1.1
Dane:
Szukane:
Wzory:
s
t
1
=
e
i
18
10
5
⋅
=
C
e
19
10
6
,
1
−
⋅
−
=
I
=
t
Q
I
=
A
t
e
i
t
Q
I
8
,
0
1
10
6
,
1
10
5
19
18
=
⋅
⋅
⋅
=
⋅
=
=
−
______________________________________________________________________
1.2
Dane:
Szukane:
Wzory:
2
6
mm
S
=
e
i
20
10
4
⋅
=
C
e
19
10
6
,
1
−
⋅
−
=
s
t
2
=
I
J
=
=
t
Q
I
=
S
I
J
=
20
19
4 10
1, 6 10
32
2
Q
i e
Q
I
A
t
−
= ⋅
⋅
⋅
⋅
=
=
=
2
/
33
,
5
6
32
mm
A
S
I
J
≈
=
=
______________________________________________________________________
1.3
Dane:
Szukane:
Wzory:
A
I
150
=
A
I
6
'
=
s
t
2
=
'
t
=
t
Q
I
=
C
t
I
Q
300
=
⋅
=
s
I
Q
t
50
'
'
=
=
______________________________________________________________________
1.4
Dane:
Szukane:
Wzory:
A
I
8
0
÷
=
s
t
30
=
Q
=
t
Q
I
=
A
I
śr
4
2
8
0
=
+
=
C
t
I
Q
śr
120
=
⋅
=
______________________________________________________________________
1.5
Dane:
Szukane:
Wzory:
Ah
Q
30
=
h
t
8
=
h
t
2
1
=
2
/
1
2
I
I
=
4
/
2
/
1
2
3
I
I
I
=
=
8
/
2
/
1
3
4
I
I
I
=
=
=
1
I
=
2
I
=
3
I
=
4
I
t
Q
I
=
Q
t
I
t
I
t
I
t
I
=
⋅
+
⋅
+
⋅
+
⋅
1
4
1
3
1
2
1
1
Q
t
I
t
I
t
I
t
I
=
⋅
+
⋅
+
⋅
+
⋅
1
1
1
1
1
1
1
1
8
4
2
Q
t
I
=
⋅
1
1
8
15
A
t
Q
I
8
15
8
1
1
=
⋅
⋅
=
A
I
4
2
=
A
I
2
3
=
A
I
1
4
=
______________________________________________________________________
1.6
Dane:
Szukane:
Wzory:
V
U
6
,
3
=
A
I
2
,
0
=
=
R
=
G
R
U
I
=
R
G
1
=
Ω
=
=
18
I
U
R
S
R
G
0556
,
0
1
≈
=
______________________________________________________________________
1.7
Dane:
Szukane:
Wzory:
V
U
10
=
=
I
R
U
I
=
Ω
⋅
=
Ω
=
Ω
=
5
10
2
200000
200 k
R
v
A
A
R
U
I
µ
50
10
5
5
=
⋅
=
=
−
______________________________________________________________________
1.8
Dane:
Szukane:
Wzory:
A
I
4
=
Ω
=
55
R
=
U
R
U
I
=
V
R
I
U
220
=
⋅
=
______________________________________________________________________
1.9
Dane:
Szukane:
Wzory:
A
I
25
,
0
=
Ω
=
12
,
0
a
R
=
U
R
U
I
=
V
R
I
U
03
,
0
=
⋅
=
______________________________________________________________________
1.10
Dane:
Szukane:
Wzory:
A
mA
I
dop
024
,
0
24
=
=
Ω
=
Ω
=
1000
1 k
R
=
U
R
U
I
=
V
R
I
U
24
=
⋅
=
______________________________________________________________________
1.11
Dane:
Szukane:
Wzory:
V
U
24
=
Ω
÷
Ω
=
100
5
R
=
1
I
=
2
I
R
U
I
=
A
I
8
,
4
5
24
1
=
=
A
I
24
,
0
100
24
2
=
=
______________________________________________________________________
1.12
Dane:
Szukane:
Wzory:
220
U
V
=
100
R
=
Ω
0,5
d
mm
=
I
=
J
=
R
U
I
=
2
4
d
S
π
⋅
=
I
J
S
=
220
2, 2
100
I
A
=
=
2
2
0,19625
4
d
S
mm
π
⋅
=
=
2
2, 2
11, 2
/
0,19625
J
A mm
=
≈
______________________________________________________________________
1.13
Dane:
Szukane:
Wzory:
1,5
AB
I
A
=
0,8
AB
R
=
Ω
3,8
A
V
V
=
B
V
=
'
B
V
=
R
U
I
=
1,5 0,8 1, 2
AB
U
V
=
⋅
=
A
AB
B
V
U
V
−
=
3,8 1, 2
2,6
B
V
V
=
−
=
'
A
AB
B
V
U
V
+
=
'
3,8 1, 2
5
B
V
V
=
+
=
______________________________________________________________________
1.14
Dane:
Szukane:
Wzory:
0 8
I
A
= ÷
2
R
= Ω
B
V
=
'
B
V
=
R
U
I
=
max
8 2
16
U
I R
V
∆
= ⋅ = ⋅ =
0
5
10
15
20
0
8
I [A]
dU [V]
dU=f(I)
______________________________________________________________________
1.15
Dane:
Szukane:
Wzory:
30
x
U
U
V
=
÷
0,6 5
I
A
=
÷
R
=
x
U
=
R
U
I
=
30
6
5
U
R
I
=
=
= Ω
0, 6 6
3, 6
x
U
V
=
⋅ =
______________________________________________________________________
1.16
Dane:
Szukane:
Wzory:
9
17, 25 10
Cu
m
ρ
−
=
⋅
Ω
1
ρ
γ
=
2
6
2
2
2
9
9
3
10
17, 25 10
17, 25 10
17, 25 10
0,01725
1
Cu
m
mm
mm
mm
m
m
m
m
ρ
−
−
−
Ω
Ω
Ω
Ω
=
⋅
=
⋅
⋅
=
⋅
=
6
6
9
6
2
2
1
1
57,97 10
57,97 10
57,97
17, 25 10
10
Cu
S
m
m
m
mm
mm
γ
−
=
≈
⋅
=
⋅
⋅
=
⋅
Ω
Ω
______________________________________________________________________
1.17
Dane:
Szukane:
Wzory:
9
18, 25 10
Cu
m
ρ
−
=
⋅
Ω
2
6
2
0,12
0,12 10
S
mm
m
−
=
=
⋅
500
l
m
=
R
=
l
R
S
ρ
=
9
6
500
18, 2 10
75,8
0,12 10
Cu
l
R
S
ρ
−
−
=
=
⋅
⋅
≈
Ω
⋅
______________________________________________________________________
1.18
Dane:
Szukane:
Wzory:
6
35 10
/
Al
S m
γ
= ⋅
150
l
m
=
1, 6
d
mm
=
R
=
1
ρ
γ
=
Al
l
R
S
γ
=
⋅
2
4
d
S
π
=
6
6
2
3,14 2, 56 10
2, 01 10
4
S
m
−
−
⋅
⋅
=
≈
⋅
6
6
150
2,13
35 10
2, 01 10
R
−
=
≈
Ω
⋅
⋅
⋅
______________________________________________________________________
1.19
Dane:
Szukane:
Wzory:
6
2, 23 10
/
S m
γ
=
⋅
12
D
mm
=
3
0, 05
0, 05 10
1, 5
1500
d
mm
m
R
k
−
=
=
⋅
=
Ω =
Ω
N
=
?
l
R
S
γ
=
⋅
2
4
d
S
π
=
O
d
π
=
2
6 2
9
2
3,14 (0, 05 10 )
1, 96 10
4
4
d
S
m
π
−
−
⋅
⋅
=
=
≈
⋅
6
9
1500 2, 32 10 1, 96 10
6,82
l
R
S
m
γ
−
= ⋅ ⋅ =
⋅
⋅
⋅
⋅
≈
6,82
180
(
)
3,14 0, 01205
l
N
D
d
π
=
=
≈
⋅
+
⋅
______________________________________________________________________
1.20
Dane:
Szukane:
Wzory:
6
55 10
/
Cu
S m
γ
= ⋅
1
1000
l
km
m
=
=
2
6
2
10
10 10
S
mm
m
−
=
= ⋅
3
3
8, 9 10
/
Cu
kg m
δ
=
⋅
?
?
?
R
m
d
=
=
=
Cu
l
R
S
γ
=
⋅
Cu
m
V
δ
=
⋅
V
S l
= ⋅
2
4
d
S
π
=
6
6
1000
1,82
55 10 10 10
R
−
=
≈
Ω
⋅
⋅ ⋅
3
6
8, 9 10 10 10
1000
89
Cu
Cu
m
V
S l
kg
δ
δ
−
=
⋅ =
⋅ ⋅ =
⋅
⋅ ⋅
⋅
=
2
4
4 10
3,57
3,14
S
mm
d
mm
π
⋅
=
=
≈
______________________________________________________________________
1.21
Dane:
Szukane:
Wzory:
6
55 10
/
Cu
S m
γ
= ⋅
6
35 10
/
Al
S m
γ
= ⋅
Cu
Al
l
l
l
=
=
Cu
Al
R
R
=
2
6
Cu
S
mm
=
Al
S
=
l
R
S
γ
=
⋅
Cu
Al
R
R
=
Cu
Cu
Al
Al
l
l
S
S
γ
γ
=
⋅
⋅
2
9, 43
Cu
Cu
Al
Al
S
S
mm
γ
γ
⋅
=
≈
⋅
______________________________________________________________________
1.22
Dane:
Szukane:
Wzory:
6
55 10
/
Cu
S m
γ
= ⋅
6
35 10
/
Al
S m
γ
= ⋅
3
3
8, 9 10
/
Cu
kg m
δ
=
⋅
3
3
2, 7 10
/
Al
kg m
δ
=
⋅
Cu
Al
l
l
l
=
=
Cu
Al
R
R
=
2
Cu
d
mm
=
Al
d
=
Cu
Al
m
m
=
l
R
S
γ
=
⋅
m
V
S l
δ
δ
= ⋅ = ⋅ ⋅
2
4
d
S
π
=
2
3,14
4
Cu
d
S
mm
π
=
=
Cu
Al
R
R
=
Cu
Cu
Al
Al
l
l
S
S
γ
γ
=
⋅
⋅
2
4, 93
Cu
Cu
Al
Al
S
S
mm
γ
γ
⋅
=
≈
⋅
4
4 4, 93
2, 51
3,14
S
d
mm
π
⋅
=
=
≈
2,1
Cu
Cu
Cu
Cu
Cu
Al
Al
Al
Al
Al
m
S
l
S
m
S
l
S
δ
δ
δ
δ
⋅
⋅
⋅
=
=
≈
⋅
⋅
⋅
______________________________________________________________________
1.23
Dane:
Szukane:
Wzory:
6
50 10
/
S m
γ
=
⋅
2
6
2
100
100 10
S
mm
m
−
=
=
⋅
1
1000
l
km
m
=
=
400
I
A
=
U
=
l
R
S
γ
=
⋅
U
I R
= ⋅
6
6
1000
0, 2
50 10 100 10
l
R
S
γ
−
=
=
=
Ω
⋅
⋅
⋅
⋅
400 0, 2
80
U
I R
V
= ⋅ =
⋅
=
______________________________________________________________________
1.24
Dane:
Szukane:
Wzory:
6
0, 3
0, 3 10
d
mm
m
−
=
=
⋅
2, 4
l
m
=
17
R
=
Ω
ρ
=
l
R
S
ρ
=
2
4
d
S
π
⋅
=
l
R
S
ρ
=
2
2
6
4
0,5 10
4
d
R
R S
R
d
m
l
l
l
π
π
ρ
−
⋅
⋅
⋅
⋅ ⋅
=
=
=
=
⋅
Ω
______________________________________________________________________
1.25
Dane:
Szukane:
Wzory:
6
55 10
/
Cu
S m
γ
= ⋅
12
U
V
=
2, 5
I
A
=
2
6
2
25
25 10
Cu
S
mm
m
=
=
⋅
ρ
=
l
R
S
γ
=
R
U
I
=
4,8
U
R
I
=
=
Ω
2 l
R
S
γ
⋅
=
3300
2
R S
l
m
γ
=
=
______________________________________________________________________
1.26
Dane:
Szukane:
Wzory:
6
35 10
/
Al
S m
γ
= ⋅
0, 3
U
V
=
2
4
2
1
6
6
6 10
Al
S
cm
cm
cm
m
−
=
⋅
=
= ⋅
30
l
m
=
I
=
J
=
l
R
S
γ
=
R
U
I
=
I
J
S
=
2
6
4
30
0,1428 10
1, 428
35 10 6 10
l
R
m
S
γ
−
−
=
=
=
⋅
Ω =
Ω
⋅
⋅ ⋅
0, 3
210
0, 001428
U
I
A
R
=
=
=
2
2
6
2
35
/
0, 35
/
0, 35 10
/
I
J
A cm
A mm
A m
S
= =
=
=
⋅
______________________________________________________________________
1.27
Dane:
Szukane:
Wzory:
6
55 10
/
Cu
S m
γ
= ⋅
6
2
2
2 10
/
2
/
J
A m
A mm
= ⋅
=
200
l
m
=
U
=
l
R
S
γ
=
R
U
I
=
I
J
S
=
6
6
2 10 200
7, 27
55 10
l
U
I R
J S
V
S
γ
⋅
⋅
= ⋅ = ⋅ ⋅
=
≈
⋅
⋅
______________________________________________________________________
1.28
Dane:
Szukane:
Wzory:
1
20
o
C
υ
=
2
70
o
C
υ
=
1
45
R
=
Ω
1
0, 004
Cu
o
C
α
=
2
R
=
(
)
1
2
1
1
R
R
α ν ν
=
+
−
(
)
1
2
1
1
45(1 0, 2)
54
R
R
α ν ν
=
+
−
=
+
=
Ω
______________________________________________________________________
1.29
Dane:
Szukane:
Wzory:
1
18
o
C
υ
=
1
0,8
R
=
Ω
2
0, 9
R
=
Ω
1
0, 004
Cu
o
C
α
=
2
υ
=
(
)
1
2
1
1
R
R
α ν ν
=
+
−
(
)
2
1
2
1
1
R
R
α ν ν
=
+
−
2
1
2
1
1
49, 25
o
R
R
C
ν
ν
α
−
=
+ =
______________________________________________________________________
1.30
Dane:
Szukane:
Wzory:
14
0, 25
U
V
I
A
=
=
3
550
0, 5
0, 5 10
l
m
d
mm
m
−
=
=
=
⋅
6
55 10
/
Cu
S m
γ
= ⋅
1
0, 004
Cu
o
C
α
=
2
υ
=
(
)
1
2
1
1
R
R
α ν ν
=
+
−
U
I
R
=
l
R
S
γ
=
⋅
2
4
d
S
π
=
Za temperaturę początkową przyjmujemy
1
20
o
C
υ
=
dlatego że współczynnik rezystancyjny
odnosi się do tej temperatury.
2
3 2
6
2
3,14(0, 5 10 )
0,196 10
4
4
d
S
m
π
−
−
⋅
=
=
=
⋅
1
6
6
550
51
55 10 0,196 10
Cu
l
R
S
γ
−
=
=
=
Ω
⋅
⋅
⋅
⋅
2
14
56
0, 25
U
R
I
=
=
=
Ω
2
1
2
1
1
44, 5
o
Cu
R
R
C
ν
ν
α
−
=
+ =
______________________________________________________________________
1.31
Dane:
Szukane:
Wzory:
1
20
o
C
υ
=
2
60
o
C
υ
=
1
100
R
=
Ω
2
116
R
=
Ω
α
=
(
)
1
2
1
1
R
R
α ν ν
=
+
−
(
)
2
1
2
1
1
R
R
α ν ν
=
+
−
2
1
2
1
1
1
0, 004
o
R
R
C
α
ν ν
−
=
=
−
______________________________________________________________________
1.32
Dane:
Szukane:
Wzory:
1
10
o
C
υ
=
2
60
o
C
υ
=
1
3, 5
I
A
=
1
0, 004
Cu
o
C
α
=
U
const
=
2
I
=
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
U
I
R
=
(
)
2
1
2
1
1
U
U
I
I
α ν ν
=
+
−
(
)
1
2
2
1
3, 5
2, 92
1, 2
1
I U
I
A
U
α ν ν
=
=
≈
+
−
______________________________________________________________________
1.33
Dane:
Szukane:
Wzory:
1
20
o
C
υ
=
2
30
o
C
υ
=
1
100
R
=
Ω
2
85
R
=
Ω
α
=
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
U
I
R
=
2
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
2
1
2
1
1
0,15
1
0, 015
10
o
R
R
C
α
ν ν
−
−
=
=
= −
−
______________________________________________________________________
1.34
Dane:
Szukane:
Wzory:
1
0, 004
Cu
o
C
α
=
2
1
1
1 %
R
R
R
= +
⋅
2
2
υ υ
− =
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
2
1
1
1
1 %
1, 01
R
R
R
R
= +
⋅ = ⋅
2
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
1
1
2
1
1, 01
[1
(
)]
R
R
α ν ν
⋅ =
+
−
2
1
1, 01 1
0, 01
2, 5
0, 004
o
C
ν ν
α
−
− =
=
=
______________________________________________________________________
1.35
Dane:
Szukane:
Wzory:
1
0, 004
Cu
o
C
α
=
4
Mn
Cu
R
R
=
2
1
1
o
C
υ υ
− =
CuMn
α
=
2
1
2
1
100%
R
R
x
R
υ
−
=
_ 2
100%
Cu
Cu
Cu
Cu
R
R
x
R
υ
−
=
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
1
5
MN
Cu
Cu
R
R
R
R
=
+
=
2
2
1
[1
(
)]
4
(1 0, 004)
5, 004
MN
Cu
Cu
Cu
Cu
R
R
R
R
R
R
α ν ν
=
+
+
−
=
+
+
=
2
1
1
5, 004
5
100%
100%
0, 08%
5
Cu
Cu
Cu
R
R
R
R
x
R
R
−
−
=
=
=
_ 2
2
1
2
1
[1
(
)]
0, 004
100%
100%
100%
0, 398%
[1
(
)]
1, 004
Cu
Cu
Cu
Cu
Cu
Cu
Cu
R
R
R
R
x
R
R
υ
α ν ν
α ν ν
−
+
−
−
=
=
=
=
+
−
2
1
2
1
1
1, 0008 1
1
0, 0008
1
o
R
R
C
α
ν ν
−
−
=
=
=
−
______________________________________________________________________
1.36
Dane:
Szukane:
Wzory:
1
0, 0046
W
o
C
α
=
1
40
R
=
Ω
2
32
R
=
Ω
1
0
o
C
υ
=
2
υ
=
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
2
1
2
1
[1
(
)]
R
R
α ν ν
=
+
−
~
2
1
2
1
1
0, 2
43, 48
0, 0046
o
R
R
C
ν
ν
α
−
−
=
+ =
≈ −
______________________________________________________________________
1.37
Dane:
Szukane:
Wzory:
1
20
R
=
Ω
2
40
R
=
Ω
12
U
V
=
1
2
R
U
U
=
=
=
1
2
R
R
R
=
+
U
I R
= ⋅
1
2
60
R
R
R
= +
=
Ω
/
0, 2
I
U R
A
=
=
1
1
2
2
0, 2 20
4
0, 2 40
8
U
I R
V
U
I R
V
= ⋅ =
⋅
=
= ⋅
=
⋅
=
______________________________________________________________________
1.38
Dane:
Szukane:
Wzory:
1
8
R
= Ω
2
16
R
=
Ω
3
10
R
=
Ω
4
21
R
=
Ω
220
U
V
=
1
2
R
U
U
=
=
=
1
2
...
R
R
R
= +
+
U
I R
= ⋅
1
2
3
4
8 16 10 21 55
R
R
R
R
R
= +
+
+
= + + +
=
Ω
/
220 / 55
4
I
U R
A
=
=
=
1
1
2
2
2
3
2
4
4 8
32
4 16
64
4 10
40
4 21 84
U
I R
V
U
I R
V
U
I R
V
U
I R
V
= ⋅ = ⋅ =
= ⋅
= ⋅ =
= ⋅
= ⋅ =
= ⋅
= ⋅ =
______________________________________________________________________
1.39
Dane:
Szukane:
Wzory:
20
R
=
Ω
0 100
N
R
= ÷
Ω
120
U
V
=
o
o
I
U
=
=
1
2
R
R
R
=
+
U
I R
= ⋅
120
z
N
R
R
R
= +
=
Ω
1
2
/
6
/
1
o
o
z
I
U R
A
I
U R
A
=
=
=
=
1
2
120 1 100
20
120 6 0 120
o
N
o
N
U
U
I R
V
U
U
I R
V
= − ⋅
=
− ⋅
=
= − ⋅
=
− ⋅ =
______________________________________________________________________
1.40
Dane:
Szukane:
Wzory:
20
R
=
Ω
6
15
N
U
V
U
V
=
=
x
R
=
1
2
R
R
R
=
+
U
I R
= ⋅
/
0, 3
N
I
U
R
A
=
=
9
30
x
N
x
x
U
U
U
V
U
R
I
= −
=
=
=
Ω
______________________________________________________________________
1.41
Dane:
Szukane:
Wzory:
1
R
= Ω
0,8
0, 32
x
N
U
V
U
V
=
=
x
R
=
1
2
R
R
R
=
+
U
I R
= ⋅
/
0, 32
2, 5
N
N
x
x
I
U
R
A
U
R
I
=
=
=
=
Ω
______________________________________________________________________
1.42
Dane:
Szukane:
Wzory:
20
200
N
I
A
l
m
=
=
6
35 10
/
Al
S m
γ
= ⋅
230
220
N
U
V
U
V
=
=
S
=
U
I R
= ⋅
l
R
S
γ
=
10
p
N
U
U
U
V
= −
=
0, 5
p
p
N
U
R
I
=
=
Ω
6
2
2
6
2
2 200
22,857 10
22,857
35 10 0, 5
l
S
m
mm
R
γ
−
⋅
⋅
=
=
=
⋅
=
⋅
⋅
______________________________________________________________________
1.43
Dane:
Szukane:
Wzory:
44
275
R
l
m
=
Ω
=
6
55 10
/
Cu
S m
γ
= ⋅
2
225
10
U
V
S
mm
=
=
o
l
I
U
U
=
=
=
U
I R
= ⋅
l
R
S
γ
=
6
6
2
2 275
1
55 10 10 10
l
l
R
S
γ
−
⋅
⋅
=
=
= Ω
⋅
⋅ ⋅
225
5
45
p
U
I
A
R
R
=
=
=
+
5
l
l
U
I R
V
= ⋅ =
220
o
l
U
U
U
V
= −
=
______________________________________________________________________
1.44
Dane:
Szukane:
Wzory:
30
30000
V
R
k
=
Ω =
Ω
60
6
V
U
V
U
V
=
=
R
=
U
I R
= ⋅
6
0, 2
30
V
V
U
I
mA
R
k
=
=
=
Ω
54
o
V
U
U
U
V
= −
=
270
o
U
R
k
I
=
=
Ω
______________________________________________________________________
1.45
Dane:
Szukane:
Wzory:
3
500
0,5 10
100
a
a
I
A
A
R
µ
−
=
=
⋅
=
Ω
1
2
3
5
20
100
U
V
U
V
U
V
=
=
=
1
2
3
R
R
R
=
=
=
U
I R
= ⋅
3
0, 5 10
100
0, 05
a
a
a
U
I
R
V
−
= ⋅
=
⋅
⋅
=
1
1
3
5 0, 05
9, 9
0, 5 10
a
U
U
R
k
I
−
−
−
=
=
=
Ω
⋅
2
1
2
3
20 5
30
0, 5 10
U
U
R
k
I
−
−
−
=
=
=
Ω
⋅
3
2
3
3
100 20
160
0, 5 10
U
U
R
k
I
−
−
−
=
=
=
Ω
⋅
______________________________________________________________________
1.46
Dane:
Szukane:
Wzory:
1
2
2
3
1
3
2
2
3
3
5
2
5
I
A
R
R
R
R
R
R
=
=
=
=
70
U
V
=
1
2
3
R
R
R
=
=
=
U
I R
= ⋅
2
1
3
2
R
R
= ⋅
3
1
5
2
R
R
= ⋅
1
2
3
1
1
1
1
1
3
5
10
5
2
2
2
R
R
R
R
R
R
R
R
R
= +
+
= + ⋅ + ⋅ = ⋅
= ⋅
1
1
5
70
7
5
10
U
R
I
U
R
I
U
R
I
=
=
=
=
= Ω
2
1
3
1
3
10, 5
2
5
17, 5
2
R
R
R
R
= ⋅ =
Ω
= ⋅ =
Ω
______________________________________________________________________
1.47
Dane:
Szukane:
Wzory:
1
2
360
40
R
R
=
Ω
=
Ω
200
U
V
=
2
U
=
U
I R
= ⋅
1
2
2
2
0, 5
20
U
I
A
R
R
U
R I
V
=
=
+
=
⋅ =
______________________________________________________________________
1.48
Dane:
Szukane:
Wzory:
1
2
750
4
R
U
U
=
Ω
=
2
R
=
U
I R
= ⋅
1
2
1
4
U
U
U
U
U
U
=
+
=
+
1
1
1
2
1
3
4
3
4
4
1000
3
250
U
U
I R
I R
R
R
R
R
R
=
⋅ = ⋅
= ⋅ =
Ω
= − =
Ω
______________________________________________________________________
1.49
Dane:
Szukane:
Wzory:
1
2
3
10
30
60
R
R
R
=
Ω
=
Ω
=
Ω
300
U
V
=
U
=
U
I R
= ⋅
1
2
3
1
1
2
2
3
3
12
1
2
23
2
3
1
2
3
300
3
100
30
90
180
120
270
300
R
R
R
R
R
R
R
R
R
R
R
R
U
I
A
R
R
R
U
I R
V
U
I R
V
U
I R
V
U
U
U
V
U
U
U
V
U
U
U
U
V
=
=
=
+
+
= ⋅ =
= ⋅
=
= ⋅
=
=
+
=
=
+
=
=
+
+
=
______________________________________________________________________
1.50
Dane:
Szukane:
Wzory:
5
1
R
k
I
mA
=
Ω
=
600
U
V
=
x
R
=
U
I R
= ⋅
3
600
5000
595
10
595
x
x
x
U
I
R
R
U
R
R
k
I
R
k
−
=
+
= − =
−
=
Ω
≥
Ω
______________________________________________________________________
1.51
Dane:
Szukane:
Wzory:
5
4
3
2
1
400
0, 25
0, 3
0, 35
0, 4
0, 45
0, 5
wzb
wzb
R
I
A
I
A
I
A
I
A
I
A
I
A
=
Ω
=
=
=
=
=
=
200
U
V
=
x
R
=
U
I R
= ⋅
1
2
R
R
R
= +
+
…
1
1
wzb
U
I
R
R
=
+
1
1
200
400
44, 44
0, 45
wzb
U
R
R
I
=
−
=
−
=
Ω
2
1
2
wzb
U
I
R
R
R
=
+
+
2
1
2
200
(
)
444, 44
55, 56
0, 4
wzb
U
R
R
R
I
=
−
+
=
−
=
Ω
3
1
2
3
wzb
U
I
R
R
R
R
=
+
+
+
3
1
2
3
200
(
)
500
71, 43
0, 35
wzb
U
R
R
R
R
I
=
−
+ +
=
−
=
Ω
4
1
2
3
4
wzb
U
I
R
R
R
R
R
=
+
+
+
+
4
1
2
3
4
200
(
)
571, 43
95, 24
0, 3
wzb
U
R
R
R
R
R
I
=
−
+ +
+
=
−
=
Ω
5
1
2
3
4
4
wzb
U
I
R
R
R
R
R
R
=
+
+
+
+
+
5
1
2
3
4
5
200
(
)
666, 67
133, 33
0, 25
wzb
U
R
R
R
R
R
R
I
=
−
+ +
+
+
=
−
=
Ω
______________________________________________________________________
1.52
Dane:
Szukane:
Wzory:
1
2
3
1
9
18
12
2
R
R
R
I
A
= Ω
= Ω
=
Ω
=
x
z
z
I
R
G
=
=
=
U
I R
= ⋅
1
2
1
1
1
R
R
R
=
+
+
…
1
1
2
2
3
3
2 9 18
18
1
18
18
1, 5
12
U
I R
V
U
I
A
R
U
I
A
R
= ⋅ = ⋅ =
=
=
=
=
=
=
1
2
3
2 1 1, 5
4, 5
I
I
I
I
A
= + + = + +
=
1
2
3
1
1
1
1
1
1
1
9
9
18
12
36
4
z
z
R
R
R
R
R
=
+
+
= +
+
=
= Ω
lub
18
4
4, 5
z
U
R
I
=
=
= Ω
1
1
0, 25
4
z
z
G
S
R
=
= =
______________________________________________________________________
1.53
Dane:
Szukane:
Wzory:
1
200
250
R
R
=
Ω
=
Ω
2
R
=
1
2
1
1
1
R
R
R
=
+
1
2
1
50000
1000
50
R R
R
R
R
⋅
=
=
=
Ω
−
______________________________________________________________________
1.54
Dane:
Szukane:
Wzory:
1
2
2
4
6
8
R
R
R
= Ω
= Ω
= Ω
12
U
V
=
1
2
3
R
G
I
I
I
=
=
=
=
=
1
2
3
1
1
1
1
R
R
R
R
=
+
+
1
G
R
=
U
I
R
=
1
2
3
1
1
1
1
1
1
1
6 4 3
13
4
6
8
24
24
R
R
R
R
+ +
=
+
+
= + + =
=
24
1,846
13
R
=
≈
Ω
1
0, 542
G
S
R
= ≈
1
1
2
2
3
3
12
3
4
12
2
6
12
1, 5
8
U
I
A
R
U
I
A
R
U
I
A
R
=
=
=
=
=
=
=
=
=
______________________________________________________________________
1.55
Dane:
Szukane:
Wzory:
1
2
60
90
R
R
=
Ω
=
Ω
1
I
A
=
1
2
I
I
=
=
1
2
1
1
1
R
R
R
=
+
U
I
R
=
1
1
1
3 2
5
60
90
180
180
180
36
5
R
R
+
=
+
=
=
=
=
Ω
36
U
I R
V
= ⋅ =
1
1
2
2
36
0, 6
60
36
0, 4
90
U
I
A
R
U
I
A
R
=
=
=
=
=
=
______________________________________________________________________
1.56
Dane:
Szukane:
Wzory:
1
2
3
4
8
10
20
15
R
R
R
R
= Ω
=
Ω
=
Ω
=
Ω
41
I
A
=
1
2
3
4
I
I
I
I
=
=
=
=
1
2
3
4
1
1
1
1
1
R
R
R
R
R
=
+
+
+
U
I
R
=
1
1
1
1
1
0,125 0,1 0, 05 0, 06667
0, 34167
8
10
20
15
1
1
1
1
1
15 12 6 8
41
0, 34167
8
10
20
15
120
120
120
2, 9268
41
R
R
R
= +
+
+
=
+
+
+
=
+ + +
= +
+
+
=
=
=
=
≈
Ω
120
U
I R
V
= ⋅ =
1
1
2
2
3
3
4
4
120
15
8
120
12
10
120
6
20
120
8
15
U
I
A
R
U
I
A
R
U
I
A
R
U
I
A
R
=
=
=
=
=
=
=
=
=
=
=
=
______________________________________________________________________
1.57
Dane:
Szukane:
Wzory:
0,18
5
a
R
I
A
=
Ω
=
0, 5
a
I
A
=
B
R
=
1
2
1
1
1
R
R
R
=
+
U
I
R
=
1
2
I
I
I
= +
0, 09
a
a
U
I
R
V
= ⋅
=
4, 5
B
a
I
I
I
A
= − =
0, 09
0, 02
4, 5
B
B
U
R
I
=
=
=
Ω
______________________________________________________________________
1.58
Dane:
Szukane:
Wzory:
0, 5
2
0, 002
b
a
R
I
mA
A
=
Ω
=
=
'
0, 04
a
I
A
=
20
U
V
=
p
R
=
1
2
1
1
1
R
R
R
=
+
U
I
R
=
1
2
I
I
I
= +
'
0, 04 0, 002
0, 038
0, 019
0, 019
9, 5
0, 002
b
a
a
a
b
b
a
a
a
I
I
I
A
U
I
R
V
U
R
I
= − =
−
=
= ⋅
=
=
=
=
Ω
: napięcie na układzie amperomierz / bocznik
20 0, 019 19, 981
p
a
U
U
U
V
= −
=
−
=
'
19, 981
9990, 5
0, 002
p
p
a
U
R
I
=
=
=
Ω
:odłączony bocznik, a do amperomierza dołączony posobnik
______________________________________________________________________
1.59
Dane:
Szukane:
Wzory:
0, 02
a
R
=
Ω
3
2
2 10
20
0, 2
0,8
a
d
mm
m
l
cm
m
I
A
−
=
= ⋅
=
=
=
6
55 10
/
Cu
S m
γ
= ⋅
odb
I
=
1
2
1
1
1
R
R
R
=
+
U
I
R
=
1
2
I
I
I
= +
l
R
S
γ
=
2
4
d
S
π
=
6
6
2
3,14 4 10
3,14 10
4
S
mm
−
−
⋅ ⋅
=
=
⋅
3
6
6
0, 2
1,158 10
55 10 3,14 10
b
R
−
−
=
=
⋅
Ω
⋅
⋅
⋅
3
0,8 0, 02
13,82
1,158 10
14, 62
b
b
b
a
a
a
b
a
b
b
a
a
a
a
b
b
odb
a
b
U
I
R
U
I
R
U
U
I
R
I
R
I
R
I
A
R
I
I
I
A
−
= ⋅
= ⋅
=
⋅
= ⋅
⋅
⋅
=
=
=
⋅
= + =
______________________________________________________________________
1.60
Dane:
Szukane:
Wzory:
1000
20
5
R
M
szt
i
km
l
km
=
Ω
=
=
x
R
=
1
R
R
n
=
100
n
i l
= ⋅ =
1
1000
10
100
R
R
M
n
=
=
=
Ω
______________________________________________________________________
1.61
Dane:
Szukane:
Wzory:
50
12
s
r
R
R
=
Ω
=
Ω
1
2
R
R
=
=
1
2
1
2
1
2
r
s
R R
R
R
R
R
R
R
⋅
=
+
= +
1
2
1
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
(
)
(
)
0
50 600
0
s
r
s
r
s
r
s
s
r
s
s
s
r
s
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
1
4
2500 2400 100
50 10
20
2
2
b
ac
b
x
a
∆ = −
=
−
=
− − ∆
−
=
=
=
2
50 10
30
2
2
b
x
a
− + ∆
+
=
=
=
2
30
R
=
Ω
1
2
50 30
20
s
R
R
R
=
−
=
−
=
Ω
______________________________________________________________________
1.62
Dane:
Szukane:
Wzory:
240
16
3
r
s
U
V
I
A
I
A
=
=
=
1
2
R
R
=
=
1
2
1
2
1
2
r
s
R R
R
R
R
R
R
R
⋅
=
+
= +
U
R
I
=
1
2
1
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
240
80
3
240
15
16
(
)
(
)
0
80 1200
0
s
s
r
R
s
r
s
r
s
r
s
s
r
s
s
s
r
s
U
R
I
U
R
I
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
=
=
=
Ω
=
=
=
Ω
=
−
⋅
=
+
−
⋅
=
−
+
⋅
=
−
⋅
⋅
=
⋅ − ⋅
− ⋅ + ⋅
=
− ⋅ +
=
2
1
4
6400 4800 1600
80 40
20
2
2
b
ac
b
x
a
∆ = −
=
−
=
− − ∆
−
=
=
=
2
80 40
60
2
2
b
x
a
− + ∆
+
=
=
=
2
60
R
=
Ω
1
2
80 60
20
s
R
R
R
=
−
=
−
=
Ω
______________________________________________________________________
1.63
Dane:
Szukane:
Wzory:
8
0, 4
1000
v
U
V
I
A
R
=
=
=
Ω
%
∆ =
U
R
I
=
1
1
1
v
o
R
R
R
=
+
8
20
0, 4
1
1
1
1
1
1
20000
20, 408
980
v
o
o
v
v
o
v
U
R
I
R
R
R
R
R
R
R R
R
R
R
=
=
=
Ω
=
+
= −
⋅
=
=
≈
Ω
−
0, 408
%
100%
100%
2%
20, 408
o
o
R
R
R
−
∆ =
=
=
______________________________________________________________________
1.64
Dane:
Szukane:
Wzory:
100, 5
0, 5
100
0, 505
20000
1
vA
a
vB
b
v
a
U
V
I
A
U
V
I
A
R
R
=
=
=
=
=
Ω
= Ω
%
∆ =
U
R
I
=
100, 5
201
0, 5
100, 5
1
200
0, 5
1
%
100%
100%
0, 5%
200
vA
A
a
vA
a
o
vA
a
a
a
oA
vA
a
oA
a
vA
oA
a
a
oA
A
oA
U
R
I
U
U
U
U
I
R
I
R
U
R
R
I
U
R
R
I
R
R
R
=
=
=
Ω
=
+
= ⋅
+ ⋅
+
=
=
−
=
− =
Ω
−
−
∆ =
⋅
=
⋅
= −
100
198, 0198
0, 505
100
0, 005
20000
100
200
0, 505 0, 005
200 198, 0198
%
100%
100%
0, 99%
200
b
B
b
b
v
v
b
v
o
b
ob
o
b
ob
b
v
ob
B
ob
U
R
I
U
I
A
R
I
I
I
U
R
I
U
R
I
I
R
R
R
=
=
=
Ω
=
=
=
= +
=
=
=
=
Ω
−
−
−
−
∆ =
=
=
______________________________________________________________________
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