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:

:

-

2-400202

-21

2-400202.021.022

:

:

2005


. 4

1. . 5

1.1 .. 5

1.2 6

1.3 8

1.4 .. 12

1.5 . 12

1.6 12

1.7 , . 14

2 . 15

2.1 (.2.0) 15

2.2 . 16

3. . 17

3.1 . 17

3.2 18

3.3 . 18

3.4 , . 19

4. . 20

4.1 (.4.0) 20

4.2 . 20

4.3 21

4.4 . 21

4.5 . 21

5. . 24

5.1 τ 24

5.2 () t = 3 τ 25

5.3 I=f(t); (Uc=f(t)) 25

. 27


.

/ , , . : I II , , , . : , , . , . , .

:

, ;

;

;

;

;

.


1.

:

R2 I2 R7

I5 E1,r02 I7

R1

I3 R5

R3 R4 I4 I6

I1 E2,r02

R6

.1.0

:

E1=30B. r01=3Om. R1=16Om. R3=22Om. R5=43Om R7=55Om.

E2=40B. r02=2Om R2=27Om. R4=33Om. R6=51Om.

1.1

I2-I5-I3=0; I2-I5-I3=0;

I5+I6-I7=0; I5+I6-I7=0;

I7-I1-I2-I4=0; I7-I1-I2-I4=0;

E2-E1=R3I3-(R5+r01) I5+(R6+r02) I6; 10=53I6-46I5+22I3;

E1=R2I2+(R5+r01) I5+R7I7; 0=55I7+27I2+46I5;

0=R4I4-R3I3-R2I2; 0=33I4-22I3-27I2;

0=I1R1-I4R4; 0=16I1-33I4;

, .


1.2

(.1.0) (.1.1):

IK3 IK2

IK4 R2 R5 E2,r02 R7

R1 R4

IK1

R3 R6

E1,r01

.1.1

4-. :

I-. :

E2-E1=IK1(R6+r02+r01+R5+R3) +IK2(R5+r01) - IK3R3;

II-. :

E1= IK2(R5+r01+R7+R2) +IK3R2-IK1(R5+r01);

III-. :

0=IK3(R4+R3+R2) - IK2R2-IK1R3-IK4R4;

IV-. :

0=IK4(R1+R4) - IK3R4;

:

10=121IK1-46IK2-22IK2;

30=128IK2-27IK3-46IK1;

0=82IK3-27IK2-22IK1-33IK4;

0=49IK4-33IK3;

49IK4-33IK3 => 49IK4=33IK3 => IK4=0,67347IK3;

0=59,77549IK3-27IK2-22IK1;


10=121IK1-46IK2-22IK2;

30=128IK2-27IK3-46IK1;

0=59,77549IK3-27IK2-22IK1;

IK1=(128IK2-27IK3-30) /46;

10=121((128IK2-27IK3-30) /46) - 46IK2-22IK3 =>

IK2=(93,02174IK3+88,91304) /290,69566;

IK1=(13,95962IK3+9,15046) /46;

0=59,77549IK3-8,63992IK3-8,3583-6,67634IK3-4,37631

12,63461=44,45923IK3 =>

IK3=0,28418 A;

IK4=0, 19139 A;

IK2=0,39680 A;

IK1=0,28516 A;

, , :

I1=IK4=0, 19139 A.

I2=IK2-IK3=0,11262 A.

I3=IK1-IK3=0,00098 A.

I4=IK3-IK4=0,09279 A.

I5=IK2-IK1=0,11164 A.

I6=IK1=0,28516 A.

I7=IK2= 0,39680 A.


1.3

a) 2:

(.1.0) (.1.2), (.1.3) (.1.4) 2, r02:

R2 R7 I/7

I/2 I/5 E1,r01

R5

R1 I/1

R4

R3 I/3 I/4 I/6

R6 r02

.1.2

R2 R7

R5

R14

R3 R602

E1, r01

.1.3

R14=(R1R4)/(R1+R4)=(16*33)/(16+33)=10,77551 Om;

R602=R6+r02=51+2=53 Om;

R214 R7

R5 R23

R314 R602

E1,r01

.1.4


R214=(R2R14) /(R2+R3+R14) =(27*10.7755) /(27+10.7755+22) =4,86719 Om;

R23=(R2R3) /(R2+R3+R14) =(27*22) /(27+22+10.7755) =9,93718 Om;

R314=(R3R14) /(R3+R14+R2) =(22*10.7755) /(22+10.7755+27) =3,96586 Om;

R2147=R214+R7= 4.8672+55=59,86719 Om;

R314602=R314+R602= 3.9659+53=56,96586 Om;

R. =R5+R23+(R2147R314602) /(R2147+R314602) +r1= =43+9.9372+(59.8672*56.9659) /(59.8672+56.9659) +3=85,12743 Om;

I/=E1/R. = 30/85.1275=0,35241 A.

I/5=I/=0,35241 A.

I/7=I/(R314+R602) /(R214+R7+R314+R602) = =0.35241*(3.96586+53) /(4.86719+55+3.96586+53) =0,17182 A.;

I/602=I/6=I/(R214+R7) /(R214+R7+R314+R602) = =0.35241*(9.93718+55) /(9.93718+55+3.96586+53) =0,18058 A.;

II (I/14):

I/14R14-I/602R602+I/7R7=0;

I/14=(I/602R602-I/7R7) /R14= (0.18058*53-0.17182*55) /10.77551=0,0111 A.;

U14=I/14R14= 0.0111*10.77551=0,11961 B.;

I/1=U14/R1= 0,11961/16=0,00748 A.;

I/4=U14/R4= 0.11961/33=0,00362 A.;

I/2=I/7-I/14= 0,17182-0,0111=0,16072 A.;

I/3=I/1+I/4+I/6= 0,00748+0,00362+0,18058=0, 19168 A.;

b) 1:

(.1.0) (.1.5), (.1.6) (.1.7) 1, r01:


R2

I//5 R7 I//7

R5 r01

R1 I//1

R3 I//3 I//4 I//6

R4

R6 E2,r02

.1.5

R14 R2 R7

R501

R3

R6 E2,r02

 

.1.6

R14=(R1R4)/(R1+R4)=(16*33)/(16+33)=10,7755 Om;

R501=R5+r01=43+3=46 Om;

R14 R27

R3 R2501

R6 R751

E2,r02

.1.7

R27=(R2R7)/(R2+R7+R501)=(27*55)/(27+55+46)=11,60156 Om;

R2501=(R2R501)/(R2+R7+R501)=(27*46)/(27+55+46)=9,70313 Om;

R7501=(R7R501)/(R2+R7+R501)=(55*46)/(27+55+46)=19,76563 Om;

R1427=R14+R27=10,7755+11,60156=22,37707 Om;

R32501=R3+R2501=22+9,70313=31,70313 Om;

R=R6+R7501+(R1427R32501)/(R1427+R32501)+r02=51+19,76563+(22,37707*31,70313)/

/(22,37707+31,70313)+2=85,8836 Om;

I//=E2/R=40/85,8836=0,46575 A.;

I//6=I//=0,46575 A.;

I//14=I//((R3+R2501)/(R14+R27+R3+R2501))=0,46575*((22+9,70313)/ /(10,7755+11,60156+22+9,70313))= 0,27303 A.;

I//3=I//*((R14+R27)/(R14+R27+R3+R2501))=0,46575*((10,7755+11,60156)/ /(10,7755+11,60156+22+9,70313))=0.19272 A.;

U14=I//14*R14=0,27303*10,77551=2,94204 B.;

I//1=U14/R1=2,94204/16=0,18388 A.;

I//4=U14/R4=2,94204/33=0,08915 A.;

II (I // 5):

E2=I // 6(R6+r02) +I // 5(R5+r01) +I // 3R3;

I // 5=(E2-I // 6(R6+r02) - I // 3R3) /(R5+r01) =(40-0,46575*(51+2) - 0, 19272*22) /(43*3) =

=0,24077 A.;

I (I // 7 I // 2):

I // 7=I // 6-I // 5=0,46575-0,24077=0,22498 A.;

I // 2=I // 7-I // 1-I // 4=0,22498-0,18388-0,08915=-0,04805 A.;

, , , :

I1=I/1+I // 1=0,00748 +0,18388 =0,2151 A.;

I2=I/2-I // 2=0,16072-0,04805=0,11267 A.;

I3=I/3-I // 3=0, 19168-0, 19272=-0,00104 A.;

I4=I/4+I // 4=0,00362+0,08915=0,09277 A.;

I5=I/5-I // 5=0,3524-0,24077=0,11163 A.;

I6=I // 6-I/6=0,46575-0,1877=0,27805 A.;

I7=I/7+I // 7=0,1718+0,22498=0,39678 A.;

1.4

E1I5+E2I6=I21R1+I22R2+I23R3+I24R4+I25(R5+r01) +I26(R6+r02) +I27R7;

3,88263+10,6064=1,124957+0, 20347+0,03994+0,059915+0,77049+3,726420+8,563179;

14,48903 ≈14,48837 ;

1.5

I
I1 0, 19139 0, 19136 0,003%
I2 0,11262 0,11267 -0,005%
I3 0,00098 0,00104 -0,006%
I4 0,09279 0,09277 0,002%
I5 0,11164 0,11164 0%
I6 0,28516 0,28517 -0,001%
I7 0,39680 0,3968 0%

1.6

R2 (.1.8):

I1 I4 IK2 R7 I7

I5

E1,r01

R1 R4

I3

IK3 IK1

R3 I6

R6 E2,rO2

.1.8

:

I : E2-E1=IK1(R6+r02+r01+R5+R3)-IK2(R5+r01)-IK3R3;

II : E1=IK2(R7+R5+r01)-IK1(R5+r01);

III : 0=Ik3(R4+R3)-IK3R3;

10=121IK1-46IK2-22IK3;

=101IK2-46IK1;

0=55IK3-22IK1; => IK1=55IK3/22;

10=280,5IK3-46IK2; => IK2=(280,5IK3-10)/46;

30=615,88043IK3-21,95652-115IK3; =>

IK3=0,10391 A.;

IK2=0,41623 A.;

IK1=0,25978 A.;

:

I5=Ik2-I1=0,156455 A.;

I7=IK2=0,41623 A.;

I3=IK1-IK3=0,155865 A.;

I4=IK3=0,10391 A.;

:

R143=(R1R3R4) /(R1+R3+R4) =11616/71=163,60563 Om.;

R143602=R143+R6+r02=216,60563 Om.;

R143602501=(R143602(R5+r01))

/(R143602+R5+r01) =9963,85898/262,60563=37,94229 Om.;

R. =R7+R1-6=92,94229 Om.;

III (.1.9):

a φa=φb+I3R3+I4R4;

I4 b φa-φb=I3R3+I4R4;

R4 Uab= φa-φb=3,42903+3,42903=6,85806 B.;

I3 R3

I2=Uab/R2+R=6,85806/119,94229=0,05718 A.;

.1.9

1.7 ,

ABCDEFG (.1.10). .

I=(E2-E1) /(R5+R3+R6+r01+r02) =10/121=0,08264 A.;

E R5 D r01 C E1 B

 


R3 I

F R6 G r02 A E2


.1.10

φA=0;

φB=φA+E2=40 B.;

φC=φB-E1=40-30=10 B.;

φD=φC-Ir01=9,75 B.;

φE=φD-IR5=6,2 B.;

φF=φE-IR3=4,4 B.;

φG=φE-IR6=0,2 B.;

φA=φG-Ir02=0 B.;

:


2

2.1 (.2.0)

R4

+

U H1 2

R3

-

.2.0

:

U=200 B.; R3=27 Om.; R4=30 Om.; (.2.1);

I, A

7

6

5

1

4

2

3

2

1

0

40 80 120 160 200 240 280 U, B

. 2.1


2.2 .

I=U/R (.2.2).

I3=U/R3=200/27=7,4 A.;

I4=U/R4=200/30=6,7 A.;

R4 2 , (H24) UH4=UH2+UR4;

24 1 , (H124) IH124=IH24+IH1;

124 R3 , (H1234) , UH1234=UH124+UR3;

H1234 .

:


3.

e R1 d C1 a

+

R2 R3

~U

c f

L2 C2

-

k L2 b

.3.0

:

U=Umsin(ωt+ψ) R1=16Om L1=33 mk

f=18 k R2=30 Om L2=5,1 mk

Um=56 B R3=42 Om C1=22 mk

ψ=-60 䠠 C2=5,0 mk

3.1

XL1=2πfL1=3,7303 Om;

XL2=2πfL2=0,5765 Om;

XC1=1/(2πfC1) =0,4021 Om;

XC2=1/(2πfC2) =1,7693 Om;

(.3.0) (.3.1):

Z1

I1 I3 I4

I2 Z3 Z4

Z2

.3.1

, :

Z1=R1-j XC1=16,0051e-j1,4 Om;

Z2=jXL1=3,7303ej90 Om;

Z3=R2+jXL2=30,0055ej1,1 Om;

Z4=R3-jXC2=42,0373 Om;

Z34=(Z3Z4) /(Z3+Z4) =17,5161-j0,0917=17,5163e-j0,3 Om;

Z=Z1+Z34+Z2=33,6720ej5,5 Om;

a :

Ů=Um/=40e-j60 B;

3.2

İ=Ů/Z=1,1879e-j65,5 A;

İ1=İ2=İ=1,1879e-j65,5 A;

Ů34=İZ34=20,8076e-j65,8 A;

İ3=Ů34/Z3=0,6935e-j66,9 A;

İ4=Ů34/Z4=0,495e-j63,4 A;

3.3

i=Imsin(ωt+ψ) A;

i=0,01513sin(113043t-65,50) A;

3.4 :

Š=Ůİ=47,516ej5,5=47,2972+j4,5542,

S=47,516 ( );

P=47,2972 ( );

Q=4,5542 ( );

P=I21R1+I22R2+I23R3=47,297 B;

Q=I21(-XC1) +I22XL1+I23XL2+I24(-XC2) =4,5402 ;

U1=İ1Z1=19,0125e-j66,9 B;

U2=İ2Z2=4,4312e-j24,5 B;

U3=U4=U34=20,8076e-j65,8 B;

Š=Š1+Š2+Š3+Š4=U1I1+U2I2+U3I3+U4I4;

47,2972+j4,5547≈47,2964+j4,5577;

3.4 ,

:

MI=0,05 A/c;

MU=1,4 A/;

lI=İ/MI lU=U/MU:

lI=lI1=lI2=23,8 ;

lI3=13,9 ;

lI4=9,9 ;

lU=28,6 ;

lUed=13,6 ;

lUda=0,3 ;

lUac=14,9 ;

lUcb=0,29 ;

lUkb=3,2 ;

lUaf=14,9 ;

lUfb=0,6 ;


4.

:


4.1 (.4.0)

RA XLA

A

RB XCB

0

B

RC XLC

C

.4.0

:

RA=280 Om; XLA=314 Om; U=340 B;

RB=118 Om; XCB=280 Om;

RC=147 Om; XLC=560 Om;

4.2

ZA= R2A+X2LA =420,70893 Om;

ZB= R2B+X2CB =303,84865 Om;

ZC= R2C+X2LC =578,97237 Om;

cosφA=RA/ZA=0,66554 => φA=480

cosφB=RB/ZB=0,38835 => φB=670

cosφC=RC/ZC=0,25389 => φC=750

4.3

IA=UA/ZA=0,80816 A;

IB=UB/ZB=1,11898 A;

IC=UC/ZC=0,58725 A; c

, .

1200 , φ . , φ, , φ.

MI=0,2 A/;

, I0=0,16 A;

4.4

i=Imsin(ωt+ψ) A; i=

4.5

PA=UIAcosφA=182,87335 ;

PB=UIBcosφB=147,749 B;

PC=UICcosφC=50,69295 B;

P=PA+PB+PC=381,3153 B;

QA=UIAsinφA=204, 19717 ;

QB=UIBsinφB=350, 20901 ;

QC=UICsinφC=192,96158 ;

Q=QA+QB+QC=747,26776 ;

SA=UIA=247,7744 ;

SB=UIB=380,4532 ;

SC=UIC=199,665 ;

S= P2+Q2 = 838,93412 ;

:

UA=UA=340ej0 B;

UB=UB=340e-j120 B;

UC=UC=340e-j240 B;

:

ZAejφA=ZA=420,70893ej48 Om;

ZBejφB=ZB=303,84865ej67 Om;

ZCejφC=ZC=578,97237ej75 Om;

:

İA=UA/ZA=0,80816e-j48 A;

İB=UB/ZB=1,11898e-j187 A;

İC=UC/ZC=0,58725e-j315 A;

:

I0=İA+İB+İC=0,16219ej18 A;

:

PA=UIAcosφA=182,87335 ;

PB=UIBcosφB=147,749 B;

PC=UICcosφC=50,69295 B;

P=PA+PB+PC=381,3153 B;

:

QA=UIAsinφA=204, 19717 ;

QB=UIBsinφB=350, 20901 ;

QC=UICsinφC=192,96158 ;

Q=QA+QB+QC=747,26776 ;

:

SA=UAIA=247,7744ej48 BA;

SB=UBIB=380,4532ej67 BA;

SC=UCIC=199,665ej75 BA;

S=SA+SB+SC=384, 19197+j747,26777=840,24555ej63 BA;


5.

:

2

+ 1


R1 R2

U

C

-

.5.0

:

U=220 B;

C=15 k;

R1=106 Om;

R2=106 Om;

:

1. ;

2. (t=5τ);

3. t=3τ;

5.1 τ

1. :

τ=(R1R2) /(R1+R2) *C=7,5 c;

uC=u+u=ue-t/τ;

i=-Ie-t/τ;

:

t=5τ=5*7,5=37,5 c;

5.2 () t = 3 τ

t = 3 τ:

i=-Ie-t/τ=-1,09 ;

t = 3 τ:

W=C*uC32/2= 0,00089 ;

5.3 I=f(t); (Uc=f(t))

: uC=ue-t/τ;

(.5.1)

t,c 0 τ
u,B 220 80,9 29,8 10,9 4,03 1,5

.5.1


(.5.2)

t,c 0 τ
i, -110 -42,98 -8,046 -1,09 -0,1612 -0,021

.5.2


:



2010