: .
, .1.
I, UR, UL, UC, , , .
R, L, C ,
i = Im sinωt.
.1. R, L, C
II
u = uR + uL + uC.
u = UmR sinωt + UmL sin(ωt + π/2) + UmC sinωt(ωt - π/2) =
= UmR sinωt + (UmL - UmC)sin(ωt + π - π/2) =
= UmR sinωt + (UmaxL - UmaxC)sinωt(ωt + π/2).
, , , , Um φ ( , 0).
u = Um sin(ωt + φ).
XL XC .
. XL XC:
) XL > XC ) XL, < XC ) XL = XC
, , U, , φ - UR, UL UC = UP
UR = U cosφ; UP = U sinφ;
I, (.), I2 (.).
. .
R = Z cosφ; X = Z sinφ;
P = S cosφ; Q = S sinφ; S =
cosφ = UR/U = R/Z = P/S.
cosφ . , , , .
:
İ = I e j 0.
= ej φ = + + = I(R + I jXL - I jXC)= I (R + j (XL - XC)).
İ, :
Z = Uej φ /Iej 0 =Zej φ = R + j (XL XC),
Z = , ;
R ;
XL XC = - ;
|
|
φ ,
φ = arctg(XL XC) /R.
R, L, C
:
, (XL>XC), 90>φ>0;
─ , ,
(XC > XL), 0 < φ < 90;
, (XC = XL), φ = 0.
XL X , , . . L = . X = XL XC = 0 Z = R . I = U/R U = const, R = const .
UL = XLI = XCI = UC.
,
UL = XLI = XLU/R; UC = XCI = XCU/R.
, XL/R , XL>R.
C UL UC π, .. .
R, L C, XL = XC, (UL) (UC) , .
.. ; , U = U,
φ = 0; cosφ = 1.
.
P = UI cosφ = UI = S,
Q = UI sinφ = 0. (QL = XLI 2) (QC = = XCI 2) , . .
ω L = 1/(ω C)
, ω, L . , ,
ω0 = 1/ .
, . XC = 1/ (ω C), , X = XL XC c . I =
= U / . ω = 0, , (X = ) (.).
.
UR = RI , , . . R = const. UR = U ω = ω0.
, , .
|
|
L , ω0 = , . ( ) . L , . . .
, UL UC, .
:
, ;
.
U, Rk, Lk, f = 50 (.) , I . , UL-R U. ..
U, | 33,8 | 34,0 | 33,9 | 33,9 | 33,9 | 33,9 | ||
L, | ||||||||
Rk, | 55,4 | 45,9 | 76,5 | 84,7 | 38,1 | 47,5 | 38,2 | 38,0 |
C, | I , | UL-R, | UC, | |
.
1. .
.
2. .
3. ( ).
4. , . :
) Xc >> XL, I A<< I
) XC > XL, I A< I
) XC XL, I A = I
) XC < XL, I A < I
) XC << XL, I A<< I
.
U, | UL-R, | UC, | I, | , | R, | XL,, | XC, | X, | Z, | S, | Q, | UR, | UL, | Up | cosφ | φ, |
5. , ..
6. .1, 3, 5; .. 1, 5 .
ψi . .
7. , , , , SHABLON (.101,111 .1):
2 . U (), L (), C, (); f 50 ;
|
|
, :
UL
UC ;
IT ,
φ
I = f(f); UL = f(f); Uc = f(f); φ = f(f)
I = f(L); UL = f(L); Uc = f(L); φ = f(Lk)
I = f(C); UL = f(C); Uc = f(C); φ = f(C)
.
8. I, Uc I, UL, φ .. I ., UC .
9. .
10.
1. R, L C ?
2.
?
3. ?
4. ?
5. ?
6. ?
7. cosφ ?
8. , R, L ?
9. ?
10. ?
11. ?
3
: ; .
I.
, , R L, - (. . 10).
I, ; I ,IL-R, ; , (S, , Q) BL BC.
I, , Y U:
,
Y - :
;
G , , ; BC, BL , :
; .
, I I IL-R , .
.
. , Ia IP , I. IL > IC, IP π/2, I φ (0 < φ < π/2). IL < IC, IP φ, I - (-π/2 < φ < 0).
, , , G B = BL BC .
:
I = YU =
|
|
. .
:
G = Y cosφ;
B = Y sinφ;
φ = arctg(B/G) = arctg((BL BC) /G).
Y = 1 /Z = 1 /(Ze j φ) =Yej φ = G jB,
G B .
(L > C), , (L < C), .
:
) , I U (BL>BC) , . 9 ;
, I (BL<BC); , . 9;
) I U (BL=BC); . 9; .
Ta , :
1. C,
2. L
3. f U.
Y = G,
BL=BC, ,
. ,cosφ = 1.
IL = IC I BL/G , BL = BC > G.
:
.
L C , , . , .
. :
.
; I ; II
.
- : , , , . , , , .
:
:
.
I - , , I 1 I 3 - .
,
Q = QL QC,
.
. 9.
:
) , .. ;
) , .. , .
, ..
, . RK LK U (. 7) 50 (, . 10). , Ic, IL-R, I. . 8.
|
|
7
LK, | ||||||||||
RK, | 40,3 | 40,3 | 43,6 | |||||||
U, | 37,8 | 37,0 | 37,8 | 39,0 | 37,6 | 38,0 | 37,8 | 38,0 |
8
3.1. . 10.
3.2. .
3.3. , :
) BL>BC, IL-R>IC (2-3 );
) BL=BC, IL-R≈IC, I=Imin(1 );
) BL<BC, IL-R<IC (2-3 );
3.4. . 9.
9
. | ||||||||||||||
U, | I, | IL-R, | IC, | P, | BL, | BC, | Y, | C, | Ia, | IL, | Cos φ | Q, . | Φ, . | |
3.5. , . 9, . 1.
3.6. (. 1,3,5 . 9),
3.7. , . 9. . 9 .
3.8. .
1. ,
2. .
3. , .
4. , . ..
5. ?
6. .
1. R, L, C : , , ?
2. . ?
3. .
4. , , cos j tg.
5. ?
6. .
, :
, - ; ; , - .
, ;
;
4
00
: , 3- 4- .
I.
19 . . , . .. - . , , , - , , - , , . 3- ( ). 3- . , , 3- .
m- , , 2π/m. 3- m=3, , , 120 (2π/3).
, 3- , , », ѻ. , (.. Ψ=0), ,
; ; .
; , , , BC ( і, і).
, .
. - ( ) (), . , ( ) . () .
. 11 , .
.11
, , , ,. . 11 , , .. .
, - . , . 11 : , , () : , , . , , , . 11.
3- , (), , (), . , . : .
, N n , .
.12
. 12 , ..
, , .
N n
, , .
, .
, .
, ,
( ): , 120.
;
. 13:
; .
, φ . , ..
.13
(UAB, UBC, UCA,) . , ,
.
, , , , , , , () , (. 14). () (, . 11).
N, , . 14 . n, N , . , n , , , - , , . (), -
,
.
(5.1),
.
( , , , ..). , , N n, . () 3- N n (c. . 11).
- , , . 11, :
. (5.2)
, (5.2) (, , ) .
, , . 13, .
3- :
.
, , , ,
.
3- .
.
2.1. , .
2.2. .
2.3. U=38 B . 10 , , , . . 12.
12
, | 40+J186 | -J300 | 43+J192 | -J300 | 40+J198 | -J90 | ||||
, | 40+J188 | 19+J136 | -J300 | 40+J214 | -J300 | -J90 | 40+J45 | |||
, | -J300 | -J300 | 84+J183 | -J300 | 43+J200 | -J300 | 84+J13 |
2.4, . ,