'Phdn tich vd hitang ddn gidi
Theo bai ra, ta c6 gian do vecto trupt nhu hinh ve: tarn giac AMB vuong tai M, voi AM = MB nen tam giac AMB vuong can tai M vi the: M, voi AM = MB nen tam giac AMB vuong can tai M vi the:
UAB=M MAB = - : 4 71 71 7t MAB = - : 4 71 71 7t • (p = = 4 6 12 7t S •COSCPAM =cos- = — 7t 1 > C O S ( p ^ ^ B - C O S - = - A Vay chpn dap an A
Cty TNHH MTV DWH Khang Viet
D. 90 V.
cau 3: Mach di#n xoay chieu gom di^n tro thuan R mic noi Hep voi cupn
day. Dat vao hai dau mach mpt di#n ap xoay chieu u = U>/2 cos(1007tt) (V). j Di#n ap hi?u dung 6 hai dau cupn day la Ud = 60 V. Dong di^n trong mach j Di#n ap hi?u dung 6 hai dau cupn day la Ud = 60 V. Dong di^n trong mach lech pha I so voi u va l?ch pha | so voi ud. Di?n ap hi?u dung a hai dau
mach CO gia tri
A. 60 V. B. 60 72 V. C. 120 V.
^hdn tich m hiccrng dan gidi
Ta CO gian do nhu hinh ve:
Tir do de dang tinh dupe:
NB = MB.sin- = 60.— = 30S 3 2 =i> UL = soVs V =i> UL = soVs V AB = - ^ = 3 0 v 5• 7t 0,5 = 60Vi s m - 6 30 i => U^B = 60V3V Chpn dap an A
Cau 4: Cho mach dien xoay chieu RLC mac noi tiep. Dat vao hai dau doan
mach mpt dien ap xoay chieu c6 dang u = uV2.cosl007it. Khi R = Ri = 90Q
va R = R2 = 160Q thi dp l^ch pha giua hifu di^n the hai dau doan mach va cuong dp dong di^n lanluptla <(>i va <t)2. Biet |<|)i| + |<t)2| = - ; C = i ^ F . cuong dp dong di^n lanluptla <(>i va <t)2. Biet |<|)i| + |<t)2| = - ; C = i ^ F .
2 ir
Dp tu cam c6 gia trj la: C.1H
71
Theo bai ra, ta c6: ^hdn tich vd hu&ng ddn gidi
(P2 = I =^ tancpj.tancpj = 1 o ^ = ^ Z L - Z C = 7RIR2 =790.160 =120 Z L - Z C = 7RIR2 =790.160 =120 Z L - Z C = 1 2 0 ZL - Zc=-120 ^[ZL=-20(1) Chpn dap an B ZL=220 2 2
Cau 5 (Trich de t h i D a i hpc 2012):
Dat dien ap xoay chieu u = Uocosco t (Uo khong doi, w thay doi diroc) vao hai dau doan mach c6 R, L, C mac no'i tiep. Khi M = co i thi cam khang va d u n g khang cua doan mach Ian iuot la Zii va Z i c . K h i a 3 = ( 0 2 thi trong doan mach xay ra hien tupng cong huong. thuc d u n g la
^ C . (Oj = 0)2
A. (0, = B . (0, =0)2 D. 0)^ = 0)2
-ic
•'IC
<Phdn tick v>d hu&ng dan gidi
Khi (0 = o),
Khi 0) = O)T
1 = ^ T 7 ^ = " l L C
1 o),C
Z , = cOjL
1 mach cong huong => Z, = Z,-.^ o 0)2^ -
2 cojC
0)2C
= 0), > 0)j = 0)2 Vay chgn dap an B
Cau 6: Cho mach dicfn A B gom di?n tro thuan R, tu C va cuon day mac noi tiep. Xet diem M noi giOa R va C, doan NB chua cuon day. Biet hi^u d i ^ n the hai dau doan mach c6 bieu thuc u^g = 120%^cos(1007rt + — ) . Cuong dp dong
6
dien hieu dung trong mach la I = 2A, u^^g lech pha nhau n/3 so v o i u ^ ^ ^ ,
Uf^,[j lech pha nhau n/6 so voi u^g . Di|n tro thuan ciia cupn day la
A. r = 20N/3 (Q) B. r = lOx/2 (Q) C. r = loVs (Q) D. r = 20V2 ( Q )
'Phdn tich ra hu&ng dan gidi
Theo bai ra ta c6 gian do vecto trugt n h u hinh ve: A H = ABcos30 = 120. — = 60^3
2 A M = ^ i ^ . A B = 40Vi
sin 120
M H = A H - A M = 20v/3
:au 7: (Trich de t h i thu Su pham Ha N p i Ian 1 nam 2013)
Doan mach noi tiep gom mpt di^n tro thuan R = 50Q, mot tu di§n co dien dung C va mot cuon day thuan cam c6 do t u cam L thay doi duoc. Dien ap
^ xoay chieu dat vao hai dau doan mach c6 bieu thuc u = U\/2cos27rft. Khi thay doi gia tri ciia t u cam toi L, = — H c u o n g do dong di?n trong mach
n
ciing pha voi dien ap giOa hai dau doan mach. Khi thay doi gia tri ciia t u
2
cam toi L 2 = — H dien ap giua hai dau cuon cam dat gia trj cue dai. Tan so f C O gia trj la?
A. 25 Hz. B. 5 0 H z . C. 100 Hz. D. 75 Hz.
(phdn tich ra hit&ng dan gidi
Khi L | - — H thi mach xay ra hit;n tuong cong huong d i ^ n nen ta c6
Z L J = Z c =^Z^. =27rf.L, =2f
Khi L 2 = - H :r> Z L = 4f thi dien ap giua hai dau cuon cam dat gia trj cue
71 2
A • • . u - 7 Z2 +R2
dai V I the: Z , = ^ -2
Chpn dap an A.
Cau 8: Cho donn mach dien xoay chieu gom cuon day m^c noi tiep voi tu
dien. Do lech pha cua d i ^ n ap giOa hai dau cupn day so voi cuong dp dong
dien trong mach la ^ . Dien ap hieu dung giOa hai dau tu dien bc^ng -Jl Ian
dien ap hieu dung giua hai dau cupn day. Dp lech pha cua d i f n ap giCra hai
dau cupn day so voi diC^n ap giua hai dau doan mach tren la
A . O .
tan<pj
2 c . - l . 3 .
D. 271
(t'hdn tich ra hu&ng dan gidi
Z, 7t ,
= - t - = t a n - = ! = > / , = r
^Theo bai ra: Li^. = V3.>/uf <t> = Vs.^Zf + r^ = 2r' |-> tan(p = = - 1 « (p = - f ^ (p (p = 1 .
W r 4 2
Bi ifuyet on niy?n mi aai nifc aai uiem wi uu vui u, luf) J - -n
Chnyta 5
C O N G S U X T vAHt S6 C O N G S U A T
NH&NG KIEN THl/C CO BAN
1. M ? c h R L C khong phan nhanh:
+ C o n g sua't tieu t h u ciia mach d i e n xoay chieu: P = UIcoscpl hay P = PR =
„ R + so cong suat: coscp = — .
+ Y n g h i a cua he so c o n g sua't coscp
- T r u o n g h o p coscp = 1 t u c ia cp = 0: m g c h c h i c6 R, hoac m a c h R L C c6 cpng h u a n g d i e n
( Z L = Zc) t h i : P = Pmax = U I = R
- T r u o n g hc^p coscp = 0 t i i c la cp = ± ^ : M a c h c h i c6 L, hoac C, hoac c6 ca L va C m a k h o n g c6 R t h i : P = Pmin = 0.
+ D e n a n g cao coscp b a n g each t h u o n g mkc t h e m t u d i ^ n t h i c h hcj'p sao cho
cam k h a n g v a d u n g k h a n g cua mach xa'p x i bang n h a u de coscp « 1 .
+ N a n g cao he so c o n g sua't coscp de g i a m c u o n g d p d o n g d i ^ n n h a m giam hao p h i d i e n n a n g t r e n d u o n g day tai d i e n .
a. R t h a y doi de P =Pmax
+ K h i L, C, CO k h o n g d o i t h i m o i lien h$ giira Z L v a Zc k h o n g thay d o i nen s u t h a y d o i cua R k h o n g gay ra h i ? n t u g « g cpng h u a n g
+ T i m c o n g sua't tieu t h u cue dai cua d o a n mach: . p
Ta c 6 P = R I 2= R R 2 + ( Z L - Z , ) 2 D o U = C o n s t n e n d e P = Pmax t h i R dat gia t r i m i n O O A
Ap d u n g bat d l i n g thuc Cosi cho 2 so d u o n g R va (Zi-Zc)^ ta du<?c: x2
R V R Z L - Z C
Vay ( R ( Z L - Z C ) ^
R ) min la 2 Z ^ - ZQ liic d o da'u " = " cua bat d a n g thuc
xay ra nen ta c6 R= Z L - Z ^ P = Pmax = 2 Z L - Z C v a I = Ima> U Z L - Z C | N / 2 ' V2
Luc do: coscp = — ; tan cp = 1
b. Hai gia tri ciia di?n tra cho cimg mpt cong suat P ( P < Pmax):
P = I 2 R = U _ R = R^+( R^+( -R ( Z L - Z C ) ' ) » max » P R ^ - U ^ R + P ( Z L - Z c f =0n
(*) La p h u o n g t r i n h bac hai theo R v i the P^P^ax d i e u kien de (*) c6 2 n g h i e m p h a n b i e t i a : | Z L - Z ^ 2P O R, + R . = Theo d j n h l y V i e t ta c6: • ' R I R 2 - ( Z L - Z C ) '
2. Mach RLrC khong phan nhdnh:
(Cupn day khong thuan cam c6 di^n tro thuan r )
+ C o n g sua't tieu t h u cua ca dpan mach xoay chieu: P = UIcoscpl hay
+ H e so cong sua't ciia ca dc?an mach: coscp = R + r
C o n g sua't tieu t h u tren d i f n t r o R: PR = P.R= U ^ R
V o i Z = ^(R+r)^ + ( Z L - Z ^ r
+ C o n g suat tieu t h u cua c u p n day: |Pr = P .r = ^
+ so'cong suat ciia d p a n mach chua cupn day: coscpa =
a. C o n g suat tieu th\ eye dai ciia ck doan m?ch: c6 L,r,C, co k h o n g d o i .
+ R thay doi de Pmax: K h i L,C, co khong d o i t h i m o i lien he giiJa Z L va Zc k h o n g thay d o i nen su thay doi cua R khong gay ra h i | n tugng cpng huong
L,r C Ta c 6 P = (R + r ) P = ( R + r ) (R + r ) 2 + ( Z L - Z , ) 2 P = (R + r ) + ( Z L - Z C ) ( Z - Z ) , d e P = Pmax ( R + r + ^^-^= ^ ) m i n t h i : 2 R + r (R + r ) R + r = Z L - Z c H a y : R = R = | Z L - Z ^ - r
C o n g suat t i e u t h y cue d a i tren (R+r): Pmax =
2 Z L - Z C
b. C o n g suat tieu thy cxfc dai tren R:
T a c 6 : P R = RI2= (R + r ) ^ + ( Z L - Z , ) ^ U2 •R 2r + R + ( Z L - Z c ) ' + r^ R 2r + X
De cong sua't toa n h i ^ t tren d i ^ n t r o dat cue d a i PRmax ta p h a i co:
R= R _ ( Z L - Z C ) ^ ) dat gia t r i m i n R R = 7 ( Z L - Z c ) ^ + r2 L u c d o PRmax= 2r + 2 ^ r 2 + ( Z L - Z c ) ^ P V i D U M A U 71
Vl dy 1: Cho hi?u d i ^ n the hai dau doan mach la: u=l(XX/6oo6 l O O r t - -
l 2
(V) va c u o n g d p d o n g d i e n qua mach: i = 8>/5 cos ^ O O T l t - - ^ ( A ) .
C o n g suat t i e u t h u tren mach co gia t r i la: ^ , A . P = 1080(W) B . P = 1020(W) C . P = 1 0 9 5 ( W ) D . P = 1059(W)
'Phan tich vd hu&ng ddn gidi
Day CO thenoi la hai todn khd de cua dang todn cong suat. Chi can van dung cong thuc tinh cong suat tieu thu cua hai dau mach P = UIcoscp sau do tim U, I va cos(p la xong. N6i de c6 nghta la cac dai lugng nay deda cho san chi can.ttm tit hai phucmg trinh la co ngay:
I 8\/5 C u o n g d p d o n g d i ^ n h i ? u d u n g : I = = - ^ = - ^ = 4>/To(A) C u o n g d p d o n g d i ^ n h i ? u d u n g : I = = - ^ = - ^ = 4>/To(A)
Va h i f u d i ^ n the h i ? u d u n g cua mach: U = ^ = = lOOVs ( V ) D p lech pha giira h i ^ u d i e n the hai dau mach v o i c u o n g d p d o n g d i ^ n :
9 = 9 u - 9 i
n f n ( _ 1
2 [ 6 j 3
= > COSCp = C O S
. 3> ~2
V a y cong suat tieu t h u ciia doan mach la:
P = U.I.cos(p = WOSAM.^ = 1 0 9 5 ( W ) . C h p n dap an C Vi du 2: M a c h d i e n g o m R, L , C n o i tiep t r o n g d o c u p n d a y t h u a n cam 1 - 4 2 ^ 10 L = — H , t u d i ? n co d i f n d u n g C = Tt 37:
F va R b i e h thien. D a t vao hai d a u m a c h m p t d i ^ n ap xoay chieu: u = 200.cos(1007t.t) ( V ) t h i cong suat
toan m a c h la 80 W tai hai gia t r j Ri, R 2 . T i m Ri, R2.
A . R = 100 Q hoac R = 100 Q. B. R = 200 Q h o a c R = 100 Q.
C. R = 200 Q hoac R = 200 Q. D . R = 200 Q hoac R = 50 Q. Phdn tich vd hu&ng ddn gidi
Theo bai ra ta co: U = 100, Z L = - .lOOn = 200 Q , Zc = — = 300Q
71 co.C
De thay, cong suat t r e n mach dat dupe tai hai gia t r i R k h i R thay d o i , suy ra P < P max.( V i P max chi tai m p t gia t r j R k h i R thay d o i la: R= | Z L - Z C | )• N e n ta co R i , R2 la n g h i ^ m ciia p h u a n g t r i n h :
R2_P IL.R+(ZL-ZC)^ =0
(100V2)^ 80 80
Chpn dap an D
.R + (200 - 300)^ =0 « R = 200 Q hoac R = 50 Q.
Vi du 3: Cho mach dien RLC; u = 300 V2 cosl00 TT t (V). R thay doi duoc;
Khi mach c6 R = Ri = 90Q thi do lech pha giOa u va i la (pi. Khi mach c6 R = R2 = 1600 thi dp lech pha giiia u va i la 92 biet (pj + 92 = ^ • Cong suat R = R2 = 1600 thi dp lech pha giiia u va i la 92 biet (pj + 92 = ^ • Cong suat ung vai Ri va R2 c6 gia tri
A. 2 5 0 V 3 W B. 360N/3W C. 360W D.250W
^hdn tick vd huang ddn gidi
Theo bai ra ta c6: q>i + ^2 = - t3"<Pi •tari92 =
R. ^1 ^"^2 R.
Phuong trinh nay thoa man dieu kien: hai gia tri cua bieh tro cho ciing mot
cong sua't vi the'ta c6: P, = P2 => P = Pj = P2 =
Chpn dap an C
300^
R ,+ R 2 90 + 160 • - 360W
Vi du 4:
Mot mach dien xoay chieu gom: » 1
Cuon cam thuan c6 L = — (H);
7t
R i M C B
Tu dien c6 C = 2.10 -4 (F); R la mot bieh tro.
Giua hai dau AB du(?c duy tri mgt hi?u dien theu = 120 V2 cos(100Kt)(V).
Dieu chinh R de cong sua't tieu thu cua doan mach cue dai. Tim R va cong sua't do. cong sua't do.
A. R = 160Q;Pm.ix = 48W B. R = 150Q ; Pnux= 48W
C. R = 160Q ; Pmnx = 53W D. R = 150Q ; Pm..x = 53W
^hdn tick vd huang Mn gidi
Cam khang cua cupn day: = coL = —.IOOK = 200f2
338
Cong sua't tieu thu tren toan mach
P = R.-R ^ + ( Z L - Z e ) '
R
Ap dung bat d^ng thuc Co-si cho hai so duong a = R va b = ^ R R
^ , . , (Z, -Zr-f •
Ta luon co: y = R + ^ > 2 Z, - Z gia tri nho nha't ciia y la:
L ""-^C
= 2Z, - Z
o R = _(ZL-ZC)^ R R = ZL -Z(2 = 200-50 = 1500 Cong sua't tieu thu tren toan mach dat cue dai: Cong sua't tieu thu tren toan mach dat cue dai:
U 2 ymin ymin Chon dap an B
120^
2.150 = 48W