,

. . ( 1) u = U m sin t . i1 = I m1 sin (t 1 ) , i2 = I m 2 sin (t 2 ) . :

I1 =

U U ; I2 = Z1 Z2

.

2 2 : Z1 = r22 + X L1 ; Z 2 = r22 + X L 2

1.

2.

I1 , I 2 1 , 2

tg1 =

X L1 X ; tg 2 = L 2 . r1 r2

i = i1 + i2 = I1m sin (t 1 ) + I 2 m sin (t 2 ) = I m sin (t ) ( 2) 2 I = I12 + I 2 + 2 I1I 2 cos(1 2 )

tg =

I1 sin 1 + I 2 sin 2 I1 cos 1 + I 2 cos 2

.

P = UI1 cos 1; P2 = UI 2 cos 2 ; 1

P = UI cos ;

Q1 = UI1 sin 1; Q2 = UI 2 sin 2 ;

Q = UI sin ;

S1 = UI1; S 2 = UI 2 ;

S=UI

.

. I u I x . . ( 1) ( 3 ). .

3

I u1 = I1 * cos 1 =

U r1 r r * = U * 12 = Ug1; g1 = 12 Z1 Z1 Z1 Z1 g2 = r2 Z12

I u 2 = I 2 * cos 2 = Ug 2 ;

I u1 , I u 2 , I x1 = I1 sin 1 = U X1 X1 * = U * 2 = U * b1 Z1 Z1 Z1 b1 = X1 Z12

g1 , g 2 -

b1 , b2 -

I x 2 = I 2 sin 2 = U * b2

b2 =

X2 2 Z2

I x1 , I x 2 - . . ( 3.) .

I1 = I r21 + I x21 = U g12 + b122 2 I 2 = I r22 + I x22 = U g 2 + b2

:

y1 =

g12 + b12 ;

y2 =

2 2 g 2 + b2

y =

g 2 + b2

.

.

I u = I u1 + I u 2 = Ug1 + Ug 2 = U ( g1 + g 2 ) = Ug I x = I x1 + I x 2 = Ub1 + Ub2 = U (b1 + b2 ) = Ub :

I = I u2 + I x2 = :

(Ug )2 + (Ub )2

= U g 2 + b 2 = Uy

y=

g 2 + b 2

:

tg1 =

b1 ; g1

tg 2 =

b2 ; g2

tg =

b ; g

:

P = U * I * cos = UIg / y = UIzg = U 2 g :

Q = UI sin = UIb / y = UIzb = U 2b :

S = P2 + Q2 = U 2 g 2 + b2 = U 2 y

1: ( 4) . r,=5 , L=0.05 , r=5 , =100 .

220 , 50 , , .xL = 2fL = 2 * 3.14 * 50 * 0.05 = 15.7 ,

xc = 1 / 2fC = 1 / 2 * 3.14 * 5. *100 *106 = 31.8 ,2 Z1 = r12 + X L = 52 + 15.7 2 = 16.5 ,2 Z 2 = r22 + X C = 52 + 31.82 = 32.2

I1 = U / Z1 = 220 16.5 = 13.33 A I 2 = U / Z 2 = 220 / 32.2 = 6.84 A

4, , .tg1 = X L / r1 = 15.7 / 5 = 3.14 tg 2 = X c / r2 = 31.8 / 5 = 6.36

1 = 720 201 2 = 810

(5) .

5. , .

, , .

P = UI cos 1 = 220 * 13.33 * 0.3 = 879.9 B 1 P2 = UI 2 cos 2 = 22 * 6.84 * 0.15 = 233.2 B P = P + P2 = 1113 1 Q1 = UI1 sin 1 = 220 *13.33 * 0.95 = 2780 BAP Q2 = UI 2 sin 2 = 220 * 6.84 0.98 = 1474 BAP Q = Q1 Q2 = 1306 BAP S1 = U * I1 = 220 *13.33 = 2926 BA S 2 = U * I 2 = 220 * 6.84 = 1504 BA S = UI = 220 * 7.92 = 1742.4 BA . . .

g1 = r1 / Z12 = 5 / 16.52 = 0.018 C b1 = X L / Z12 = 15.7 / 16.52 = 0.058 2 g 2 = r2 / Z 2 = 5 / 32.22 = 0.005 2 b2 = X c / Z 2 = 31.8 / 32.22 = 0.031

g = g1 + g 2 = 0.018 + 0.005 = 0.023 b = b1 b2 = 0.058 .0031 = 0.027 y= g 2 + b 2 = 0.0232 + 0.027 2 = 0.036

.

I u1 = U * g1 = 220 * 0.018 = 3.96 A I u 2 = U * g 2 = 220 * 0.005 = 1.1 A I x1 = U * b1 = 220 * 0.058 = 12.76 A I x 2 = U * b2 = 220 * (0.031) = 6.82 A I u = U * g = 220 * 0.023 = 5.06 A I x = U * g = 220 * 0.027 = 5.94 A .

y1 = y2 =

g12 + b12 = 0.0182 + 0.0582 = 0.06 2 2 g 2 + b2 = 0.0052 + 0.027 2 = 0.06

I1 = U * y1 = 220 * 0.06 = 13.3 A I 2 = U * y2 = 220 * 0.31 = 6.83 A

I=U*Y=220*0.036=7.92 A . .

P = U 2 g = 2202 * 0.023 = 1113 B Q = U 2b = 2202 * 0.027 = 1306 BAP S = U 2 y = 2202 * 0.036 = 1742.4 BA .

6 ,