Hai t~p Ly thuy~t m~ch chlwng 1

1.1 (trang 59)

Hinh 1-29a milch dan lien, nghia la s61ien thong m = I

a)

S6 bi~n ap (nMnh) d(Jc l~p = s6 dinh - s6 lien thong = 2 - 1 = 1

S6 biSn dong (nhanh) d(Jc l~p = s6 nhanh - s6 dinh + s6 lien thOng

s6 phuang trinh d(Jc l~p K2

I s6 phuang trinh dQc l~p K I :\

I b) ) c)

i l + i2 - i J = 0 t Ui = Ll2

Ll2 = UJ

=3-2+1=2

= sf> nhanh - sf> dinh + s6 lien thof.lg =3-2+1=2

= s6 dinh - sf> lien thong. =2-1=1

, "

. ' .. if)'

,

, '.~

Hinh 1-29b milch dun lien, nghia la s6 lien thong m = I

I!

S6 biSn ap(nhanh) dgcl?:p=sb dinh - s5 hen thong = 3 - 1 = 2

s6 bi~n dong (nhanh) d(Jc \~p = sf> nhanh - s6 dinh + sb lien thong

s6 phuang trlnh d(Jc I~p K2

I

i \

s6 phLlUng trlnh d9C l~p K I

=5-3+1=3

= s6 nhanh - s6 dinh + s6 lien thong =5-3+1=3

= s5 dinh - sf., lien thong -" 1 - 2-..J-

\,,.... ! i\' \ \\

---, -

T= .. ~,d -=;

_._-'--~ -".~.

. --- --- ~._--!

Hinh }-29c ill~ch don lien, nghTa Ii s6 lien thong ill = I

a)

s6 bi~n ap (nMnh) dc l~p = s6 dinh - s6 lien thong = 5 - I = 4

S6 bi~n dong (nMnh) dc I~p K2 = s6nhanh - s6 dinh + s6 Iien thong =8-4+1=5

So phuong trinh dQcl?j)l( I . .- so i:iiiJ1i - so hen thong =5-1=4 ..

1.2 (trang 59)

H~ phuong trinh K I & K2:

j ~i' ~i, Til. =0 '2+/~-I(o=O

i, - i, - i, = 0 (1.2.1)

u, -u, - u, = 0

u!-u, +u, =0

11 1 +U?, +lI = 0h

2.

-_._-

--- -- - ---- ---

.. ~=_.- ~.. _==- .,~,== ·-_c,,'_-""-C. - ----.::-;:;-~-. "_.. ~--,--:;-

'_._~=

Thay s6 vilO ta eo:

-i, -iJ +0,9 = 0

i, + 0,49- 0.9 = 0

iJ -0,49-0,01 =0 (1.2.2)160-158-u, =0 -. 20-11,+11,=0

160 +20 +1I" = a

(1.2.2b) ~ iz == - 0,4 (A) (l.2.2e) ~ i) == 0,5 (A) (1.2.2a) ~ i I == 0,4 (A) (1.2.2d) ~ us==2 (Y) (l.2.2t) ~ U6 == - 180 (Y) (1.2.2e) ~ U4 == 22 (V)

Can b~ng cong su~t toim m~ch: •

P == u1i l + U2i2 + u3b + U4i4 + usis+ U6in == 160.0,4 + 20(-0,4) + 158.0,5 + 22.0,49 + 2.0,01 + (-180)0,9 ==

1.3 (trang 60) r

a) Dinh

Nhanh () I

-J 1 - J

2 1 -I 3 I -I

r b) ,

DinhNhanh

() I I "-1 I----_. --- ._---- - - ~ - -". --_.- .. _-- .... - .. - .. J 0 1 - I +--, ,2 ) 1 -,

I 3 -1 I 0 4 -I ] 0

I 5 I 1 I - i .J I°

,

3

c)

~---f",IJ:uinh--1 2 3 4 5 6

- 0 I

-I 0 0 I 0

-Dlnh

1 2 3-- I

L---~c-Ho - 1• 0 -1 _______ 0 _ _,_------- -_.0 I , -I 0 0 - I 1 - 1 0

I I

--' I

d)

LL

Nhanh I

1 2 3 4 I

-----l_

5 6 7 8

0 1

-J -I I 0 0 0 0

-

I

I

D1nh 1 1 ~

-1 0 0 I 0 0------1o --+-___ 0 I 0

- I J 0 -J 0 0

-

J 0 0 1----- I-- -0

. ------ o

-.:.:---Q------J- - J

I

4 0 0 0 -I -1

0 -0

-1

I ,

I I I

J ,

J.4 (trang 60) I r

a) ChQn cay la nhanh 2

----1: Nhanh l

1 2 3

J,

I

1 1

-1 0

Yang! --'

I[ 3 0 - ) 1

~ !

=1 .

L'I

4

--

-.-'- -~- -=-.::,--.. _-=

_.------=-=-- -=-"-=--C--- -- - -- ----'-- --- --b) Ch9n cay Iii nhimh :2 & 3 Yang I

Nhanh ~- --r -- --- _._'----- -- - -- , 4 5 J 1 0 0 2 -1 0 - 1 .3 0 -1 I""., 4 0 I 0 5 0 0 I, I I...

- --_._- --Yong

Nhanh -3

~--

4 6 J I 0 1 2 0 -I 1 ----------- - --- - -------_.._- 3 1 0

~-

0 io I I o ------- - -_._- - -'.__..-' .__ .. -" _...... - . . -----,,------ -

1 - I o 6 o o

d) Ch9n ciiy 18 nhanh 1, 2, 3 & _4 _ I I Yang JNhanh r::---5 ---~------

6 7! 8 ~ j ----"--1----+-----'-':-1-- --------'--0-----1 0 ..j

_ 2 -0'-------+-,.--'----'-I----j,o-----'1 ! 0 '

3 0 0 -1 -Ir---=----'--- f-- -----'-----!-------'--------+----=-----I-------1 4 -1 0 0 -I5 -+---1"-----+---=0'-------1---=0'------ 0

- ---0- - - __ =_-__ -:---=----~:----1-1-~=-=_==_-~o_=_=~_=~~_;-_==_-~l:.~~~_::.~t=~==--~---o-----~---____7 __+---__~O --+-__-'-O~ ..J I 'I- -0--------1

8 _.L-I 0___ 0 ~ 0 I I

1.5 (trang 60)

a) 1. C6 3 nhanh, :2 dinh 2. (tbng t~t cii cac dong di~n nhanh nhan v&i h~ 5& clla mQt cQi b~ng kh6ng)

i I + i2 + iJ = 0; U = A

-~:: -~

--=-.~~:e,-:~"=;c~~:~:- .~~'7~ - ~--~--=-~=-

_...~----~--

b) -- 1. C6 5-nhanh, 3 dlnh

2. -I I - b - i) - i4 == 0 i l + i2 + is = 0

1.6 (trang 60)

a) s6 m~t luai b~.ng 56 bu canh. S6 nut/dinh tinh nhu 5au :

S6 phuong trinh 09C !(ip K2 == 56 nhanh - 56 dinh + s6 lien thong, m~t khac 56 phuong trlnh o

~ - -~- ~--~- ~~

-- ----~~~._----

2. H~ phucmg trinh o

-- ---=---=--0---==_

3. H~ phuong trinh dc)c l?p v6i bi6n Iii aptren cae phAn tu thv Q9ng (Iii cac di~n ap tren ca,c di$n tra):

(1.15.6)

4. Cac rna tr?n :

I

D

•

8

Bai t~p L)' thu)'6t m::clJ cillmng .3

3.7 (trang l34)

I .

a. Pip dong 1l/1I:i1!~ , I

Chieu cac dong nhu hinh ve. Phuong trtnh KJ ella d,1u VflO ngu6n dong. Hai phuong trinh K2 eho hai iniit luai.

(+ i :.:. i,';-::"I~i'":"----l

" Z.il + Z), = Ell: ZJ, + Z,i, = E, '

, '

. ( 11 1) 'J' E, E,q -+--+-- = +-+A 2, 1:, Z, 2, Z,

, .

~'i

C!i(.lll cae clong 'long jVI eli:. 1,., l nh{inh D

, "

C'lj~U eac dong nhu hinhve. Hai phuong lrinll K1 cho diiu vao 8: d~u ra.cua ngu6n " dimg. B3 phuong lrin11 K2 eho 3 mil 111·oi.

~. I

, • .,'"

l" I

,-"

------------ ----j;----- ---------

.~ ,

", i

b, Pip t/rti /Illt ,.1 ,

G9i t\ 10. nut phb trcil hl:1l tr;'li, 'n L'\ Illit phia ti'en bcn phai.'

' (I' l' , i1) /'fq~ ,-+-+-- -(I) ---=. A Z Z' ./ ZII I -'.'! 6 5 ..Js ' ( I J' l') ,1

((1 - +--+-- - (f1 - = t1'0 7Z Z 1'" Z :I L,., ~5 '""'5

, , t, E', '" +-+-' 7 Z i'-I ·'1

J' L, I:,+ - +-7 z·/JJ .... 4

, I

, i

I " ,

,,, Gi,i. SCI ngu6n' dl'mg khl;p.l1l,lch qua nkinll 5. t::hqll dC,dong V()llg i"" in ,~\: [I') , I ,.

I ,_ 1:1;11uQ'~ In cae d()ng vong cl:la de n(lt tit ldli~ang ph:i,j,chung d~u cllllg chi~ ki111 , ,

dOTICI ho ' "" ,,', " ,o .' " .' I ' ,II , , i , "I

---'------------r- I i

,

I

D ), Hinh,)-28c.

a, Plo ddllZ.!l.bar!ft ;\;. I: ..

Chi~lI cflc dil11gnh;lnh nlm hlnh ve. Vi@t J phuong tr;;'ih KI di0:' nut; ..:L . 10 , ., I

nguon d~>l1g, d;iu ra ngllon dc)ng & nll! ngo,li cung ben tr,ii. Ba plmO'n[; trlnl' K2 eho 3 mat llreri,

-=-==.,. - . - -1--

- 1-, ",:[;==i;'" .;;.'i'

il-i, + ij.=j" if ~- i l +~=-o-

Z)I +Z), -Z)2:::;0

• • • ,I,

7f-Z[-Z"[,=0..... J"',J oC ,-4 $.5

ZJl +Z), - Z). = -Eo o '"

,

" '

., , • "I • •

.,C;hC; I) n,tH:. d5u V;1O ngu6n dong, duu'ra ngu6n d6ng & nut ngo,li ctmg ben trai,GaD I dfru A, 13 &-c'.-', ., .,,.. i '. ' . . . - _. .

;1 I

. 1 1 1 .;, 1 t· I .(_+_+_)_rn --Cip --=)rp.'·Z· . Z Z .'1'0 Z· . C Z ... , J S ... S -"I

.' (1 . 1 1) .... I, l' J' rn _.+--+-- -rp --(fJ -=". z z· 7 .' Z f'C Z·-"2 4 4-;5 ' ... s '''2

. ( Ii 1)--" 1 ".-1-- Eo rn __ + __ +_ -'rp _.,.-(n -- = --'rc Z· Z Z ' Z ('/1 Z' Z

"'0 _J I .... 2 I ';: 2 0

Gi: SU- ngu6n dongkhep n1i;1ch qua nh:inh 5. ChC)n cac cl6ng vongil' ,, j", & j,., lflr Itrq1. Iii dlc dong vong clla dc nUllr;li, ph;ii 8: (broi, chtl11~~ dfn ctmg chi6u kim d61g h6. 'I

z), ,+ Z, 0,., - j,., + j) +'Z, 0,·, - i,.,) = 0 Z)", + Z,O"2 -ho)+ Z,(1,., - i,., -j) = ()

• • I·' • .

Z,(1,., -1,.,)+Z,(1,., -1,.,)+Z01,., = -Eo[

,

,~ , , I '

I

. I ;~1 I I

I'; I, ,

!

D

11

__

«

--__..o_::~·-·

~-----.--------__~ __~07="~-o ~

--- -~ ~~~ -------

3.8 (trang 134)

•

i + i -- i ",--j1 2 }Jz), + ?J, == £,

Z,l, + !-)~) == f',lThay 56 vaa ta co:

, I

i, + i, -1, ==0 60L:90" i, + 0 + loooi, == lS5,5L: -1l,2" Y+30L90 C j,+lOOoi)==210L6,55° !~

Gi:ii h~ phtrang trillh li'Gn lim dlrQ'c:

I-==-0()~~03J' 1~08-03J' 1=0 7 , ' " , , " 'J ,~, , ,"','

, ' I "" ' ,

~~u j == 1O,A lhi Gac nghi~11l co d;lI1g (chi dd}iJm Irakhi ngll6/1 dUl/g klzili: ( ': I '

I, = -3.93 + U.37j ; i,' -5.86 - O,I'lj; ,() == 0.20 t O.20j 'I; ,

-----,-;-------- I I!- ---

,I

. ,, . 1 1 1) /' E, E,

((1 (--, +~---- + -- ==. +-- + ,-',r,'" '7 Z· Z Z.L. l ./'1 "J . "1 J1

, I

, 1 \ I 132 - )36 209 + )24 rp (-+~-,-+--)= -+---~- -~ if;, == 2,DOe ~I- 2+ I,: Ie -ISj '" 2bov

')GO /Jil i 000 /(,(1 )30

,:' . It

Ttr

" '

i =0,= 200_=0~(A) . ' Z, 1000 ~. •

'. L ')/v dOli'" vOllg

•

,

, {~~ +. Z);~n --Z)",.= =Z).~~, , Z,l,.,. ,Z, + Z,)I.., - ZJ E,

, : {CJ

I \,' ,

-- ~ ~-=.-=---~.;;--,--- ----~=,------=- -- '~

-~--,

\ j = l~' - -~;,~!-",

1"' , Z,/., + L,L, -I- //, ,.

' /.

!,', -, /c,~; '. "/ /.

l~ll. .'. .'!: /~! .oJ + Zj/l

Tir do ttnh dlIqe l":k dOIl~ Illt:lI1h: ., -; . Z Z • f' /, • ... " ." , + f = 1 '" E ----~-']._-- f, = f", - In ,= E, _" .'

, 1'1 'ZZ ZZ 7Z . Z,7., + 7.,2, ,', l,ZI"""! + -J~-'\+/"'.I.JI

, , ~ Z,1 = 1 =}. --,__.c_,__ J J' ~ -, I ,- ~ ,... ,

1.,1., -I- 7.,7., -I- Z,Z,

3.12 (tmn" 135)--· ." . Gi,ii nn~h b~mg plllf01lL!,I,h:''1) 1112 dinh. 'L1 ell phuong trinh \h~ dild1:

(J .12,1)

~ qJ, = t (V) .. n' , oDong trang cae nh21I1h:

i'!: I'ill: ,

,

If, =O(V), SllY ra dll\1g [rang cac'IlI1{;nh:N~\l neSi tfi~ hai Illit thi . "

.

"

3.1 J (trang 135)

Chung minh b5ng each tinh di~n ~p trcn hai clillt clo'.lI1 111(1cb kbi clla Jll~)l clbng di~u hOi'; ch?y qua m(lch. Chll )' di~n

---~

~ ,

3.15 (trang (35)' ;~ .

L~p phucmg lrinh dn bhll g ~ip eha 11I~~el\ :;\J'dp S:. Lhlr cAp tr\ dlW'~ 11¢ plmuqg ~inh:

(I; + jOJL,)j, - jeu:l/j, == Lf {-'}roAlj, +.(i.:, + jiuL,)j, == °

J:)~\ll bili thi0u miL dCr ki¢ll Z! ncn kJl0nC', LirJiI duoe d~\p 56 C\I lh~. Clli s0 ella ~ 1fI k0 sl:: b tri hi~u d\ln", ClL\ di~n :1IJ rO'i IrCll L,.

3.16 (trang 13(l)

Ttr con); thire tinll cong suCIL tl'ong m~1C1l khi n\)i thu~n:' . " ,

P == ru-, == 2rI-0 50 == 21'(2, j)2

suy ra di~n tro' ella eu

I-~-

3.17 (IriHtgl36l1bafrIGircrfcong slid/ h6cim4 __-- ---. ---- -- . --_._------'- ..._.-----,------- - _.~~

.. _:Giai~5ngphllQ'll!?philp dongyor)g, CI;0n 2 ,dong. ,'(llIg I & 2 l1 lwi 111;1~ So' dp & ! thu cap. G hiJi dell t1iu;UJ -chicu kim d6ng ho.-Vict phuong trlnh c:'m bang lip:

. . ' . I , .{(ll + Z, + 2~H )/1" - (l, ~ 2 M )i,., =: rj

• (3.17.1) . - (ll + Z" )/", + (2, +,; )J,,~ =: a

, ,

•

,., ..... ..'.. f(~o+.~~O.+:~.~/=.~+.j~c*-~.O~i",~~20~!5_0+ 220_ j40)i", == 1-(20+ j50+ j40)1", +(20+ j50+100)J", =0 .--'--...-.---.---...-'-'~-- ..-, ..

-" ,: {ii" == 0,7578!.- jl,1874 "., i } == O,f)

"

, ' , \,,~. _______x.

--,-~

, ,. _~__-L-

3.11\ (tnrlg 136)

a) Tnrow~ 1](YI'-cl1t~n :2 et') l:ii ' If!. ~ ,'_.(./c;"'; Ct(6'l) _ _ (c',,(Co-f'#~[ , •

CU(lll thtl" J 1~(i.T!1\lt:J1JIGn lrol1g d0 kJHj~lg ~(~ d6ng L,~p bl]l[allg trinll dn ban, ap cllo 11l;\ch cWyq\l;1n I &2, c,i hai d(lIlg 1\0u Ct\ chi~\1 th)~:ll1 kim d6ng 11.\:

.Z/. - Z,.J, =(j. t' ,

i {-Z",,),+(2,+I',)[,=0 .",' ,

(200 + jl OOO)i, - j2000i, =: 220 (I ;=0,2081- )0,1486 ( ) {

. ~

- j2000i, + (400 -1- )4000 + J6(0)i, == 0 {f, == 0,0892 + jO,a I '19 I I)

U, == 2",/, - z"" i, =: )300(0,208 [- jO.l486) - )600(0,0892 + )0,0 \49) =:

== 53,51 -I- jil,n (V)

b) Truong 11t;Tp Cll

, ~

---~-

._-~._~.. • __-L__~

. ,

:,--- -b) ]jC!I1g-Yang-~_,:,~~~e==~'~==':'~'~'''M","''~_'_' ._,.,~-,.-~~ .. -,,~ -.-----------------d , i

, "I '.. '" • IChQn dong yang 1 & 2 Jan luqt clla cac mat IlIai tnii & phai. ea hai deu thu(in chj~u kim d6ng hb.' ,.'.' ,

, ,

'AI U,.,(Z, + Z,'+2ZA/IJ)+ i",(-z) +ZMi,-ZMl3)=E, . li,.,(-Z, --Z"I3'+ZMIl)+i",(Z,+Z)-2Z,,,,) =-E, "

, I'"~

3.22 (trang 137)

, Bi~n t16i ph5n m?ch c1i~n tam giac phfa ben pl1

, ,

rr " !, .' 'I , ,II, •

J

l

(' "1' ')r=R =R/3 . J . ..:....:. ).JR

, i

Thea oau bai thihai l1Weh 3-39a & 3-39b luang duang nhnu'ncn r: = I';•.ta Ut!C!c , f'i"

" .! r I

R/3 =41'/3 -) R =,41' =·,LJ = 12 n i

\~f I'I

3.23 (trang 13 7) , ., '

I; H~phua'ng tdnh lh~ dinh ella de nut 2 & 3: , ."

ill I I,,

(-+-+-)'P, --rpJ --£=0 r r r r r

I g .r· g I " Y I)(->.L.. ,

. _--ic- _ " lit I 1 --'P,, +(- +- +-)rpJ --£:: 0

r r r r r g 2 K] 2

Vi 1fJ, =IfJJ nen til' (3.23.1 a) ta tinh duge:

-,',I' ,

I' 1fJ, =E' (3.2: .2). r+r

I ." " I'

(3.2 .3) , r

•• _.- .. -_··----- 1 •__, _, '.~._.". ' ,. ,.,__ .- f'

Til', rpl = (P (3.23.2) & (3.23.3) la e6:J , j'I

r r I .,' .... "_J=--=

,.;

~ r,lj =rJ, fh i (3~2 .4) • T+r

I J r+rI :r

,,'

, .

c

F- 7 - , sv

4.1 (trang 153)

. M?ch di~n tuy~n tinh nen ta co th~ x~p ch6ng dap Ung, Cl,1 th~ J.a chia thanh ba bai toan v&i ba ngu6n khac nhau (tren cling m9t m?ch di~n). CM y khi ngu6n m9t chi~u thi kh6ng co t1,1 va CU9n cam.

-- . Chia lam ba tnrang hqp: chi co ngu6n m9t chj~u, chi co ngu6n 00 & chi co ngu6n 300 (tinh tren cling m9t m?ch di~n).

Dong hi~u dl,1ng bkg t60g bloh phuO'ng clla cac trj hi~u d\lhg thanh ph~n.

1. Tru:img hp'P ngu6n mrf chdu

Kh6ng co li,l & c1l9n cam, dong trong m?ch:

IDe = 0,51r = 0,5/10 = 0,05 (A) (4.1.1}

2. Tru'ong hp'P ngu6n xoay chidu ttin sci goc 00

T6ng khang:

(4.1.2)

T6ng tr6': z ~ r + jX = 10+ j16,67 = 19,44L59,04'l9l . -\'(4'i.+l.rJJ'f)---

•

Dong hi~u dVng trong m?ch:

J = U" =_1_=0,051 CA) (4.1.4) o• z 19.44

3. Truimg h9P ngu6n xoay chdu tan s6 goc 30)

Thng khang:

'30 25 ] j3 250 = jll,54 (.0) (4.1.5)

25 - j21,67 ,/'30+. 3j

JA

·

z =r + jx =10 +jl 1,54 =15,27L49,09° (0) (4.1.6) Dong hi~u dl,mg trong ffi\lch:

I =V'w =~ =0 026 (A) (4.1.7)Jro Z 15,27 '

X€p ch6ng cac cap ung ta co dong hi~u dl,lng trang m?ch:

f = )(f/J(.)' + (1",)' + (I'mi = )0,05' + 0,051' +0.026' = 0,076 (A) (4.1.8)

vii dong di~n tuc thai:

i(l) = IDe + Iro J2sin( (j){ - 59,040) + f,ro J2sin(3col - 49,09") (4.1.9)

. Cong suitt ffi\lCh cj~n:

P = rl = 10.0,0762 = 0,058 (W) (4.1.10)

4.2 (trang 153) r

M?ch di~n tuy€n tinh nenta CO th~ x€p ch5ng dap ung, C\l th~ Iii chia thanh ba bili toan vai ba ngu6n kMc nhau (tren cling ffi9t ffi\lch dien). Chia laffi hai ch€ 09: chi co ngu6n 104 & chi co ngu6n 3.104• Chuy r{mgkhLtiNl-fY timg cM 111) ngu6n. ddngchiiinse--

------oangtong-thea ham thai gia~ cua hai dong nhdnh chtr khong tinh theo tong binh phu(jng.

Tri hi~u d~ng b~ng t6ng binh phuong cua cae tr! hj~u dl,mg thanh phfuJ.

Chi s6 ctta von met:

(4.2.1)

J. chi Qr) ngu6n 10"

Dong ch?y qua L co trj hi~u d\lng:

~-- _.~----==----

I _0:.-:. _~~---. __#"~ - - --- _

'-C~-- J' c;jffj +(I1ro )' = 10:46' +0,026' = 0,46 (A) (4.2.10)

4.3 (trang 153)

M\lch di~n tuy~n tinh nen ta co th~ x~p ch6ng dap tmg, Cl,l th~ la'chia thanh ba bai toan vai ba ngubn kh:k nhau (tren cung mot m\lch di~n). Chu y r~ng khi ngu6n m!'>t chi~u thi khong c6 t1,1 va cu('m cam.

Chia lam ba tnrong hgp: chi c6 ngu6n mQl chi~u, chi c6 ngubn 314 & chi co ngu6n 924 (tinh tren cling rnQt rniilch di~n).

Trl hi~u d\mgb~ng t6ngblnh phuong clla cac trj hi~u d1,1ng thanh ph~n.

4.5 (trang 153)

M?ch di~n tuy~n tinh nen ta c6 th~ x~p chbng dap ung, cl,l th~ 11'1 chia thanh ba bi!i toan vai ba ngubn khac nhau (tren cung rnQl m?ch di¢n). Chu y khi ngubn m!'>t chi~u thi kh6ng c6 t1,1 & cUQn cam. .

Chia bai toan ra lam hai truong hqp: chi xet ngubn mQt chi~u vi! chi xet ngubn xaay chi~u. Sau d6 t6ng hqp l\li k~t qua: trj hi~u d1,1ng b~ng t5ng blnh phuong cua cac tri hi~Ll d\lng thi!nh ph~n. i r

1. Ngu6n m(jt chidu

Khong c6 dong xoay chieu trong cUQn So' dp nen kh6ng c6 di~n ap he; cam tll l11ii1cL_. __ thtr-r

(4.2.2)

Dong ch?y qua C co trj hi~u dl,lTIg:

10 /..fi = 0,070 (A)

JI02 +( I )210'10-6

'J •••Dong eh?y trong m?eh ehfnh:

i w = i l .,,, + i, ," = 0,50L - 45° + 0,070L84,29° =0,46L -38~22° (A)

2. chi a(J ngu6n 3, 104

Dong eh?y qua L co tri hi~u dl,lng:

Dong eh?y qua C co tri hi~u dl,lTIg:

= • 2/..fi =~,041 (A) 1102+( 1)2

V 3.10'10-6

i Jw = i l.)" + i, )" = 0,045L - 71,57° +0,041L73,300 = 0,026L -7,51° (A)

Chi s6 eua ampe k~ tren nhanh L:

Chi s6 eua ampe k~ tren nhanh C: •

(4.2.3)

(4.2.4)

. (A.2.S)

(4.2,6)

(4.2,7)

(4,2,8)

(4.2.9)

Chi s6 eua ampe k~ nnanh ehfnh:

---- - ._------- ~-~-----------~-

Dong nay gay nen m91 di~n ap h6 cam (len L2) co gia trj hi~u d\lng:

Uue = zMI/A(' = (314.3)0,2 = 188,13 (V)

Khi d6 dj~n lip h6 cam gay nen m91 dong di~n thu dp co tri hi~udl,mg:

I = U'I( = 188. O,IO(A) 'AI .)r,' + (wL,)' .)1000' +(314.5)'

Tdng hqp k~t qua ta tinh qugc trj hi~u dl,mg clla cae dong sa dp & thu dp:

I, =.)lib(' + liA(' =.)0,115' + 0,1 0' =0,15 (A)

f

(4.5.4)

(4.5.5)

(4.5.6)

(4.5.7)

D

J5

,,-- -- - ---'r:::-_-=::'--==~' • -_.0'1"- JL;; ci..

~ - -----···1 --_. . '". - ~""""~'"4l~

-.::=----.~:::;;;::::==... =.t--=-Baictt-Fe-m-r-e'lTg:-4 I

'6.1 (trang 2()iL , ,

Di~n Ira Clia m;ing: ,r '7' p/I2 = J0011,52=44,44 n • p- ••

Tir cor.g lhtic tfnh c6ngsu~t .' P = Vlcos

([ ,-,:-,:::.=~'==-~~~~~:-,

-'--,"- 'I ~I ./

-~_.---'-L:::~~ =;=~=I

I I'-----,-_.

.~~----,

0: ,.1)

Stl (It) t'-!Ort 1111 !lrlJll!.! d\rc1n;~ L") c;k th;jng :,:\ , ~:all' ,', , I

). '" -!.. = ---~·:_-o- ,-, U)7.L -l8,43' S \ '. .~~ ) . Z ·1,47L1~,'1} .

i = ri,,_ = ~~ I,~ l/G,~ "'10,52

c

- -- -~._-==--~------

!= V" = 181.11 =i2,32A (6.3.4)Ilr + ;mr+ 211 115 + ;10 + 4.24 + ;1.4111

2. SU d\lng djnh ly Norton

Sa df, Norton tuang duang co cac thong s6 sau:

1 1 y=-= 0.22

- ---------

-------

"'~" ~F'_"'..... _

---"-----=-""----

V?y dong ch~y qua ngu6n:

I _Eo _ 220 _ 9 00 --- - )04 (6.5.4)I/Z, II 1/22.14+/7.7411 ..

Cong su~t ngu6n phat ra:

6.6 (trang 205)

Thay ba nhanh ben traj b~ng m91 m~ng m9t cila co ngu6n. M~ng nay c6 t6ng tra vao Zv (tfnh' dugc sau khi ch?p m~ch ngu6n ap. khi d6 m~ng 1TI9t cira chi co Z, song song v6i ZJ):

z = Z,Z) = (10 + j20)(25 - j50) = 2o.s8 + j17.64Q (6.6.1 ), Z, +Z) 10+ j20+25- j50 .

Va c6 di~n ap ha m~ch:

u =Z E =(25-j50) 30 =33.53-jI4.J2V (6.62)" .1 Z, +2, . 10+ )20 + 25 - j50 .

_D~(;6ng su,it dua d~n tai Ian nhk rai phai thoa man di~lI ki~n:

Z, =Z" =20.58- i17.65Q (6.6,))

Khi d6 hieu su~t cua may philt cti~n tuang duang la 50%. D2 tinh hi~u su~t thlre eua ngu6n La tinh dong ch~y qua tai: I ,"

j = U, = 33,53-)14,12 =081-j'034A (664), , 64 ?O 8 ' ' ,Z,. + Z, 20,58 + j17, + _ .5 - II 7.64

C{lIlg su

6.7 (trang 205)

Cong suitt clia nguon philt ra se b~ng tong cong suitt clia m;;lng mQt cLra vii cong sufit tren tili:

(6.7.1 )

Vi m(lllg nay c6 nguon ffiQt chi~u nen Pu = UI, thay vao (6.7.1) ta dugc quan h~ giiia cong su~t • >!l tren tili veri dong chi!-y qua n6:

P,(I) = PlI - Po = UI- rI2 (6.7.2)( ' . ~J. i . \ .'

Quan h~ giua cong su~t nay v&i tili: /1 :=

2 U 2P(r,) = r,l = r, (--) (6.7.3)r+r,(~.: ' .

Hi~u su~t ella may philt di~n tuang duang:

1/(1) = P'(l) = Ul-r~_ = J _ rl (674)Ul Ul U

>"'1' t ! \" \ ". I. \ I

I

•

38

Bai t~p chuO'og 7

7.1 (trang 242)

•1. B(is6A

B¢ s6 A c6 dl;Ulg: ~' =A"V, + A"i,{ (7.1.1 ) I, = A"U, + A"I,

Xet truang h9')J i, = 0 (hcr m

"-"~_._--

2. B(5 s6 z B9 s6 Z co d~ng:

V, = 2" I, + 2"i, { (7.1.7)[i, = 2" i, + Zll i,

Xet truimg hgp i, = 0 (ha ffi~eh dAu raj, thea (7.1.4) thi:

(7.1.8)

D6 chinh la (7.1.7a) khi i, = 0, suy ra 12" = 500 - j20001. M?t khac cling VO; 1, = 0, VJ chinh la di~n ap tren xc:

(7.1.9)

D6 chinh Iii (7.1.7.b) khi i, = 0. suy ra

Xel truong hgp I, = 0 (h6 m~ch d~u VilO), V, chinh Iii di~n ap tren xc:

i, = _!!J.. = v, (7.1.10)Z, - )2000

-? V, = )20001, (7.1.l1) ,., D6 chinh la (7.1.7a) khi i, = 0, suy ra lZ'l =/20001. M~l khac cling vo; i, = 0, ta 'tfnh dl1qc:

rj. =-(Z, + 2r)i, =-(-)2000 + 2.500)i, =(-1000 + )2000)1, (71.l2)

._-" D6" ehinh la (7.1.7b) khi i, = O. SlIY ra 12;, - - 1000; /20001

3. B~ s,) Y

oC6 the tinh b&ng cach liy nghjch dao b9 s6 Z 7.3 (trang 242)

Can Cl! vilO cac gia tri clla 3 trong 4 ph~n tl! ciJa b9 s6 A, la e6 th& noi r~ng ffil;lng ffi9t elia nay

• ., • ,f ,

g6m cae phan til: tuyen lfnh (kh6ng co tMnh phan luy thira) vii luang ho (kh6ng co ngllon phu thuoc). Y~y c6 th~

_" A _ 1+ AIlAJI 1+ j4(-jO,r)~_28 ""7 2"- (7.3.2)- All -0.5 '

Tir d6 ta I!ip dm;rc h~ phuang trinh:

V, = -0,5V, + j4i, .~.

{ (7.3.3 )i, = - jO,IV) - 2,8i)

Dong di~n ad§u ra:

(7.3.4)

Thay vilO (7.3.3)'ta dugc:

U, =-0,5.100+ j4.1 =-50+ j4 (7.3.5){1, = - jO,I.1 00 - 2,8.1 = -2,8 - jl O·

S, = (;,], = (-50 +j4)(-2,8 + jl 0) = 100 - j51 ) W (7.3 .6) TJ = P2 = 100.1 = 100% (7.3.7)P, 100

7.5 (trang 243)

B¢ s6 A c6 di;ll1g: ,t )

{ ~' =AII V2 + A,JJ (7.5.1 )I, =A21V 2 + An I2 ,.i

Xet tnrirng hgp i J = 0 (M milch dau raj, khi d6:

. . . 1· I· . V 2 =ZM 1, -+ 1, =-V2 =-.-V2 =-jO,IU2 (7.5.2) ___________ Z" 110 _

(7.5.3) chfnh hi (7.5.1 b) khi i 2 = 0, suy ra 81/ = -joJI, Miiit khac v6'i i) = 0, ta ding c6:

. . V . 2· 3+jl0. . V, =2.,1, =,2,,-' -+ V, =-'V, = V, =(1- jO,3)V, (7.5.3).' . Z Z'1O· .

[ , " )

D6 chfnh Iii (7.5.1 a) khi i 2 ';' 0, suy ra [4/J =1- iO,3j

Xet tnrirng hgp [i, = 0 (ngin m\lch dau raj, khi d6 ta I~p dugc h~ phlrang trinh thea phuang philp dong nha.nh cha m~ch sa cftp vi! thu cftp: •

3-~

-----

-------

--- ----=- --"----~-- ~- -

.--====

(7.5.4)

(7.5.4b) suy ra: . Z,. 10+ j30 . . . 1,=--1,= 1,=(3-J)1, (7.5.5)ZIO - M J

Do chfnh Iii (7.5. Ib) khi ci, = o. suy ra K::= 3- J Thay (7.55) vao (7.5.4a) la co:

. . . z· . ZZ . U, =Z,1,-Z,,1, =z, Z' 1, -Z",1, =(T-Z,,)f, (7.5.6)

~I M

=«(3+ j1O;;I O+ j30) jIO)j, =(19+ jI7)i, (7.5.7.)O

Do chinh lil (7.5.1 a) khi 0, = 0, suy ra GI2 = 19 + jJ3 7.6 (trang 243)

B¢ 56 A c6 d~ng: . . . ,- 1J~= AIIU;+A"l;---{ (7.6.1)j, = AlIO, + A,), ,

Xet tnrimg hgp i, = 0 (h& m~ch dilu raj, khi d6 (r n6i ti~p xc)//(xl. n6i ti~p 2r). t6ng tra vila ha m~ch:' i f

Z =(r- jx,)(2r+ jx,) = (10- jIO)(20+ JIO) 10+ j3,33n (7.6.2)

Ih r+ jXL +2r- JXe' 10- jI0+20+ jlO

-.-----Xet-tr-UO'ng-hqp-07=0 (ngfulm

'- '

f)~ linh be> s6 A la co lh~ ap d\lng cac cong lhuc (7-28) !rang SGK.

7.8 (lrang 243)

Hilm lruy~n d

------=--- - - --"- ---==--

Z = AIIZ, + A" = (J + )O,25)JOOO+(J500+ )250) = 1500- jlOOon (7.8.8)

" Al,Z, + A,l iO,0005 *1 000 + (1 + jO,5)

2. Tinh b6ng biin adi In"c liip Iren mr;lch ai¢n

M\lch di~n co du truc [(2r n6i ti~p Z.)llxcJ n6i ti~p r. Ta Idn lUq! tinh cac dong & ap tn~n Clla viw &~.

j\ = [;\ = [;\ [;\ = [;\ Z r + x, (2r + Z, ) .500 + - j2000(l 000 + 1000) 1500 - jl 000 (789)

x, +2r + Z, - j2000 + I000+ 1000

Xc (2r + Z,) j - j2000(l 000 + 1000) j

j, = XI + 2r + Z, \ = - j2000 + 1000 + J000 \ = (0 5 _ '05)j (7.8.10) 2r + Z, J000 + 1000 ' J, ,

.. . U . U, = Z,1, = 1000(0,5 - jO,5)1\ = (500 - )500) , = (0,38 - jO,077)U, (7.8.11 )

1500- jlOOO

. IiI (7.8.1 0) suy ra K,. tiI (7.8.11) suy ra K", tiI (7.8.9) suy ra Z,,,

Nhdn IhJy Irong truung hr,Jp nay lhi linh loan Ir!cC li6p lic mtfch Jiijn nhanh 171m la dung h6 sri A. D6 la vi mtfch c6 dtfng dun ghin.

7.9 (trang 243) I

T6ng tra vao eua ffi\lng hai eua (rIIZ\) n6i ti~p L:

rZ rZ Z,. =Z, +--'- =)wL +--'- (7.9.1 )

. r+Z r+7 r ~

[;, r-~-

(7.9.1)K = _U_, = _r....,+"",jw_L_ = __r_ "u, [;\ r+ )OJL D

, r V6i hitm truyen d\lt nity khi r du nho so v6i IO[ thi K" co d\lng -.- va d6 ehinh lit loan tif vi

.' j(u[

phan.

-------- _.~

sv Bili tfp-ctJU'01Ig-HF

10.1 llnmg291L

Trang tnremg h9]J khoa K rna, ta l!ip phuong tdnh th~ nut (th~ g6c 0 la nll! ben trai. 0' Ia nut ben phai):

(10.1.1)

Chu ydng t6ng d~n cua 3 pha b~ng nhau va t6ng ap clla 3 pha b~ng O. Dong tren tai:

E 1 = -::---,-- 220· = 5 80 - '803 A (10.1.2)

2,r+ 2, 1+ )2 +12 +j16 ' J, . Ap tren tai:

u, = z,i = (12 +j16)(5,80 - )8,03) = 198.13 -/3.57 f/ (10.1.3)

Cong suAt clla tai:

P=r,I' =12.9,9]' =\177 W (101.4)

Dong khoa K l\ii thi tinh tr\ing him vi~c cua m\ich v~n khOng 06i vi di~n th~ nut 0 v~n b~ng oi~n th~ neil 0'. ta van linh duqe dong thea eong there (I U.I.2).

10.3 (trang 298) Biin a6i mC/ch lam giac 22 thanh mC/ch sao, 3 aidm Irung tfnh citn§ tlien lhi lach rient; mol rho ra tinh lhiing .1'6. suy ra cac ph" con fr;i helng ceich cang them flO hock 2 !!I/) The! nlwnh hun. ('/1 the chuydn Z2 thimh Z21. (Z]I song song vm Z;) n6; tiir vui f: dong quo 2., h6ng diJng !juo 1." chia cho can 3.

Bi~n d6i m\ich sao 2; thanh mi;lch tam giac 2; '. M\ich tam giac miy co cac qtnh song song vai cae qmh Clla mi,lch tam giac 22. G9P h(lj mi;lch tam giac nay (thay cae c~p t

I = E, = 240 L - 240 0

= 4 66TJo-69 A U{)c3c6F-_. ..

...~=.(. Z I"':; ")16" .,,' .Z",+ _ _.. +/_ .. +/.

f)~ tinh dong i, ta se tfnh t6ng cua dong qua Z2 DbL AB( l'"/~HL dong 'l.lIal,l. n9j AC(/" /2 ). f)~ tinh hai dong nay ta tinh cae th~ nut tPA', ¢iH' & ¢i,.:

rfA' = EA - ziA = 240 - )5.(3,46 - )7,38) =' 203,09 - )17,31 V (10.3.7) 1;. = Eli - ziH = 240L -120° - )5.(-8,12 + jO,69) = -116,54- )167,23 V (10.3.8) ¢,. = E, - zi( = 240L: - 2400 - )5.(4,66 + j6,69) = -86,55 + )184,54 V (10.3.9)

Tir d6 tfnh du9'c eae dong di~n & dien ap:

i - 1;,-rp. _ 203.09-)17.31-(-11.6,54-)167,23) 2,35·-.iO.20A (10.310)

'HI' - Z, - 129,90 + )75

- ((JA - ((J, 203,09 - )17,3 1- (-86,55 + )184.54) 00 3I I, -)2,1 A (10.3.11)

A(,.22 - Z, 129,90 + )75

i2A = iAH.7.2 +iAC.l2 = 2,35 - )0,20 +1,00 - )2,13 = 3,35 - )2.33 A (10.3.12) ii, = j, - i" = 3,46 - j7,38 - (3,35 - j2,33) = 0,18 - j5.05 A (10.3.13)

.... lco, = J-:Z, = (0,]~,05)(25 + j43,30) = 221.64 - jl2 1.17 V (10.3.14) .~

10.4 (trang 298) ~. '. Ml,lch ba pha khong ddi xlrng Khong noi rD ~Cdrcb(,r,!!, JizJl.mdc.song song hay nrfi tiip nhlmR Ihulmg thi cac bong den dltO'C mac song song. .

Tu cong su5.l & di~n ap La tinh uU

.--._--- --~-----=-----=

Tif1liLlalilllLdLJ'l_" Ji~" up lren cae lai: ---~~-- -----

V" = fA -0" = 110-(-43.48+ )44.44) = 153.48-j44.441' (10.4.8) O. = EH -0A = 110L -120° -(-43,48+ j44,44) ~ -11,52- j139.7 V (10.49) • • 0 ' V = E, -0A = 110L -240 -(--43,48+ j44,44) = -11,52 + j50.82 V (10.4.10)

10.5 (trang 298)

f:)~ lim chi 56 ella cae d6ng h6 c6ng sufrlla 51: tim cae dong l.jua L, & L2. 1)i~n up AU:

. "0 0U iI, =U,,-U'!I =200L5310'-240=-120+j160=200L126.87 V (10.5.1)

L~p phuang trinh dong vong cho 2 mitt lucri AOB (i,.,) & BOe (i,.,), chi~u cae dong .vong Iheo chi~u kim d6ng h6:

JJwL, i,., +}

....__.._- ~-~ SV

.. -------_._

Hili t~p chU"O'ng I I

11.3 (trang 3 J4)

Tili (d9ng co) m~e lam giae nen khOng co Ihilnh phfrn zero. Ta 5e phaR Ifeh lam giae di~n ap ngu6n thanh cae thimb phfrn d6i x(mg. Dong trong t(mg pha 5e b~ng t6ng cae dong Ihuan & nguge. Truae h~1 ta phan Ifeh lhilnh cae ap thu~n & nguqc: .

UAR, = (UAR + aUfl(' + a'U('A) /3 = (424LJ 35° + ILl 20° • 300 + IL2400 • 300L - 90°) /3 (11.3.1) =- 237 +1'237 V

VAH' =(U AR + a'VHC + aVr·A)/3 =(424L135°.+ IL2400 • 300 + lLl20' • 300L - 90°) /3 (11.3.2) = -63.3 +1'63,3 V

UHe' = a'UA8' = IL240 0 (-237 + 1'237) =323 + 1'86,6 V (11.3.3) · . 0

UHr ·, =aUAR, =IL120 (-63,3+j63,3)=-23,18-1'86,52V (11.3.4) · . 0

UrA , = aUAH , = IL120 (-237 + 1'23717 -86,6- )323 V (11.3.5) · 2 . 0 . .

Uc.42 =a UAH? = lL120 (-63,3 + J63,3) =86,5 + ] 23,2 V (11.3.6)

Til do la tfnh duge cae dong pha (b~ng t6ng cae dong Ihu~n & nguqe):

j = UAR, + UAR, = -237+ j237 + -63,3+ 1'63,3 =--095+ '979A (11.3.7)AH Z, Z, 40+ 1'30 20+ )20 ,) ,

j . = URII + URn = 323 + 1'86,6 + - 23,18 - 1'86,52 347 _ '408 A (11.3.8)

H( Z, Z2 40+1'30 20+ )20 ' J, .. ~ r

j. = UCAl + UCAl = -86,6- 1'32j + 86,5 + 1'23,3 = -252 _ '571 A (11.3.9) (A Z, Z, 40+ 1'30 20+ )20 ,) ,

Ciing 5u~t eila d9ng co: ...._-._

P =PA+ PH + Pc· =Re(UARjAH) + Re(UHciH") + Re(U")"A) (1 (3.10) = Re[424L135" (-0,95 + j9,79)] + Re[300' (3,47 - j4,08)] + Re[300L - 90° • (-2,52 - j5, 71)]

= 5973 W

o 11.4 (trang 315)

Thay th~ h~ th6ng di~n ap khiing d6i x(mg (; eh6 co ~\l' e6 U~", U~" & V;" b~ng cae thanh ph~n d6i ximg, sau d6 tach ra thilnh 3 bili toan d6i x(mg,la l~p duge 3 sa d6 tht! t\l' thu~n, nghieh vil

zero. So d6 tht! t\l' thu~n nhu hinh 11.4.1. Chil Yr~ng VI'I & jI'l Iii ap (so vai d~t) & dong (ehily xu6ng d~t) t?i eh6 co S\l' e6: it & j Iii ap & dong eua ngu6n.

, ,

Hinh 11.4.1 .. Til sa dE, tren rut ra duge:

(11.4.1)

Sa d6 thu tl! nguge nhu hinh 11.4.2.

'(0) ZI A2 2m! Z2dc

rT(I) .... A 2

Hinh 11.4.2

L~p phuang trinh sa d6 tren:

• (I)

jill = VAl Al 2

1ri (11.4.2) 2,m/ +2M

4 r. S806 thu tlj' zero 'l;hoJ r~ 11-4,S, COwl..'!' rll'~g cioio; l11&e saD'l)!1iiq nBi c7at-nen tong uJifl.lng

-tVi9, vti1 ~ cl\-a:1 nFcfW'tdI:.JJc6 xvi5f>rJc/il;/- (li1 chung v~n khat J:h6ng). CQng'o ll\ng tra

"1 , .. (.1)

---.-~-¥ohl;&~'{6~ DeniA.c(e. ncr fl\.qcJdal (dtv~V'~ /4~' SCJn~ vaL uAo) _

,.. ,., ~T'~~ I . O~r

Hinh 11.4.3

L~p phuang trinh eho sa d6 tren:

• (I)

jill _ u,o AD - (1143)

20m(

--------===== - ~gOlh fa chung ta con ~o -ba phuang trlnh rna ta SI! c6. Do la ap pha B bAng ap pha C & bAng

khang, dong pha A bAng khang:

(;t[) - OBa2(;(I) + a(;111 + (;111 - 0B - AI A2 AD - (11.4.4)

(;(1) _ OBa(;(1) + a2(;[1) + (;[11 - 0 • (' - . AI 42 AO - (11.4.5)

'(l) - O~ j(11 + j(l) + J'([) - 0J A - """" Al A2 AO - (11.4.6)

Til (1104.1 -7 6) ta I~p du9'C he phuang tdnh voi 6

--

c

--"--~---=--- ---~-~

-=----=-== 11.5 (trang 315) . Phuang philp xJp ch6ng tlizp ling

- /' /! /! - ~1 ??' ? 5' 0 '- ? 83/ I - AM + ~u(" + 45,