Phuang phdp vec ta bugc.
EF^ = OE^ + O F ' - 20E.OFcos98,13"
OF

EF sr. 280

EF

=

rr =^ siua
Sm

96

w'.

JJ

, mil

0,6 =^ U R = O E . s i n a = 120(V)
Bwiij

cjf, (•».,.; J { ! ) • / ( « ; .•V.,T. f . r t r

Chon A

'


BS

trp

kl^n

thiic

V^t

II LTDIf

trin

kinh

VTV2.

t^p

2 - Cbu

VSn

Btin

D. 1/ N/3 A va tre pha K/6 S O voi dien ap giiia hai dau doan mach.
Huong dan
nf

Khi mac noi tiep, ve gian do
vec to truot, tu tam giac vuong
can A M B :

MBA = MAB

Up
V i du 31: Co hai hop kin X va Y chi chua cac phan tu ghep noi tiep va trong
chung chi c6 the chua cac dien tro thuan, cuon cam va tu dien. Khi dat dien
ap xoay chieu 220 V - 50 Hz vao hai dau X, thi dong dien c6 gia trj hieu
!; dung 2 A va som pha so voi dien ap la n/2. Neu thay X boi Y thi dong dien
; CO gia trj hieu dung van bMng 2 A nhung ciing pha voi dien ap. Khi dat dien
, ap do vao doan mach gom X va Y mac noi tiep thi dong dien c6 gia trj hieu
J dung la
^
A. V2 (A) va tre pha 7T/4 SO voi dien ap.
B. yfl (A) va som pha 7T/4 SO voi dien ap.

Jt/4
\220V

C. 0,5 y/l (A) va som pha n/3 so voi dien ap.
D. 0,5 %/2 (A) va tre pha TT/3 so voi dien.
Huang dan

M-

U
220
Zv — Zv — — — = 110(Q)
I
2
Khi mac noi tiep, ve gian do vecta trugt, t u tam giac vuong can A M B :

0

M A B = 45'

Zn

110

Tir gian do suy ra dong dien som pha han dien ap la n/4 => Chon B.
Vi dv 32: Lan luot dat dien ap xoay chieu 220 V - 50 Hz vao cac dung cu P va
Q thi dong dien trong mach deu c6 gia tri hieu dung bang 1 A nhung do'
voi P thi dong som pha hon so voi dien ap do la n/3 con doi voi Q thi dong
cijng pha voi dien ap do. Biet trong cac dung cy P va Q chi chua cac diC'i^
tra thuan, cuon cam va tu dien. Khi mac dien ap tren vao mach chua P va Q
mac noi tiep thi dong di^n trong mach c6 gia trj hieu dung la
; A . 0,125 V2 A va tre pha n/4 so voi dien ap giua hai dau doan mach.

sin

MBA

Z,,

V
220V

Up

,0

^

30'

220,,,,
u
=*Up-—(V)
73
sin AMB
tr

220
220V3

.1.

\

M

1 1

V3
:A)
3

B

Tu gian do suy ra dong dien som pha hon dien ap la 71/6 => Chon C.
n du 33: Lan hrgt dat diCfn ap xoay chieu 220 V - 50 Hz vao cac dung cu P va

Q thi dong dien trong mach deu c6 gia trj hieu dung bang 5,5 A nhung doi
voi P thi dong tre pha hon so voi dien ap do la n/6 con doi voi Q thi dong
som pha hon so voi dien ap do la n/2. Biet trong cac dung cu P va Q chi
chua cac dien tro thuan, cuon cam va tu dien. Khi m^c dien ap tren vao
mach chua P va Q mSc noi tiep thi dong dien trong mach c6 gia tri hieu
dung la
A. 11 V2 A va tie pha n/3 so voi dien ap giua
hai dau doan mach.
'

'

'

'

'1/

B. 1] 72 A va som pha n/6 so voi dien ap
giua hai dau doan mach.
C. 5,5 A va som pha n/6 so voi dien ap giua
hai dau doan mach.
D. 5,5 A va tre pha n/3 so voi dien ap giua hai
dau doan mach.
'
Humgdan

2,. = z„ = H , | £ . „ , „ ,

I

5,D
Khi mac noi tiep, ve gian do vec to trugt, tu tam giac vuong can AMB:
Up = Uo = U = 220(V)=>I =

220 = 5,5(A)
40

Tu gian do suy ra dong dien som pha hon dien ap la n/6
=::>ChonC.

I'J' \

B. 0,125 N/2 A va som pha n/A so voi dien ap giiia hai dau doan mach.
C. 1/N/3 A va som pha n/6 so voi dien ap giua hai dau doan mach.
99


Cty
Bo ttv

hien

tliiic

Vat li LTDII

tren henh

5) Dung gian do vec to de viet bieu thiic dong dien hoac dien ap
* Neu cho biet t u a n g minh cac dai lugng tlii nen d u n g pliuong pliap dai so

hoac p h u o n g phap so phiic de vie't bieu thuc.
* Neu con c6 mot vai dai luong chua biet thi de vie't bieu thuc mot each hieu
qua nhat la d u n g gian do vec to.
Vi du 1: Mot doan mach gom dien tro thuan R noi tiep voi tu dien c6 dien
d u n g l/(37t) (mF). Dat vao hai dau doan mach mot dien ap xoay chieu:
u = 120cosl007rt (V). Dien ap hieu dung giua hai dau dien tra bang 60 V.
Tinh R va vie't bieu thiic dong dien qua mach?
A. R = 30 Q va i = 2 V2 cos(l OOTit + 7i/4) (A).
B. R = 30 Q va i = N/2 COS(1 OOTit - 7t/4) (A). ^
C. R = ^0^/3 Q va i = 4cos(1007it - 7t/6) (A).
D. R = 30 p ya i = 4cos(lQ07Tt + K/6) (A).
Zc

'

R = Zc =

30(n);U2..u2

30Q

_^Z-R + i ( 0 - Z c ) '

1= —

Huong dan
60^2

60^ + vl

120 • = 272Z1
30 - i.30

=^ Uc = 6 0 = U R

!*,,V',0?:

i = V2(cos 100TTt + - (A): Chon A.
4 chieu u = 60 >/2 cosl007:t (V) vao hai dau doan mach
Vi du 2: Dat dien ap xoay
AB gom hai doan mach AD va DB mac noi tiep. Doan AD gojn dien tro
thuan R m a c noi tiep voi cuon cam thuan L = 0,2/7i (H), doan DB chi c6 tu
dien C. Dien ap hieu dung tren doan AD la 60 (V) va tren doan DB la 60 (V).
Bieu thuc dong dien qua mach la
A. i = V2cos(1007tt + 7i/4)(A).
R
L C
B. i = 4.cos(1007rt + 7r/3)(A).
''''' r - t > ' > ' u . A
B
C. i = 4.cos(100T:t - n/6) (A).
D. i =1,5 N/2 cos(1007tt + 7t/6) (A).

Huong dan

Cdch 1: KS't hap phwang phdp dai sova phmmg phap sophu'c
UL = 30
'
60^=0?^+(UL-60f
UK = 30V3

60^ = UK + UL + 60^ - 120UL ^ U c = 6 0
'a
60^
I = ^ = 1,5(A)
60^ - UK + UL
1 nn

TISHHMrtVDWH

Khang

Vi^,

VTV2. t^p 2 - Chu V^n Blen

R = i:?^ = 20V3

Z.=Hc=40

=>Z=R+

i (ZL-Zc) = 2073+,

u _
- =
\,5^Z-nZ 20V3 + / ( 2 0 - 4 0 )
6
100;r/ + - ( / i ) = > C h o n D .
6
J

Cach 2: Phimng phap gian do vec ta huge
' i»
Zi, = LJL = 20(n)

,

i.!

(20-40)

It

60
V,

60

•

;:

AOUU^D la tarn giac deu hen: a = 7t/6 va Ui, = UAD/2 = 30 (V).
Dong dien som p h a hon dien ap la Tt/6 va c6 gia tri hieu dung:
I = i : ^ = l,5(A)
i = l,5V2cos

100Ttt + - +

-

(A)=>ChonD.

6 6
Cdch 3: Pkiecrng phdp gian do vec to'tnt'fft
I
'-J.
AADC la tam giac d e u nen: a = n/6 va UL = UAD/2 = 30 (V).
Dong dien s a m pha h a n dien ap la n/6 va c6 gia trj hieu dung:
I = - ^ = 1,5(A)
cl
i = l,5V2cos 100TVt + - + •Chon D.
6 6
Vi du 3: Mach dien g o m cuoii day mac noi tiep vai tu dien C. Dat vao hai dau
doan mach dien ap xoay chieu u = 200cos(1007tt + 71/12) (V) thi dien ap giira
hai dau cuon day va hai dau tu dien c6 cijng gia tri hieu d u n g n h u n g lech
pha nhau 120°. Bieu thuc dien ap giiia hai dau cuon day la
A. ucd = 100 V2 cos(1007tt + n/3) (V). B. ucd = 200cos(1007tt + n/6) (V).
C. Ucd = 200cos(1007it + 71/3) (V).
D. ucd = 200cos(1007rt + 57i/12) (V).
Tir gian do ta suy ra,
AAMB la tam giac
deu, vi vay, Ucd c6
cung bien d o n h u u
nhung sam pha han
U la 7r/3 => Chon D.

Huang dan
[ft

L,r

M

M

miG

-B

jj

'cd.

60"
• I

A
, U

100V2V

Uc
B

101


S'f/y

A/an

thurc

V^t

l i LTDI1

tren

hcnh

VTVJ.

l.ijt

2 -

Chu

Vdn

B i e n

i d^ 4: Dat d i e n ap xoay chieu u = 100 N/6 cos(100Kt + n/4) (V) vac) iiai dau
doan mach g o m m o t cuon day va m o t tu dien mac noi tiep. D u n g v o n idien t r o rat Ion Ian l u g t d o dien ap giira hai dau cuon cam v i i hai ban tu

Huang

R

r
•-HI—c =^—rmsx<—•

dan

Xtr gian d o ta de tha'y, A A M B la tam
giac v u o n g can tai M nen:

W2

i:

U,^(_ trG pha h
d i e n t h i tha'y c h u n g co gia t r j Ian i u o t la 1 0 0 V va 200 V. Bieu thuc dien ap

/a)

gii>a hai dau cuon day la:
A . U a l = 100 N/2 C 0 S ( 1 OOTtt + 71/2) (V). "

- = 60>/2cos

F) <

'

c

B. Uccl=200cOS(1007tt + 7t/4)(V).

(V)=>ChonD.

Chii y: Dim vao dm hicii vuoiii^ plin va dung pineang phdp loai trie c6 thcplidt hien

C. ucd = 200 N/2 C O S ( 1 OOTtt + 3n/4) (V).

nhanh phuvng du dung lud kliong can phdi su dung hct du kien ciia hai todti.

D . ucd = 100>/2 cos(1007ct + 371/4) (V).
J,

4j

y

M "f »\

Huaitgdan

V i d u 6: Doan mach A B g o m A M chua dien t r o t h u a n R mac no'i tiep v o i m o t
tu dien, M B chua cuon day co d i ^ n t r o thuan r = R. D a t vao hai d a u A B dien
ap xoay chieu u = 100 ^I2 coslOOnt (V) t h i dien ap giua hai d i e m A M va g i i i a
hai d i e m M B l§ch pha so v o i c u o n g d o d o n g di§n Ian l u g t la 7T/6 va

n/3.

Bieu thuc dien ap giua hai d i e m A M la

lOOV

A

A . U A M = 50 V2 cos(lOOTtt - Tt/3) V.

B. U A M = 50 V2 cos(lOOTtt - Tt/6) V .

C. U A M = 100cos(100Ttt - TT/3) V.

D. U A M = 100cos(100Ttt - Tt/6) V.
Huang

Uc

u

Vi

200V

100V3V

U/,^M

^^'^

ph''' ho'" ^ la

dan

con

sam pha h o n / la 7t/3 nen U ^ j ^ 1

U^B

hay A A M B v u o n g tai M . T u d o suy ra

B

U^^i tre pha h o n U^^u m o t goc a sao
cho A M = ABcosa. Ta nhan tha'y chi
p h u o n g an A thoa m a n d i e u kien nay
=>ChonA.

Tit gian d o ta de tha'y, A A M B la t a m giac v u o n g tai A ( v i MB^ = AB^ + A M ^ )
Uj.j sdm phahanU

Id—

^A,rif;d E9ig''qSrfi^iffc';j,iJf^^^^

TV H
u<.d =100V2cos 1 0 0 T t t + - + - ( V ) = > C h o n D .

4

2J

,

roi mac n o i tiep v o i cuon day. Dat vao hai dau mach m o t d i ^ n ap xoay
chieu u = 120cosl007tt(V). D i ^ n ap hieu d u n g 6 hai dau doan mach RC la
60V va hai d a u c u o n day la 60 V . Bieu thuc dien ap hai dau d o a n mach
RC la
A . U R c = 60cos(100nt + H/4) V.

B. U R C = 60 V2 cos(100Tit + n/4) V.

C.

D.

60cOS(1007Tt - 7T/4) V .

U R C =

nen vegian do vec ta trugtl

„

K

,,-,4,.

..

-

'

••'

V i d u 7: Tren doan mach xoay chieu k h o n g phan nhanh co b o i i d i e m theo
d i i n g t h u t u A , M , N va B. Gii>a hai d i e m A va M chi co c u o n cam thuan,
giCra hai d i e m M va N chi co dien tro thuan, giua 2 d i e m N va B chi co tu

dyi 5: M a c h d i $ n xoay chieu g o m d i e n t r o t h u a n R mac noi tiep v o i t u dien

URC =

CM y: Khi cho lien qua den dien dp Ian luvt deviei bieu thiec dien dp bat cheo ta

60 -Jl cos(lOOTtt - Tl/4) V .

dien. D i e n ap hieu d u n g tren doan A N la 300 V va lech pha v o l d i f n ap tren
N B la 5TT/6. Bieu thuc d i e n ap tren N B la

U N B =

50V6 cos(1007it - 27i/3) V.

i D i ^ n ap tuc t h a i tren M B la
;;A. UMB = 1 0 0 N / 3 c o s ( 1 0 0 7 i t - 5 T t / 1 2 ) V.

'
"^'^-^-VK^

^B.uMB = 100>/2cos(100Txt-Tt/2) V.

,

;'C. UMB = 5 0 V 3 c o s ( 1 0 0 T t t - 5 7 T / 1 2 ) V .

' D . uMB = 100V6cos(100Ttt-Tt/3) V .

•}!?.'•
'•

#

:

>;-v:

; ,
103


Huang dan

V i du 2: Cho doan mach xoay chieu A B gom dien tro R va m o t cuon day mac
noi tiep. Dien ap dat vac hai dau doan mach c6 tan so' f va c6 gia t r i hieu

N

M

d u n g U k h o n g d o i . D i e n ap giiia hai dau doan mach lech pha \i

/5J1/6

la 7T/4. De he so cong suat toan mcich bc^ng 1 thi n g u o i ta phai mac n o i tiep
v a i mach m o t tu d i e n va k h i d o cong suat tieu thu tren mach la 200 W . H o i
khi chua mac t h e m tu t h i cong suat tieu thu tren mach bang bao nhieu?
A . lOOW.

SOVJV

B. 1 5 0 W .

C. 7 5 W .

D . 170,7 W .

Huong dan
' li

.

'j

< U u i (I

Si)

ill

u

fi

m

M

Iff

^ *

art'

rj

, i , i >,'!i

2

v

T u cong thuc: P = — cos 9 = I',,^^^,

i

R

B

P = 200cos^ ^ .... lOO(W)

i *

M N = 300cos60" =150
A M N B vuong tai N •

Chon A.

MN

lOOitt

2ii;

NB

Tt

+ 3
3

p
i;
= V3 =i> a = —
3
;v)=>ChonD.,

"hat" phai dii ng' gidn dS vie ta dc tinh cos- (p.

U K . , , SCJT?!

,
,
hdn UK,,, /d —
3

V i du 3: ( D H - 2 0 n ) M o t doan mach A B g o m hai doan mach A M va M B mac
noi tifep. Doan mach A M g o m dien tro thuan R i mac no'i tiep v o i tu dien c6
dien d u n g C, d o a n mach M B g o m dien tro thuan R2 mac noi tiep v o i cuon
cam t h u a n c6 d o t u cam L . Dat dien ap xoay chieu c6 tan so'va gia trj hieu
d u n g k h o n g d o i vao hai dau doan mach A B . K h i do doan mach A B tieu t h u

BAi TOAN LIEN QUAN DEN THAY DOI CAU TRUC MACH, HQP KIN,
GIATRI TUTCTHCri
/•i/>r|, f.rlrf 'Wt

^humtg phdp gidi

. K h i R va u = Uocos(a)t + cp) giir nguyen, cac phan tit khac thay doi.

MA

o

cong sua't bang 120 W va c6 he so'cong suat bang 1. N e u no'i tat hai dau tu
dien t h i d i e n ap g i i i a hai dau doan mach A M va M B c6 c i m g gia trj hieu
d u n g n h u n g lech pha nhau n/3, cong suat tieu thu tren doan mach A B trong
t r u o n g h o p nay bang

A. 7 5 W .

B. 160W.

C u o n g d o hieu d u n g t i n h bang cong thuc: I = — = —.— = — cos p i
K h i hen quan den cong suat tieu t h u toan mach, t u cong thuc P = l^R, thay
U

U R

Mack

CR2L cong hi/dng; P =

MachR^R^L-.V

d i n h t h i c u a n g d o hieu d u n g , cong suat va he so cong suat ciia mach Ian

=

~. -V ^, , , U
I 7 coso,
I , 0,8
, ,
T u cong thuc: I = —cos^p =>-^2-=
12. ^ _ 1 ^ _ i _ ^ = 4 ( A )
R
I i costpi
3 0,6
Tir cong thuc: P = — cos' ip =
04

cos ipi

Mir
Ri + R ,

\ , : l v ' .»

-cos' 9 = Pcos' 9 = 120cos' 9

L

Noi tat c

Huang dan

11
90

0,8)
0,6

P2 = 160(W)

D. 180 W .

M

la 0,8. T i n h c u o n g do hieu d u n g va cong suat m a c h tieu t h u .

^2

R, + R.

C

l u o t la 3 A , 90 W va 0,6. K h i thay L C bang L ' C t h i he so cong suat ciia mach

COS1P2

C.90W.

Huattg dan

U

I = - = - . - = - C 0 S 9 , ta nhan dugc: P = — c o s ^ = P^^,,^huing cos' 9
R
H du 1: D o a n mach k h o n g p h a n nhanh RLC dat d u o i d i e n ap xoay chieu on

U

2

cos 9

' Kinh n;^liiciii: Mat xich ci'tn dipi;^ toan nm/ lii cos-cp, vi vqy, ngiedi ta nay ra 1/ tinrn'^

M B = V M N ' + N B ^ = lOoVs ( V )
tana =

cos

hu.ing

A.

L

A—C

Rl

M

JR2

Diang p h u o n g phap vec to truot, tam giac can A M B t i n h duoc cp = 30° nen:
P' = 120cos'30" = 9 0 ( W ) = > C h o n C .

,

,

105


Cty

d u 4: C h o doan mach xoay chieu A B g o m d i e n t r o R va m o t cuon day mac
noi tie'p. Dien ap dat vao hai dau doan mach c6 tan so'50 H z va c6 gia t r i

hieu d u n g U k h o n g d o i . D i e n ap g i i i a hai dau ciia R va giCra hai dau cua
cuon day c6 c u n g gia t r i hieu d u n g n h u n g lech pha nhau goc n/3. De h§ so

mach tu dien (noi tat hai ban cue cua no) t l i i cong suat tieu t h u tren toan
iTiach bang
^.P/2.

-;;
B.0,2P.

j

IVlach RLC: U,

U,- - 2 U ,

B. 7 5 W .

C86,6W.
Huong

dan

M a c h R L : P' = r R = - —

D u n g p h u o n g phap vec to t r u g t , tarn giac can

B

A M B t i n h d u o c cp = 30".

P = PCH COS

9

L«c cfau; 9 = 30"

'

UL

, J

Sau CO conghadng : Pc, = lOO(W)

60"

P = Pen cos^ ^ = lOOcos^^o" = 75(W) => Chon B.

Chu y:

Ur ^

UR

•I

/ i d u 5: ( D H - 2012) D a t d i e n ap u = 150>/2 coslOOTtt (V) vao hai d a u doan

U

zf

R.5

phan tu mo In noi tat thi phan tie do xcm nhie khong khong c6 trong

mach.
V i d y 7: M o t mach d i $ n g o m cac phan t u dien t r o thuan R, cuon thuan cam L
va tu dien C mac noi tie'p. Dat vao mach dien m o t d i e n ap xoay chieu on
d j n h . D i e n ap hieu d u n g tren m o i phan t u deu bang nhau va bang 200 V.
Neu lam ngan mach tu dien (noi tat hai ban cue ciia no) t h i d i ^ n ap hieu
d u n g tren dien tro t h u a n R se bang

tu d i e n . C o n g sua't tieu t h u d i e n cua doan mach bang 250 W . N o i hai ban tu

A.IOOV2 V.

B. 200 V.

d i e n bang m o t day d a n c6 dien t r a k h o n g d a n g ke. K h i d o , d i e n ap h i ^ u

C. 2 O O V 2 V .
Huong

d u n g giij-a hai d a u dien t r o bang dien ap hieu d u n g giCra hai d a u c u g n day

A.

60 N/3 Q .

B. 30 N/3

a.

Huaiig

c. isVsn.

Mach RLC:
D.45N/3n.

L i i c d a u cong suat mach tieu t h u : P =

(R + r) =

U^CR + r)-

(R + r ) V ( Z L - Z c f

(1).

Sau d o t u n o i tat, ve gian d o vec to t r u g t va tir gian d o ta n h a n t h a y A A M B
can tai M : Z ^ B = R = 6 0 ( Q )

B

r = ZMBCOs60'' = 3 0 ( n )

250 = 90^+(30N/3-ZC)

A.

R = Z,=Ze
U = ^ U f ^ + ( U , - U e ) ^ = 200(V)
= 100N/2 ( V ) => Chon A.

noi tie'p. Doan mach A M co dien tro thuan 40 Q mac no'i tie'p v o i t u dien,
doan mach M B chi co cuon day c6 dien tro thuan 20 Q, c6 cam k h a n g Zi..
Dong d i ^ n qua mach va dien ap giua hai dau d o a n m a c h A B l u o n lech pha
nhau 60" ngay ca k h i doan mach M B bj noi tat. T i n h Z L .

B.80V3C}.
Huang

UT

Thay r va Z L vao (1):
150^.90

= 200V

V i d u 8: M o t doan mach xoay chieu A B g o m hai doan mach A M va M B mac

A.60V3Q.

Z L = Z M B sineo" =30N/3(n)

= U, =

D . lOOV.

dan

Mach RL: u ' = \JI + Uf =^ 200' = 2\j\

dan

•I

Zc = 3 0 7 3 ( 0 ) =i. Chon B.
V i d y 6: M p t m a c h d i ? n g o m cac p h a n t u d i ^ n t r a t h u a n R, c u p n t h u a n cam L

Truoc k h i noi tat: tan 9 =
Sau k h i noi tSt: tan 9 =

C. 100 N/3 Q.

h i e u d y n g tren R. C o n g suat tieu t h u t r o n g t o a n mach la P. N e u l a m ngSn

-

D.60Q.

dan

Z,

-Zr
— ^ = tan60"
R+ r

M

= tan (-60")

Noi tat MB

T u do giai ra: Z, = 100N/3 ( 0 ) => Chon C.
A—C

va t u d i ^ n C mac n o i tie'p. Dat vao mach d i f n m g t d i ^ n ap xnay chieu on
d j n h . D i ^ n ap h i ^ u d u n g tren L va C bang n h a u va b a n g h a i I a n d i ? n ap

^
R

-4)

P
= -=»ChonB.

mach mac noi tie'p g o m dien t r o thuan 60 Q, cuon day (c6 d i e n t r o thuan) va

va bSng 50 N/3 V. D u n g khang cua tu dien c6 gia t r i bang

dan

Z, = Z,- = 2R =^ P ^ I^R = —
" ^
R- + (z, - z , . ;

mac them tu thi cong suat tieu t h u tren mach bang bao nhieu?
A. SOW.

D . P.

C.2P.
Huong

cong suat hang 1 t h i n g u o i ta phai mac noi tie'p v o l mach m o t t u c6 d i e n
d u n g 100 |aF va k h i d o cong suat tieu thu tren mach la 100 W . H o i k h i chua

TNtinMTVDVVHKhahgl^

Do/ vai „iach RLC, khi R va u = UQ cos(u;t +
'^ongdien tnivc va sau khi noi tat C Ian Imt la

R
M

) giit nguyen, neii bieu thuc cua
,

di}\':>i''SX^:^.

107


lia trf) Men Ihilfc Vdt li L mil

trenhenh

VTV2. t^p 2-Cha

Ofj- T/Vi/it MTV n V VH Hhang

VSn Bien

yi d u 9: (CD-2009) Dat dien ap xoay chieu c6 gia t r i hieu d u n g 60 V vao hai

i2 + ^ i l
i | = I\/2 cos(uJt + i p j , )

_

M:

Vift

9l

Z c = 2Z,

=

-(V

i j = 1V2 cos(u!t: + 9 1 2 )

dau doan mach R, L, C mSc noi tie'p thi c u o n g do d o n g dien qua doan mach

la

tano-, =

i i = I(>cos(100-n:t + 7r/4) ( A ) . N e u ngat bo tu dien C (noi tSt) t h i c u o n g do

d o n g dien qua doan mach la h = Iiicos(]007rt - K/12) ( A ) . D i e n ap giua hai
1)

Dm vai mach RLC, khi R va u = U(, c o s ( u t + 9^,) ^n';? nguyen, neu bicu thwc cua
dong dien tritvc va sau khi ndi tat L Ian hrgt la
i j = I\/2 cos(u;t +

dau doan mach la
A . Li = 60 V2 cos(1007it - 71/12) (V).

B. u = 60 Jl cos(1007:t - 71/6) ( V ) .

C. u = 60 >/2cos(1007rt +71/12) (V).

D . u = 60 xy2 cos(1007it + :x/6) ( V ) .

Huong dan
9u =

Z,

-2Zr

U | , COs(ajt

9l

9i2 - ^ i l

[92=-"

Trieac vd sau mat C m d /2 = /,

tan 92 =

\-Tnidc : tan 9 , =
u - = U o C o s ( ^ t + 43^,)

R^ + ( Z , - Z c )^ = R^ + zf ^ZQ=

2Z^

R

'

Z, ^ Z r
R

,

'

R

=> 9 l = —(\> i j = I() COS

U t + 9 y + (\

1)

TrUdcvdsaumat

Cmdl^=

I2

R^ + ( Z L - Z C ) ^ = R^ + Z ^

Z C = 2ZL
+Sau : tan 92 =

>:

+7>-ui:)'c;tan9j = -z — z
_j_TV,//J^ .
,^. _ __L R C ^

^ 92 = « =^ i2 = I() cos

ujt +

9y - a

z

*i2

RL ^ (•an(-a)

+ S a u ; tan92 = - ~ = tancv => 92 = " =^ '2 =

9] = - a

LOt

= IQ COS

«1

+ S^u ~

,

9il

^i2.^^^ChonC.
I
»„•>
f
12
V i d u 10: Dat dien ap xoay chieu on d j n h vao hai dau doan mach C mac noi
tiep g o m dien t r d thuan R = 100 Q, cuon cam thuan c6 cam k h a n g Z L va tu

«2

dien CO d u n g khang Zc t h i cuong cto d o n g d i e n qua doan mach la ii =
Iiicos(1007i:t + K/4) ( A ) . Neu ngat bo cuon cam (no'i tat) t h i c u o n g do d o n g
a =

1 I!.'.

9il - 9 i 2

, ^^ (6:

dien qua doan mach la i2 = I()cos(1007rt + 3n/4) ( A ) . D u n g k h a n g cua tu bang
A. 100Q.

B.200Q.

2)
T'rw'dc ud sau mat L ma

^ I2

.,,1 rjn
T)2 +
R

M = Uocos(ojt + 9 , , )

Hf, r i ' ^ i '

( 2 L - Z ( - ) = R + Z ^ =^ Z L = 2 Z c

z —z

+Sau : tan 92 =

R

=

-Zc
R

o rhesrs -nmrl,>

z

^ = —
R = tan a => 9^ = a

= IQ cos

+Tradc:

tan V
9 1l =

,,J5;«i .if..

Z,

—

-Zc
R

R

:

':.4Ay;rvrt + u r i j o n e o ) S V s ; i

m d I j = I2 => R^ + ( Z ^ -Z^f

Trade vd sau mat

: tan

D.50Q,

Huong dan

u = Uo cos(ut + s:)u)

+Triidc

C. 150Q.

=

+ZQ

= tan(\ 9 i = rt => i 1 = IQ cos

=>Z^=

IZQ

uJt + 9,, - a

':

= tan ( - a )

92 = ""^i

'2 = ^0

wt +

+ a

-Pi 2

-z

-VSau : tan 92 = — — = tan ( - a ) =^ 92 —

^2 = ^0 '^os wt + 9 u + (-V
•Pi2

_ 9il +912
2

4

—^ = tana = 1
R

Chon A .

^1 d u 11: M o t doan mach xoay chieu g o m cuon day c6 dien t r a thuan R, do
tir cam L noi tie'p v o i m o t tu dien c6 dien d u n g C dat d u o i hieu dien the
Xoay chieu c6 gia trj hieu d y n g on djnh. C u o n g do d o n g dien qua mgch la
108

109