doko.vn 159078 bai tap mach dien 2
TRANSCRIPT
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1U
1I
O x
3U
3I
ll/2
Bi tp: Mch in 2 Bi 1:
Cho ng dy vi cc thng s sau:
0
-3
0
-9
0
6
0
1
l = 100 km
R = 6 /m
L = 1,6.10 H/km
C = 6,4.10 F/km
G = 10 S/km
f = 100 Hz
U = 1 kV
0
1I = 500 -15 A
1/ Xc nh cc h s: C, Z , V,
2/ Xc nh U v h s phn x sng gia ng dy
Gii: a/Ta c:
2 f 2. .100 200 (rad/s)
o o o
-6 -6
o o o
o o
Z R j L = 6 + j ( )
Y G j C 10 +4,0212.10 j (S)
Z .Y 0,0037 + 0,0034j (1/km)
= 0,0037 (neper/km)
= 0,0034
(rad/km)
oC
o
5
3
ZZ 1013,2 - 664,56j ( )
Y
V= 1,8428.10 (km/s)
V= 1,8428.10 (km)
f
b/ Ta c:
5 4
1 1 C 1
5 4
2 1 C 1
1A U Z .I 2,8816.10 - 9,4922.10 j
2
1A U Z .I -2,8716.10 9.4922.10 j
2
-
Mc khc: x x
x 1 2 x x
x x1 2x x x
C C
U A .e A .e U U
A AI .e .e I I
Z Z
Ti im: x = l/2 th .l / 2 .l / 2
3 l / 2 1 2 l / 2 l / 2
5 4
U U A .e A .e U U
-1,3683.10 - 6,4567.10 j (V)
-136,83 - 64,567j (kV)
.l / 2 .l / 21 23 l / 2 l / 2 l / 2
C C
A AI I .e .e I I
Z Z
479,95 144,69j (A)
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1U
1I
Ox
2U
2I
l
cZ
Bi 2:
c
-3
2
l 30 km
Z 500
=3.10 Neper/km
Z 500
GTHD ca in p du ng dy l U1 = 120V a/ Xc nh GTHD ca U2;I2 cui ng dy
b/ Xc nh hiu sut truyn ti ca ng dy.
Gii:
a/ Do: c cZ R ng dy gn nh vn hnh ch ho hp ti nn: 0 . Tc
l mi im trn ng dy ch c ST m khng c SPX Xy dng cng thc theo h trc nh hnh v:
x x x
x 1 2 x x x x 1
x x x1 2 1x x x x x
C C C
U A .e A .e U U U U A .e
(1)A A AI .e .e I I I I .e
Z Z Z
Ta c
.0
1 (x 0) (x 0) 1 1
1 1
U U U A .e A
U A
U1
1
j.
1 1 U 1 1U U U .e A (2)
Th (2) vo (1) ta c:
-
U1
U1
U1
U1
U1
U1
j. ( j )x
x 1
j.
( j )x1x
C
j( x)x
x 1
j( x)x1x
C
j( l)l
2 (x l) 1
j( l)l12 (x l)
C
l (30.
2 1
U U .e .e
U .eI .e
Z
U U .e e
UI .e e
Z
U U U .e e
UI I .e e
Z
U U .e 120.e
3
3
3.10 )
l (30.3.10 )12
C
109.6717 (V)
U 120I .e .e 0.2193 (A)
Z 500
b/ Hiu sut truyn ti : Ta c
2
1
P.100%
P
Vi: 2 2
1 1
2 2 2 U I
1 1 1 U I
P U .I .cos( )
P U .I .cos( )
Ch ho hp ti nn:
1 1
2 2
1 1 1 1
2 2 2 2
1 1c c
1 1
2 2c c
2 2
1 1
2 2
U I
U I
U U ; I I
U U ; I I
U UZ R
I I
U UZ R
I I
U ;I cu`ng pha
U ;I cu`ng pha
cos( ) 1
cos( ) 1
-
l1 1 2 1
.0 l1 1 11 (x 0) 2
C C C
l l11
C2 2
11 11
C
2 l
U A 120 U U .e
; A U UI I .e I .e
Z Z Z
UU .e . .e
ZU .I.100% 100%
UU .IU .
Z
e .100%
85%
-
1U
1I
Ox
2U
2I
l
2Z
Bi 3:
Cho ng dy khng tiu tn c:
3
2(t )
l 100 km
3,4.10 rad / km
U 110 2 sin( t) kV
Xc ng U2(t) u ng dy trong cc trng hp c: a/ Z2 = Zc
b/ Z2 = 0,5Zc
Gii:
Ta c:
x 2 2 c
2x 2
c
U U cos x jI Z sin x
UI I cos x j sin x
Z
M 2
2
2
UI
Z nn:
cx 2 2 (x) (x)
2
2
2 cx
2
c c(x)
2 2
ZU U cos x j sin x U .M
Z
ZM cos x sin x
Z
Z Zsin xarctan arctan tan x
Z cos x Z
a/ c
2 C
2
ZZ = Z 1
Z
2 2
x
(x)
M cos x sin x 1
sin xarctan arctan tan x
cos x
1 (x l)
1 (x l)
1 2 1 1
1(t )
M M 1
arctan tan l 0,34 (rad)
U U .M 110.1 0,34 110 0,34
U 110 2 sin( t 0,34) (kV)
-
b/
c2 C
2
ZZ = 0,5.Z 2
Z
22 2 2
x
(x)
M cos x 2sin x cos x 4sin x
sin xarctan 2. arctan 2.tan x
cos x
2 2
1 (x l)
1 (x l)
1 2 1 1
1(t )
M M cos l 4sin l 1,915
arctan tan l 0,616 (rad)
U U .M 110.1,915 0.6157 210,62 0,616
U 210,62 2 sin( t 0,616 ) (kV)
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L
1I
Ox
2U
2I
l
1U1V
Z
Bi 4:
Mt ng dy khng tiu tn. C chiu di l, ZC = RC, dng in c tn s f, ti cui ng dy l cun cm L. Xc nh L h ng dy v ti tr thnh mch cng hng p Gii:
1
( x )
1V
1
x 2 2 c
2x 2
c
2 L 2
x 2 L c
Lx 2
c
L cV
L
c
U Z
I
U U cos x jI Z sin x
UI I cos x j sin x
Z
U j.X .I
U j.I X cos x Z sin x
XI I cos x sin x
Z
X cos x Z sin xZ j
Xcos x sin x
Z
1
1
L c
L
c
L cV
L
c
V
L c
L c
c
X Z tan xj
X1 tan x
Z
X Z tan lZ j
X1 tan l
Z
Z 0
X Z tan l 0
X Z tan l
ZL tan l
2. .f
-
1I
Ox
2hU
2I
l
1U1V
Z
Bi 5:
( x )
1
1
x 2 2 c
2x 2
c
2 2h
2
x 2h
2hx
c
2hV c
2h
c
V c
V
U U cos x jI Z sin x
UI I cos x j sin x
Z
U U
I 0
U U cos x
UI j sin x
Z
U cos xZ j.Z .cotan x
Uj sin x
Z
Z j.Z .cotan l
Z 0 cotan l 0
l k 2
6
k=1,3,5,....,2n+1,....
2 f 2 f (dd tren ko: V=c)
V c
2 fl ck f k 2,5.10 k (Hz)
c 2 4.l
2,5.k (MHz)
k 1 3 5 9 11
f(MHz) 2.5 7.5 12.5 17.5 22.5
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Bi tp 6 : Cho mch in nh hnh v:
ng kho K khi (t) me E sin( t ) (V) t gi tr cc i m
Xc nh 2(t )i bit:
1 2
m
R 25 R 50
L 0.25H C 400 F
E 400V f 50Hz
Gii:
Ta c: 2(t) 2td(t) 2xl(t)i i i
Xc nh 2xl(t)i
Mch in sau ng m ch xc lp
L
C
X 2 f.L 78,5
1X 7,96
2 f.C
Ti thi im t = 0 thc hin qu trnh ng ct
Nn o
(t) m me E sin E 90 o
(t)e 400sin(314t 90 )
E 400j (V)
Ta c:
ab 2 1 CZ R //(R j.X ) 17 3,5j ( )
o
xl
L ab
E 400jI 5,2 167,2 (A)
j.X Z 78,5j 17 3,5j
o
ab LU E jX .I 90,5 178.8 (V)
oab2xl
2
UI 1,8 178,8 (A)
R
LX
2R
1R
CX
xlI a
E
b
1xlI
2xlI
L
2R
1R
C
K
i 1i
2i
( t )e
-
2xl(t)i 1,8sin(3,14t 178.8 ) (A)
Xc nh 2td(t)i
Xc nh s m c tnh p:
ab 2
v(p) ab 1 6
2
12,5pZ R // pL
50 0,25p
1 12,5p 1Z Z R 25
pC 50 0,25p p.400.10
75p 7500p 50000
(200 p)p
2
v(p)
2
1
2
75p 7500p 50000Z 0
(200 p)p
75p 7500p 50000 0
p 50 64,55j
p 50 64,55j
50t
2td(t)i 2.A.e .cos(64,55t+ )
Trong A v l cc h s cn xc nh.
Xc nh s kin: v trong biu thc thnh phn t do c hai h s cn xc nh nn ta cn xc nh 2 s kin l i2(0);i2(0)
Xc nh: i(o),uc(o) theo lut ng m chnh: (0) ( 0)
c(0) c( 0)
i i
u u
Xt mch trc ng m (khi kho K cha m)
L c
1
o
X X 78,5 7,96tg 2,8216
R 25
70,4
pL
2R
1R
1/ pC
a
b
L
1R
C
i
( t )e
-
mm 2 2 2 2
1 L C
E 400I 5,34(A)
R (X X ) 25 (78,5 7,96)
o
(t)i 5,34.sin(314t 160,4 ) (A)
Cm m CU I .X 5,34.7,96 42,50 (V) o
C(t)u 42,50.sin(314t 250,4 ) (V)
o
(0)
o
C(0)
i 5,34.sin( 160,4 ) 1,79 (A)
u 42,50.sin( 250,4 ) 40.03 (V)
H phng trnh m t sau ng m:
( t ) 1(t ) 2(t )
2(t ) 2 (t )
2(t ) 2 1(t ) 1(t ) 1
i i i 0
diL i .R e
dt
1i .R i .dt i .R 0
C
(I)
Thay t = 0 vo h (I) ta c
(0) 1(0) 2(0)
'
(0) 2(0) 2 (0)
2(0) 2 C(0) 1(0) 1
i i i 0
L.i i .R e
i .R u i .R 0
1(0) 2(0)
'
(0) 2(0)
2(0) 1(0)
1,79 i i 0
0,25.i 50.i 400
50.i 40,03 25.i 0
1(0) 2(0)
1(0) 2(0)
'
(0) 2(0)
i i 1,79
25.i 50.i 40,03
0,25.i 50.i 400
1(0)
2(0)
'
(0)
i 1,7272 (A)
i 0,0628 (A)
i 1578,44 (A /s)
o hm cc v ca cc phng trnh trong h pt(I)
L
2R
1R
C
K
i 1i
2i
( t )e
-
( t ) 1(t ) 2(t )
( t ) 2(t ) 2 (t )
2(t ) 2 1(t ) 1(t ) 1
i i i 0
Li i .R e
1i .R i i .R 0
C
(t ) 1(t ) 2(t )
(t ) 2(t ) (t )
2(t ) 1(t ) 1(t )
i i i 0
0,25.i i .50 e
i .50 2500.i i .25 0
(0) 1(0) 2(0)
(0) 2(0) (0)
2(0) 1(0) 1(0)
i i i 0
0,25.i i .50 e
i .50 2500.i i .25 0
1(0) 2(0)
2(0) 1(0)
(0) 2(0) (0)
1587,44 i i 0
i .50 2500.1,7272 i .25 0
0,25.i i .50 e
1(0) 2(0)
1(0) 2(0)
(0) 2(0) (0)
i i 1587,44
i .25 i .50 4318
0,25.i i .50 e
1(0)
2(0)
i 1000,72 (A /s)
i 586,72 (A /s)
Ta c:
2(t) 2td(t) 2xl(t)i i i
o
2xl(t)i 1,8sin(3,14t 178.8 ) (A) 50t
2td(t)i 2.A.e .cos(64,55t+ ) (A)
2(0) 2td(0) 2xl(0)i i i
0,0628 2.A.cos( ) 0,0377
A.cos( ) 0,01255 (1)
Ta c:
2(t) 2td(t) 2xl(t)i i i
o
2xl(t)i 314.1,8.cos(3,14t 178.8 ) (A/s)
50t2td(t)i 2A.e 50.cos(64,55t ) 64,55.sin(64,55t ) (A/s)
2(0) 2td(0) 2xl(0)
o
i i i
586,72 2A 50.cos 64,55.sin 314.1,8.cos( 178.8 )
21,72 129,1.Asin 100Acos (2)
T (1)(2) ta c
o
Acos 0,54
129,1.Asin 100Acos 21,72
Acos 0,01255 tg 14,18
Asin 0,178 Asin 0,178
85,97
A 0,178
Vy: o
2xl(t)i 1,8sin(3,14t 178.8 ) (A)
-
[email protected] 50t o
2td(t)i 0,35e .cos(64,55t+85,97 ) (A)
o 50t o
2(t)i 1,8sin(3,14t 178.8 ) 0,35e .cos(64,55t+85,97 ) (A)
-
Bi tp 7: Cho mch in nh hnh v:
Xc nh ( t )i bit cc ngun trong mch l ngun hng v cc thng s sau:
1 2 3
3 4
1 2
R 300 R R 600
C 300 F C 200 F
E 36 V E 6 V
Gii: A. Phng php tch phn kinh in:
Ta c: (t) td(t) xl(t)i i i
Xc nh xl(t )i
Mch in sau ng m ch xc lp
V ngun E1 l ngun hng nn Ic = 0 Ti thi im trc ng ct
1xl(t) xl
1 3
E 36i I 0.04(A)
R R 900
Xc nh td(t )i
Xc nh s m c tnh p: Mch in sau ng m c i s ha theo p
1E 2E
1R
3R
2R
3C
4C
K
12i(t)
3U 4U
1E
1R
3R 3C
xlI
4C
xlI
cI 0
-
v(p) 1 33 4
3 4
3 4
4
1 1Z R // R
pC pC
1 1200 200
1 1 p(C C )
pC pC
1200
5.10 p
v(p) 4
4
1Z 200 0
5.10 p
1200
5.10 p
p 10
Dng ca thnh phn t do l: 10t
td(t)i A.e
Trong A h s cn xc nh. Xc nh s kin: v trong biu thc thnh phn t do c mt h s cn xc nh nn ta cn xc nh 1 s kin l i(0) Xc nh: u3(o),u4(o) theo lut ng m khng chnh: Xt mch trc ng m (khi kho K cha m)
1E 2E
1R
3R
2R
3C
i(t)
3( 0)U 4( 0)U
4C
1R
3R
3
1
pC4
1
pC
H mch
-
13(t) 3
1 3
3( 0)
Eu U 0.04 600 24V
R R
u 24
4(t) 4 2
4( 0)
u u E 6V
u 6(V)
Theo lut ng m khng chnh:
3 4 3(0) 3 3( 0) 4 4( 0)
3(0)
3(0) 4(0)
(C C )U C U C U
500 U 300 24 200 6
U U 12 V
H phng trnh m t sau ng m:
1 3(t)
(t )
1
1 3(0)
(0)
1
E Ui
R
E U 36 12i 0.08(A)
R 300
Xc nh A:
(0) xl(0)A i i 0.04
Vy: 10t
2(t)i 0.04 (1 e )
B/ Gii bng phng php ton t LAPLACE
Cc s kin c lp c tnh nh trn (phng php tch phn kinh in):
3(0) 4(0)U U 12 V
S ton t ha:
1E
1R
3R 3C
i(t)
3(t)U
4C
-
Chn 2(p) 0
Ta c in th nh to im 1:
3(0) 4(0)1
3 4 1(p)
1 2 1
3 4
3 4 11(p) 3 3(0) 4 4(0)
1
3 4
1(p)
1(p) 4 3
1(p)
U UE
1 1 p p ppC pC
1 1R R R
pC pC
E5 10 5 10 p C .U C .U
pR
0.125 10 5 10 p 0.006
p
0.12 0.006p 240 12p
p(5 10 p 5 10 ) p(p 10)
24 12
p p 10
(V)
Do : 10t
1(t )
10t1 1(t )
(t )
1
24 12e
E 36 24 12ei
R 300
10t
(t)i 0.04(1 e )
1E
p
1(p)I
1R
3R
3
1
pC 4
1
pC
3(0)U
p
4(0)U
p
3(p)I
C(p)I
C3(p)I
C4(p)I1
2
-
Bi tp 8:
Hy xc nh dng in i(t) khi dch chuyn K sang v tr 3. Bit khi kha K cn v tr 1 th mch ch xc lp Gii: A. Khi t < 25 ms
Tnh s kin c lp: i(0) Trc khi kha K chuyn t v tr 1 sang 2:
( 0)
1
E 6i 3 (A)
R 2
Theo LDM chnh ta c: L(0) L( 0)i i 3 (A)
S phc ha:
Ta c:
(0)
(p)
2
E 6Li 0.1 3
60 3p 40 pp pI 1.5 3
pL R p 0.1 4 p p 40 p p 40 p 40
40t 40t 40t
(t)i 1.5(1 e ) 3e 1.5(1 e )
1
2
3
E 6 (E)
L 100 mH
R 2
R 4
R 6
1R 2R 3R
1 2 3E
( t )i
L
Cho mch in vi cc thng s
sau:
E
p
pL (0)Li
2R
t = 0 chuyn K t 1 sang 2 t = 25 ms chuyn K t 2 sang 3
-
B. Khi t > 25ms
Tnh s kin c lp: i1(0) Trc khi kha K chuyn t v tr 2 sang 3:
3
3
40 25 10
1( 0) (t 2.5 10 )i i 1.5(1 e ) 2.05 (A)
S phc ha:
Ta c:
1(0)
(p)1
3
E 6Li 0.1 2.05
60 2.05p 60 pp pI 2.05
pL R p 0.1 6 p p 60 p p 60 p 60
60t 60t 60t
(t)1i (1 e ) 2.05e 1 1.05e
E
p
pL (0)Li
3R
-
Bi tp 9:
Tnh s kin c lp: uC(0)
C(0) C( 0)u u E 100 (V)
S phc ha:
Chn 2 0
Ta c:
C(0)
1(p)
1 2 1
1(p) C(0)
1 2 1
4 4
1(p)
4
1(p)
1(p) 4
uE
1 1 p ppC
1R R R
pC
1 1 EpC Cu
R R pR
1000.01 10 p 10 100
200p
0.50.01 10 p 0.01
p
0.5 0.01p 5000 100p 100 150 100
p p 100 p p 100 p 100p 10 p 0.01
100t 100t 100t
1(t) 50(1 e ) 100e 50(1 e )
E
p
1R
1
pC
2R
C(0)u
p
1
2
E
1R
C2R
K
2i
1i
Ci
-
Ta c: 100t
C(t) 1(t) 2(t) 1(t)
100tC(t) 100t
2(t)
2
u 50(1 e )
u 50(1 e )i 0.25(1 e )
R 200