3.2.1.
, .
, , , , , () (), , .
, () ().
: 1) - I; 2) - U; 3) () . :
R = U / I (3.8)
, , R.
I ( ), (. 3). , Ix > I, , Ix , .
:
R = R/(n-1), (3.9)
R = U / I = U / (Ix - I), (3.10)
R - , n = Ix / I - ( ).
. , , (. 4, 5). , . 4 ( (3.9) (3.10)) - . . 5 , I1 R1, R2 R3 (R) (3.10).
. 4 . 5
R R (. 6). R
, , 0,1% ( ). R R :
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R = R (m-1), (3.11)
R = U / I = (Ux -U) / I 3.12)
m = Ux / U, Ux - R.
. I=50100, R, U=I*R.
R=U/I-R. (3.13)
, , (. 7) , R (3.11-3.13), , . 8.
, . R., , 1 .
. , . , , ( ) .
. 7 . 8
- (.9) (.10). , VD1 , VD2 R, R, , . .10 . , . , VD3, VD4, (VD1, VD3) .
(Im, Um), (I,U) (I, U) ,
= I / I (U/U); Ka = I / I (U/U) (3.14)
. 9 . 10
2.
:
I = I = Im / p = Ö2 *I / p. (3.15)
:
I = I =2* Im / p = 0,9 *I 3.16)
() . . () 2,22 - 1,11 - . () .
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I = I * 2 =I *2*1,11=2,22*I.
I = I * = 1,11*I,
=I/I - , 1,11 - .
2
, | , | |||
1 | 1,11 | 1,41 | ||
1,11 | 1,41 | |||
1,57 | 2,0 | |||
1,16 | 1,73 | |||
1,0 | 1,0 | |||
(. 3.,14). I
I = I * 2 = 2,22*I; (3.17)
I = I * = 1,11*I (3.18)
2.2.
3.7. 260 I=100 R=2000 20 . I < 10 .
:
R=R / (n-1)=2000/((10*10-3/100*10-6)-1) = 20,2 ;
: I= I-I = 10*10-3 - 0,1*10-3 = 9,9*10-3, U = I*R = 100*10 -6*2*103= 200*10-3 , R =U/I = 200*10 -3/9,9*10 -3= 20,2 .
, R , . 260 ( ) CI=5/, R=20,2 CII=0,5/.
3.8. R1, R2, R3 (.5) : I1 = 30 , I2 = 3,0 , I3 = 0,3 I = 150 R = 1500 .
:
1) R1+R2+R3=IR/(I3-I)=150*106*1500/(0,3*103 0,15*103)=1500
2) R1=I(R+R1+R2+R3)/I1=I*SR/I1=150*106 (1500+1500)/(30*103)=15
3) R1 + R2 = ISR/I2 = 150*106 *3000/(3*103)= 150
4)R2 = (R1+R2)-R2 = 150 - 15 = 135
5)R3 = (R1+R2+R3)-(R1+R2) = 1500-150 = 1350 .
(3.9)
I = I1R1/ SR = I2(R1+R2)/ SR = I3(R1+R2+R3)/ SR...;
R1= I3*I*R/I1(I3 - I)...;
R2 = (I1-I2)I3*I*R/(I2 - I)I2*I1...;
R3 = (I2-I3)I*R/(I3 - I)I2....
3.9. 24-155: I=6 , U=100 . 100 . U=I . R (. 6) .
:
1) R=U/I=16,66 ; m=U/U=1/(100*103)=10;
(3.11) R=16,667*9=150
( (3.12) R = (1 0,1) / (6*103)=150 ).
2) R 1 10 /;
3)
R=R+R=16,667+150 = 166,97
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3.10. .8 : 1B, 5, 10, - I = 100 R = 1000 .
:
1B R1=Un1 / I R=I/(100*106)1000=9000 ;
5 R1+R2=Un2 /I R=5/(100*106)1000=49 ;
R2=49 9=40 .
10 R1+R2+R3=Un /I R=10/100*10 5-6 0-1000 ;
R3=99-49=50 .
3.11. : Iα1 , Iα2 . .
.
I:
I1=Iα1*/2=Iα*/2,22; I2 =Iα2*/=I2*/1,11.
3.12. Im = 15,5 (.9). : 1) , ; 2) , .
.
1) , :
I = Im/ p = 15,5/3,14 = 4,96 .
2) :
Iα =I*2=4,96*2,22=11 . (, I=ImÖ2 =15,5Ö2 = 11.)
3.13. 3.12, (.10).
.
1) :
I = 2Im / p = 2*15,5/3,14 = 9,92 .
2) Iα =I*K=9,92*1,11=11 , .
3.14. (.11) Im = 50 , f = 100 . . : 1) ; 2) .
.
= 1,16, = 1,73.
I = Im / Kax = 0,578*Im, Ic = I/K = 0,578Im/1,16 = 0,5Im.
1) Iα = I*K = 0,5*50*1,11 = 27,8 .
2)
I = Iα * /=27,8*1,16/1,11=29 .
3.15. (.12) Im = 25, t 4 0 = 100, T 4 0 = 1 . . : 1) ; 2) , , :
.
I = I / K; I = Im/K; K = K =ÖT / t = ÖQ
1)
Iα =I*2K=Im(t / )*2=25*[100*10-6/(1*10 3)]*2*1,11=5,55
2)
I =(I / )*Kx =5,55*3,16/(2*1,11) = 7,9
. 11 . 12
3.3.
3.3.1.
. (.13): , ( ) () . Z0 Z0, Z1'.
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Z = [(Z1 0 +Z2)(Z3 +Z4)]/(Z1 0 +Z2 +Z3+Z4)=
=Z1 0 (1+m)*n/(1+n); (3.19)
Z0 = [(Z1 0 +Z3)(Z2 +Z4)]/(Z1 0 +Z2+Z3+Z4)=
=Z1 0 (1+n)*m/(1+m); (3.20)
Z1' = Z1 0 (1+n) (3.21)
Z10 - Z1 ; m = Z2/Z10; n = Z3 /Z10.
. , .
( , ), - . Q tg d:
.14 Q= w *L1 / R1 = 1/ (w *C4 *R4) (3.29)
tg d = w * C4 * R4 (3.30)
.15 Q= = w *L1 / R1 = w *C4 *R4 (3.31)
tg d =1/ (w * C4 * R4) (3.32)
. 14 . 15
, , ..
Z1Z4 =Z2Z3, (3.22)
Z1,Z2,Z3,Z4 - .
i- , ..
Zi =Ri +jXi Zi =zi *e jji , (3.23)
Ri,Xi - i- ; zi - i- ; ji - i- .
:
R1R4 X1X4 = R2R3 X2X3 (3.24)
R1X4 + X1R4 = R2X3 + X2R3 (3.25)
z1 * z4 = z2 * z3 (3.26)
j1+ j4 = j 2 + j 3 (3.27)
. (. 14-19).
(. 20) . :
R1*R4 =R2 * R3 (3.28)
. 16 . 17
. 18 . 19
3.3.2.
3.16. .20 . R1, , R2 = 100 , R3 = 25 , R4 = 50 .
.
:
R1*R4 = R2*R3,
R1 = R2*R3/R4 = 100*25/50 = 50 .
3.17. (.20): R2 = 10 ; R3 = 1500 ; R4 = 1000 ; R = 100 ; R = 10 . : 1) R1 ; 2) R..; 3) R..; 4) R1. 2, 3, 4 .
.
R1, R.., R.. :
R1= R2*R3/R4 = 10*1500/1000 = 15 ;
R..=R + R 4. = R + R1*n(1+m)/(1+n) = 34,75 O;
R..=R +R. = R + R1*m(1+n)/(1+m) = 706 ,
m = R2/R1 = 10/15; n = R3/R10 = 1500/15 = 100.
R , R1 ... I, . R1 = E/I. R1 , ... I1, R1.
R1 = E/I1; I1 =[E/(R+R.)]*[(R2+R4)/(R1+R2+R3+R4)].
R1 , R1.=(R+R.)(R1+R2+R3+R4)/(R2+R4)=R..(R1+R2+R3+R4)/(R2+R4) = 1765 O,
R1. = R1.'(1+K) = R1(1+n)(1+K), =R/R.=R/(RR);
=100/(706-100)= 0,165; R1. = 15(1+100)(1+0,165) = 1765 .
3.18. R. (.20), R = 0, R1= 1 , R2 =2 , R3 = 1,5, R4 = 3 .
.
R =R.; R.= (R1+R3)*(R2+R4)/(R1+R2+R3+R4) = 1667 .
3.19. , .18 . R L, , R2=5 , L2=0,1 , R3=10 , R4=20 .
.
R=R1; L=L1, , 3=4=0 (3.24) :
R1*20w*L1*0 = 5*10w*0,1*0; R=R1=50/20=2,5 .
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(3.25) L
2,5*0+20*wL1 = 5*0+10* w *0,1; L=L1=10*0,1*w / 20w= 0,05 .
3.20. , .19 :R2=2000 ; C0=100 ; R4=10 ; C4=0,005 ; d3tg d3=0; d4tg d4=0; f=50 . R, C tg d.
.
Rx =(C4/C0)*R2 =0,005*10-6*2000/(100*10-12) = 100 ;
Cx = (R4/R2)*C0 = 10000*100*10-12/2000 = 500 ;
tg d = wCR = 2*3,14*50*500*10-6*105 = 0,005 .
3.21. (.20) :R2=10 ; R3=1500 ; R4=1000 ; R=100 ; Si, Sou Sow Ri, U=4 .
.
Sou = In*m*n/[(1+m)(1+n)]
In, m, n :
In=Un/Rn.=Un(R1+R2+R3+R4)/[(R1+R2)(R3+R4)]=Un(1+n)/R1(1+m)n;
m = R2/R1 = 10/16; n = R3/R1 = 1500/15 = 100.
, :
Sou=Un*m /[R1(1+m)2] = 4*10*152 /[15*15(15+10) 2] = 64*10-3 /.
RI :
Sou = Sou*R10 = 64*10-3*15 = 0,96 B
S0I =Sou/(R+R.)= 64*10-3/[100+(15+1500)(10+1000)/2525]=90*10-6 A/
RI
S0I = Sou/R+R. = 0,96/(100+606) = 13,6*10-4 A.
Sow = Soi2*R = 13,62*10-8 * 100 = 185*10-6 .