Электротехника. Часть 1. Электрические цепи

  • Published on
    08-Dec-2016

  • View
    220

  • Download
    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

    Atad (6.1)

    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

Recommended

View more >