# Электротехника. Часть 1. Электрические цепи

• Published on
08-Dec-2016

• View
220

2

Embed Size (px)

Transcript

• - ,

1.

- 2005

• 1.

- 2005

• 621.3 .., .., ., .., . . /

1, . : , 2005 41 .

- -.

- - .

, - , -, -.

-

. ..

- , , 2005 .., .., .., .., 2005.

• , , ,

1.

. . . - . . 00408 5.11.99 25.05.05 . 500 . 849

• - - - , - 197101, -, ., 49

x

• 1

-

: , , - .

, - . - .

1.

(.1.1) , , -, , .

.1.1

6-15. - 0,01 10 0,001 1000 .

- 100-101. "" "" . "1" "1" - -

V

-

1

1

Y1 Y2

R0

• (), 1 10, 1.1, 4830, 567 5025. , - . - " " .

"1" "" , - I .

"" "1" - R0, .

- 1-83. 1.1 - "Y1" (t), "Y2" - u(t) (.1.2).

2.

- , - , - 1.1. - , , - 1.1. , - .

3.

9 . - 1.1 - . - "-" . - "" " " U -, . - I .

• .1.1. 1.

I = U/z: R = R1; X = 0; z = R1; = artg (X/R) = 0.

2.

I = U/z: R =0; X = -xc; xc =1/C; z = xc; = arctg(-) = -/2.

3.

I = U/z; R = R; X = xL; xL = L;

z = RL)(RX 2222 +=+ ;

= arctg(X/R) = arctg(L /R). 4.

I=U/z: R=R+R1; X= xL; xL= L;

z= R1)(RL)(RX 2222 ++=+ ;

= artg(X/R)= artg(L /R). 5.

I=U/z: R=R1; X= -xc; xc=1/C;

z= R1C)(1/RX 2222 +=+ = artg(X/R)= artg(-1 /RC).

6.

I=U/z: R=R1+R; X= xL -xc= L -1/C;

Z= ( ) R1)(R C 1/-LRX 2222 ++=+

= artg(X/R)= artg[(L -1 /C)/(R+R1). 7.

I=Uy: g=1/R1; b= -bc; bc = C ;

y= ( )1/R1C)(bg 222 2+=+ = artg(b/g)= artg (-C R1)

8.

I=Uy; y= bg 22+ ; g=g1+g; b=b1+b;

g1=1/R1; g=R/[ R2+(L)2]; b1=0; b= L /[ R2+(L)2]; = artg(b/g).

9.

I=Uy; y= bg 22+ ; g=g1+g; b=b1+b;

g=R/[ R2+(L)2]; b= L /[ R2+(L)2]; g1=R1/[ R12+(1/C)2]; b1= -1/C [ R12+(1/C)2]; = artg(b/g).

1 1 R1

1 1 R L

1 1 R L R1

1 1 C R1

1 1 C R1 R L

1 1 C

1 1 C

R1

1 1 R L

R1

1 1 R L

R1 C

• - - , 1-83. - , 1.2. = 180h/h, h - , - , h - - .

, .1.2, > 0, - < 0. - 1.2. 1.2

R1 R L U I I

1 2

. .. 9

hh

u(t)

(t)Um

Im

.1.2

• 1. . 2. . 3. 1.2. 4. ( -

), ( ) .

5. .

. I - , 1.1., ; z,R,X- , ; y,g,b - , -; xc,bc -; xL,bL .

• 2

-

, .

-

, . - .

1.

1.1. - , . - .

1.2. -. .

2.

, 1. - 1 "1" "1" (.1.1) , , - 2.1, 2 - , 2.2.

3.

.2.1 .2.2

1 1 C R1 R L

V1 V2 V3

1 1 R L

R1 C

1

2

• 3.1. 1 .

- , 2.1, - , "1" "1" (.1.1). : R1 = (50 100) , L = (50 110) , C = (0.5 1) .

- , f0 , f0 = 1/ 2LC .

- "" , V 10 30 .

- U, .

- f0 I0, UR10, - U0 , Uc0. 0. - 2.1. V1, V2 V3 ( . 2.1), - - , 1.

- 8-10 I(f), (f), UR1(f), U(f) Uc(f) 0.5 f0 1.5 f0, U - 2.1.

2.1. U= R1= R= L= C=

f0= Q= f0= Q=

f,

I, UR1, U, U, I, UR1, U, U, (f0)

-

• , 6 1.1. UR1, U Uc 1.1. Q Q -

Q=/(R1+R) Q= Uc0/U, = CL - -

.

3.2. 2 - , 2.2 , -

, "1" "1" (.1.1). : R1 = (50 100) , L = (50 110) , = (0,5 1) .

- ,

f0 =0/2, 0 =22

2

2

R1

RLC1

.

- "" , 10 30 .

- U, .

- f0 I0, I10, I20 0 . 2.2. I10 I20, 1 2, - - , 1.

- 8 - 10 I(f), (f), I1(f) I2(f) 0.5 f0 1.5 f0, - U - 2.2.

-, 9 1.1. I1, I2 - 1.1.

• 0

0

22LCRR1

L Q

+= .

Q - 2f - I(f), .

2.2

U = R1 = R = L = C =

f0= Q= f0= Q=

f, I, I1, I2, I, I1, I2,

(f0)

1. . 2. . . 3. I(f), UK(f), UC(f), (f) 1 . 4. I(f), I1(f), I2(f), (f) 2 . 5. . 6. .

• 3

.

, .

1.

(. 3.1) , , , .

6-15.

. 3.1

0,01 10[] 0,001 1000[].

100-101. b -. a1 b1 - , , . 3.2-3.4 538 5025. - 3-10, - U . . a 1 - 5014, - I .

2.

2.1. . 2.2.

. 2.3. -

.

3.

3.1. , r1, L1

r2 L2 . - . f0 -

V

a a1

1

• UC0 UL0, - Ur0 U. - 8 10 - .

3.1.1 6-7

- , 3.2, - ( 3.1).

. 3.2,

.3.2, .3.2,

- U. - , f0 . - . - -. 3.1. - r = U / I0, xL = UC0 / I0, L = xL / 2f0 3.1.

3.1

M C I

0 U UC0 f0 r L

6-7 1-2

3.1.2 1-2

- , 3.2, - ( 3.1). - , 3.1.1 3.1.

3.2 .

. 3.3

r1

L1

M

6

r2

L2

583 1

2 7

C2

V1 1

1

r1

L1

M

1

r2

L2

583 6

7 2

C2

V1 1

1

r1

L1

M

1

r2

L2

583 6

7 2

1

V2

1

• .3.3

- (. 3.3) (. 3.1). - f. - U2. - 3.2.

3.2

M f I U1 U2 M K

-

-

- 3.2. . L1 L2 3.1. , , .

3.3 - .

. - (. 3.4,), - 7 2 1, 1

. 3.4,a . 3.4,

- I f . - U U1 U2 . 3.4. - (.3.4,), 1 2 (.3.4,). - 3.4. - -,

.21 LL

MK

= = U2 / 2f I,

z U I1 1= / ; x z r 1 12

12= ; L x f

1 1 2= / ;

z U I2 2= / ; x z r 2 22

22= ; L x f

2 2 2= /

r1

L1

M

1

r2

L2

6

7 2

V2 V1

r1

L1

M

2

r2

L2

6

7 1

V2 V1

1 1

1 1

• r, L, M 3-1, 3-2. - 3.4 , - L1=L1M, L2=L2M, - , .

3.4

M f U1 U2 U I L1 L2 L1 L2

7-2 7-1

1. . 2. . . 3. ,

. 4. .

• 4

- - .

-

, .

1.

4.1.

75/44 -

50 , (), 50 - .

. . , .

.4.1

50K

B 44 / 75

0'

V1

0

0 0

V2

V P

• 50 - , - . , , , . - . , - -.

"" (.4.2) "" (.4.3) -2.

.4.2 .4.3 2 , -

, - . , - 58 -. 37 . - , - Z Y 4.1.

V1 3-10 U , V2 - U00 00 , . - . 5014 I0 00 . (.4.3) -

r

2HTH

L

0'

r

2HTH

L

c

R

2HTH

L

r

1

2HTH

L

2

2HTH

3

2HTH

L r

L rc

• 2 1, 2 3, .

4.1 S, Z = z ej, Y = y e-j,

0 0 5 672 370 1.4910-3 -370

10 336 370 2.9810-3 -370

15 224 370 4.4610-3 -370

20 168 370 5.9510-3 -370

25 134 370 7.4410-3 -370

30 112 370 8.9210-3 -370

35 96 370 10.410-3 -370

40 84 370 11.910-3 -370 45 74.6370 13.410-3 -370

50 67.1370 14.910-3 -370

55 60.1370 16.410-3 -370

60 55.9370 17.910-3 -370

2. 2.1. , " ", -.

2.1.1. . 2.1.2. . 2.1.3. . 2.1.4. . 2.1.5. ( ) . 2.1.6. . 2.1.7. . 2.2. -, , . 2.2.1. . 2.2.2. . 2.2.3. . 2.2.4. .

• 2.2.5. . 2.2.6. .

3.

3.1. 2.1.

- "" (. 4.2) - 50, . 4.1. - - (2.1.1-2.1.7). - - . - 20 60 . (.4.1). , , ( ) - - 75/44. .2.1.7 - .

- 75/44 , - , 4.1. - : U(V1) U00`(V1) I0() U,IA,PA (50 - ) U,IB,PB (50 - B) U,IC,P (50 C).

3.2. .2.2.

- " " (. 4.3) 50, . 4.1. - - (2.2.1-2.2.6). - - . - 20 60 . (.4.1). , ,

• ( ) - - 75/44.

- 75/44 , - , 4.2. : U(V1) I(1) Ic(2) I(3) U,IA,P (50 - ) U,IB,P (50 - B) U,I,P (50 C).

4.

4.2 , , 4.4. , .

4.3 , - , 4.4. - EA = 44ej0; E B= 44e - j120; EC = 44e j120. 4.3.

U00 =

CBA

YYYYEYEYE

++++

. U0 = EA U00 ;U0 =EB U00 ; U0 = E U00 . IA = Y U0 ; IB = Y U0; IC = Y U0. I0 = IA + IB + IC

UAB = EA EB; UBC = EB EC ; UCA= EC EA . I= YUAB ; I = Y UBC ; I = Y UCA . IA = I I; IB = I I; IC = I I .

IA

UA

A

Y IB

IC Y

Y B

C

c

I

I

I

UB

U

IA

U0

A

0Y

IB IC

I0 Y Y

U0

0

B

C

Uc0 U00

c

• P = UI cos

1. . 2. 4.2 4.3. 3. . . 4. , . 5. .

• 5

:

- - ; - ; - - .

- , - , - .

1.

(. 1) - , , , - .

- 6-15. , , . 0.01 10 B 10-3 1000 .

100-101. .

- 1-83 f 0 = 1000 .

k - - , LK . - fk = k f0 . Rk.

Rk , - KU = 0,1. , - .

• .1

2.

. - .

u1(t), u2(t) u3(t) - . - . - . u4(t) , . u5(t) u6(t), - , -

. - ().

3. (.1). , - . - 10 , 10 30[].

3 44

1 2

-

1 2

3 4

-

1 2

3 4

- ()

3 4

1 2

Y1

R1

R2

R3

R4

R5

R6

L1

L2

L3

L4

L5

L6

Y2

C

Y1 Y2

• . f0 = 1000 - Y1 . Y1 R1 Y2 c L1. - - ; - .

4.

. 4.1. -

, . - , - . Umk /U .

4.2. . RL RC . - - . -. .

. 4.3. -

. 4.4. RL -

. 4.5. R -

.

4.4 4.5 , R RL RC. : .

5. -

1 2. . 4.1 4.2 .

4.3 .

• , 2, - 1000 Y1 .

1, 2,,6 - , 3.

1. . 4.4 . RL, , -

. - 1000 .

DE - L= 20 100[], -, R = 400[].

, - 3. .. R , Imk = Umk/R. 2.

RC, , - . 1000 .

DE - C = 0,5[] R = 200 1200 [], .

, - 3. .. R , Imk = Umk/R. 2.

6-15. 100-101. .

1-83. 4830. 5025. 567.

• 1 .

UM

k

Umk

Umk/UM Umk

Umk/UM

1 2 3 4 5 6

UM

2 RL L = []

RC C = []

.

k Umk B Umk/Um1 Imk

A Imk/Im1 Imk

A Imk/Im1 Imk

A Imk/Im1 Imk

A Imk/Im1

1 2 3 4 5 6

- , . , .

1 : - Umk, ; - Umk /UM.

Umk Imk RL RC. - Umk /Um1 Imk /Im1.

2 : - Imk ; - Umk /Um1 Imk /Im1 .

• , , -

. - . - A0, Bmk Cmk . - . :

, U0 =A0,

4.2 , -

: RL u1(t) RC u3(t). Bmk, Cmk Umk . :

Rk = 30[] .

2.

U B Cmk mk mk= +2 2 k

mk

mkarctg C

B=

u t U U t U t U k tm m mk ki( ) sin( ) sin( ) sin( ) = + + + + + + + + 0 1 1 2 22

u t U U k tmkk

k( ) sin( ); = + +0

I U

RC

mkmk=

+

221

,( ) ( )

I U

R R Lmk

mk

k

=+ +2 2

,

• 6

-

- .

" -" , -. - .

-

- , - mU+

mU T (. 6.1). RC RL.

. -

- (. 6.2). - - - , - 6.1.

- - RC-

. 6.1. .

. 6.2.

• , - - .

RL- - , .

- , , .

. = /)( tAeta ( )= /1)( teAta

( ) == /td eAtad ( ) == /1 td e

0,10 d dt . - , , 5,0t , .. -

5,05,0 44,12ln

tt

= (6.2)

6.1

RC

( )RC

eU(t)u

eUtu

eR

Uti

tmC

tmR

tmRC

==

=

=

/

/

/

21

2)(

2)(

mC

mCC

RR

mR

RCRC

mRC

UuUuu

uuUu

iiR

Ui

===

===

==

=

+

+

+

)(;)0()0(

0)0()(;2)0(

0)0()(

;2)0(

RL

( )( )

RL

eUtu

eU(t)u

eR

Uti

tmL

tmR

tmRL

=

=

=

=

/

/

/

2)(

21

21)(

0)0()(;2)0(

)0()(;)0(

)(

;)0()0(

===

===

=

==

+

+

+

LL

mL

mRR

mR

mRL

mRLRL

uuUu

UuuUuR

Ui

RUii

• RLC. - , -

(. 6.3). - (. 6.2) -, .. . -

012 =++ pRCLCp , R, L C. - ,

R. -

22

11

11pp

== ,

21 > . , - :

20

2133

== , (6.3)

L

R2

= , LC1

0 = . (6.1), -

0,9 9,0t

. 6.3.

• 9,09,0

1 3,110ln33 t

t== . (6.4)

-

L

R2

= 21

=LC

. (6.5)

1mi , 2mi T:

Tii

m

m

= 21

ln

T

=2

. (6.6)

6.2.

0

;

1;2

12

0

0

20

22,1

==

=

pp

LCLR

p

( ) ( )( )

( ) ;21)(;2)(

;)()(;2)(

12

21

21

2121

2121

21

=

=

=

=

tptpmC

tptpmL

Rtptpm

epeppp

Utu

epeppp

Utu

RtitueeppL

Uti

RR uuiii

==

===

+

+

0)()0()0(

;0)()0()0(

• >

=

==

=

0

0

20

2,1

1

;2

LC

LR

jp

( )( )[ ]

=

=

=

+=

=

=

arctg;

cos21)(

;cos2)(

;)()(;sin2)(

0

teUtu

teUtu

RtituteL

Uti

tmC

tmL

Rtm

1. . 1.1. RC-. 1.2. RL-. 2. RLC-. 2.1. . 2.2 . .

1. 6-15 2. 1-83 3. 4830 4. 5025 5. 567

• 1. . a) , . 6.4. b) ,

, . c)

6-15, 1 7 8 . d) . 6.4

3 4, . e) , -

(. 6.5 ). - ( ).

f) (RC-) (RL-) - , 6-15 , ( b(t) . 6.5 ).

. 6.4.

• g) 6-15 - Um - .

h) - -, , - - , - , 6.3, - - ( 6.1), - - 6.4.

i) - - -, - , -

)(tb .

6.3

.

.6.5

.

YI )()( tatiRC = ( )R

KNi YYRC

I0

=+

0

RC

YII )()( tbtuC = ( ) ( ) ( ) II00 YYCCC KNuuu === +

YII )()( tatuL = ( ) II0 YYC KNu =+ 0 RL YI )()( tbtiRL = ( ) ( ) ( )

R

KNiii YYRLRLRL

I00

=== +

6.3: YN

. 6.5.

• (, . 6.5 ( ) 6,20 =+a .); III , YY KK - YI YII, - .

j) tN (2,3 . 6.5 ) , tK , - tt KNt =5,0 , (6.2). 6.1 6.4.

k) 4 2 (. 6.4) - .. e-j RL -.

2. RLC-. 2.1. .

a) - , . 6.4.

b) - 6000 , , .

c) 6-15, 7 8