w w R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R (2)Obliczania dokładne prądów i napięć I A U V I A I A U V U V I A I A U V U V I A I A U V U V I A I A U V U V I A I A U V U V I A I A U V U V Obl

(1)

Obliczenia dokładne rezystancji zastępczej

R11,14 =20 Ω

R11,14,12 =6,666667 Ω R11,14,12,13 =16,66667 Ω R11,14,12,13,10 =6,25 Ω R11,14,12,13,10,9 =16,25 Ω R11,14,12,13,10,9,8 =6,190476 Ω R11,14,12,13,10,9,8,7 =16,19048 Ω R11,14,12,13,10,9,8,7,6 =6,181818 Ω R11,14,12,13,10,9,8,7,6,3 =16,18182 Ω R11,14,12,13,10,9,8,7,6,3,4 =6,180556 Ω R11,14,12,13,10,9,8,7,6,3,4,5 =16,18056 Ω R11,14,12,13,10,9,8,7,6,3,4,5,2 =6,180371 Ω R11,14,12,13,10,9,8,7,6,3,4,5,2,1,w =26,18037 Ω

Zadanie:

Oblicz wartości prądów płynących przez wszystkie rezystory.

R₁=R₂=R₃=R₄=R₅=R₆=R₇=R₈=R₉=R₁₀=R₁₁=R₁₂=R₁₃=R₁₄=10Ω, E=10V.

Rozwiązanie zadania:

Obliczenie rezystancji zastępczej obwodu:

Ω

= Ω + Ω + Ω

= + +

=

Ω Ω =

+ Ω

Ω

⋅

= Ω +

= ⋅

Ω

= Ω + Ω

= +

=

Ω Ω =

+ Ω

Ω

⋅

= Ω +

= ⋅

Ω

= Ω + Ω

= +

=

Ω Ω =

+ Ω

Ω

⋅

= Ω +

= ⋅

Ω

= Ω + Ω

= +

=

Ω Ω =

+ Ω

Ω

⋅

= Ω +

= ⋅

Ω

= Ω + Ω

= +

=

Ω Ω =

+ Ω

Ω

⋅

= Ω +

= ⋅

Ω

= Ω + Ω

= +

=

Ω Ω =

+ Ω

Ω

⋅

= Ω +

= ⋅

Ω

= Ω + Ω

= +

=

18 , 26 10

10 18 , 6

18 , 10 6 18 , 16

10 18 , 16

18 , 16 10 18 , 6

18 , 10 6 18 , 16

10 18 , 16

18 , 16 10 18 , 6

18 , 10 6 19 , 16

10 19 , 16

19 , 16 10 19 , 6

19 , 10 6 25 , 16

10 25 , 16

25 , 16 10 25 , 6

25 , 10 6 67 , 16

10 67 , 16

67 , 16 10 67 , 6

67 , 10 6 20

10 20

20 10

10

1 2 , 5 , 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11 , 1 , 2 , 5 , 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

2 5 , 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

2 5 , 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11 2 , 5 , 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

5 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11 5 , 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

4 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

4 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11 4 , 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

3 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11 3 , 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

6 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

6 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11 6 , 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

7 8 , 9 , 10 , 13 , 12 , 14 , 11 7 , 8 , 9 , 10 , 13 , 12 , 14 , 11

8 9 , 10 , 13 , 12 , 14 , 11

8 9 , 10 , 13 , 12 , 14 , 11 8 , 9 , 10 , 13 , 12 , 14 , 11

9 10 , 13 , 12 , 14 , 11 9 , 10 , 13 , 12 , 14 , 11

10 13 , 12 , 14 , 11

10 13 , 12 , 14 , 11 10 , 13 , 12 , 14 , 11

13 12 , 14 , 11 13 , 12 , 14 , 11

12 14 , 11

12 14 , 11 12 , 14 , 11

14 11 14 , 11

w

w R R R

R

R R

R R R

R R

R

R R

R R R

R R

R

R R

R R R

R R

R

R R

R R R

R R

R

R R

R R R

R R

R

R R

R R R

(2)

Obliczania dokładne prądów i napięć I1 =0,381966 A U2 =2,360689 V I2 =0,236069 A I5 =0,145897 A U5 =1,458967 V U4 =0,901722 V I4 =0,090172 A I3 =0,055724 A U3 =0,557244 V U6 =0,344478 V I6 =0,034448 A I7 =0,021277 A U7 =0,212766 V U8 =0,131712 V I8 =0,013171 A I9 =0,008105 A U9 =0,081054 V U10 =0,050659 V I10 =0,005066 A I13 =0,00304 A U13 =0,030395 V U12 =0,020263 V I12 =0,002026 A I11 =0,001013 A U11 =0,010132 V U14 =0,010132 V

Obliczanie wartości prądów i napięć:

V A

R I U

V A

R I U

A A

A I

I I I I

V A R

I U

V V

V U

U U

V A

R I U

A A

A I

I I

V A R

I U

V V

V U

U U

V A

R I U

A A

A I

I I I I

V A R

I U

V V

V U

U U

V A

R I U

A A

A I

I I

V A R

I U

V V

V U

U U

V A

R I U

A A

I I I I

V A R

I U

V V

V U

U U

V A

R I U

A A

A I

I I

V A R

I U

V A

V R

R I E U

V A R

I E

w z

0101 , 0 10 00101 , 0

00101 , 0 00203 , 0 00507 , 0 0131 , 0 0213 , 0

00203 , 10 0

0203 , 0

0203 , 0 0304 , 0 0507 , 0

0304 , 0 10 00304 , 0

00304 , 0 00507 , 0 0081 , 0

00507 , 10 0

0507 , 0

0507 , 0 081 , 0 131 , 0

081 , 0 10 0081 , 0

0081 , 0 0131 , 0 0344 , 0 0902 , 0 146 , 0 0131 , 10 0

131 , 0

131 , 0 213 , 0 344 , 0

213 , 0 10 0213 , 0

0213 , 0 0344 , 0 0557 , 0

0344 , 10 0

344 , 0

344 , 0 557 , 0 902 , 0

557 , 0 10 0557 , 0

0557 , 0 0902 , 0 236 , 0 382 , 0

0902 , 10 0

902 , 0

902 , 0 46 , 1 36 , 2

46 , 1 10 146 , 0

146 , 0 236 , 0 382 , 0

236 , 10 0

36 , 2

36 , 2 ) 10 10 ( 382 , 0 10 ) (

382 , 18 0 , 26

10

14 11 14

11 11 11

12 10 8 7 11

12 12 12

13 10 12

13 13 13

10 9 13

10 10 10

9 8 10

9 9 9

8 6 4 5 9

8 8 8

7 6 8

7 7 7

6 3 7

6 6 6

3 4 6

3 3 3

4 2 1 3

4 4 4

5 2 4

5 5 5

2 1 5

2 2 2

1 1

2 1

= Ω

⋅

=

⋅

=

= Ω

⋅

=

⋅

=

−

=

−

=

Ω =

=

−

=

−

=

= Ω

⋅

=

⋅

=

−

=

−

=

Ω =

=

−

=

−

=

= Ω

⋅

=

⋅

=

−

=

−

=

Ω =

=

−

=

−

=

= Ω

⋅

=

⋅

=

−

=

−

=

Ω =

=

−

=

−

=

= Ω

⋅

=

⋅

=

−

=

−

=

Ω =

=

−

=

−

=

= Ω

⋅

=

⋅

=

−

=

−

=

Ω =

=

= Ω + Ω

⋅

−

= +

⋅

−

=

Ω =

=