7.51
Dane:
Szukane:
Wzory:
0, 5
120
50
L
H
R
f
Hz
=
=
Ω
=
Z
=
1
1
2
C
x
C
fC
ω
π
=
=
2
L
x
L
fL
ω
π
=
=
2
2
L
Z
R
x
=
+
2
L
x
L
fL
ω
π
=
=
(
)
(
)
2
2
2
2
2
2
2
120
2 3,14 50 0, 5
14400 24649
197, 6
L
Z
R
x
R
fL
π
=
+
=
+
=
+ ⋅
⋅ ⋅
=
=
+
≈
Ω
______________________________________________________________________
7.52
Dane:
Szukane:
Wzory:
8
5
10
10
400
4 10
50
C
nF
F
R
k
f
Hz
−
=
=
=
Ω = ⋅
Ω
=
Z
ϕ
=
=
1
1
2
C
x
C
fC
ω
π
=
=
2
L
x
L
fL
ω
π
=
=
2
2
Z
R
x
=
+
8
8
1
1
1
10
318471
2
2 3,14 50 10
314
C
x
C
fC
ω
π
−
=
=
=
=
=
Ω
⋅
⋅ ⋅
R
x
L
Z
(
)
2
2
2
2
2
5
2
10
3
1
4 10
318471
2
16 10
101423777841
511 10
0, 511
C
Z
R
x
R
fC
M
π
=
+
=
+
=
⋅
+
=
=
⋅
+
≈
⋅
Ω =
Ω
5
5
0
3,1847 10
tg
0, 7962
4 10
38 32 '
C
x
R
ϕ
ϕ
⋅
=
=
=
⋅
= −
______________________________________________________________________
7.53
Dane:
Szukane:
Wzory:
0, 5
120
0 :1000
L
H
R
f
Hz
=
=
Ω
=
( )
Z
F f
=
1
1
2
C
x
C
fC
ω
π
=
=
2
L
x
L
fL
ω
π
=
=
2
2
L
Z
R
x
=
+
2
L
x
L
fL
ω
π
=
=
(
)
2
2
2
2
2
L
Z
R
x
R
fL
π
=
+
=
+
R
X
C
Z
φ
0
500
1000
1500
2000
2500
3000
3500
0
200
400
600
800
1000
Ω
f[Hz]
Z=F(f)
______________________________________________________________________
7.54
Dane:
Szukane:
Wzory:
0, 51
120
230
50
L
H
R
U
V
f
Hz
=
=
Ω
=
=
R
L
Z
I
U
U
=
=
=
=
1
1
2
C
x
C
fC
ω
π
=
=
2
L
x
L
fL
ω
π
=
=
2
2
L
Z
R
x
=
+
U
I
Z
=
2
2 3,14 50 0, 51 160
L
x
L
fL
ω
π
=
=
= ⋅
⋅ ⋅
≈
Ω
2
2
2
2
120
160
40000
200
L
Z
R
x
=
+
=
+
=
=
Ω
230
1,15
200
U
I
A
Z
=
=
=
1,15 120 138
1,15 160
184
R
L
L
U
IR
V
U
Ix
V
=
=
⋅
=
=
=
⋅
=
______________________________________________________________________
7.55
Dane:
Szukane:
Wzory:
0, 255
80
24
50
L
H
R
U
V
f
Hz
=
=
Ω
=
=
R
L
I
U
U
ϕ
=
=
=
=
1
1
2
C
x
C
fC
ω
π
=
=
2
L
x
L
fL
ω
π
=
=
2
2
L
Z
R
x
=
+
U
I
Z
=
2
2 3,14 50 0, 255
80
L
x
L
fL
ω
π
=
=
= ⋅
⋅ ⋅
≈
Ω
2
2
2
2
80
80
12800
113
L
Z
R
x
=
+
=
+
=
=
Ω
24
0, 212
113
U
I
A
Z
=
=
=
0, 212 80 17
0, 212 80 17
R
L
L
U
IR
V
U
Ix
V
=
=
⋅ =
=
=
⋅ =
U
R
I
U
L
U
φ
R
x
L
Z
φ
0
17
tg
1
17
45
L
R
U
U
ϕ
ϕ
=
=
=
=
______________________________________________________________________
7.56
Dane:
Szukane:
Wzory:
0, 255
80
24
50
L
H
R
U
V
f
Hz
=
=
Ω
=
=
sin
m
u
U
t
ω
=
R
L
R
L
I
U
U
i
u
u
ϕ
=
=
=
=
=
=
=
1
1
2
C
x
C
fC
ω
π
=
=
2
L
x
L
fL
ω
π
=
=
2
2
L
Z
R
x
=
+
U
I
Z
=
2
2 3,14 50 0, 255
80
L
x
L
fL
ω
π
=
=
= ⋅
⋅ ⋅
≈
Ω
2
2
2
2
80
80
12800
113
L
Z
R
x
=
+
=
+
=
=
Ω
24
0, 212
113
U
I
A
Z
=
=
=
0, 212 80 17
0, 212 80 17
R
L
L
U
IR
V
U
Ix
V
=
=
⋅ =
=
=
⋅ =
U
R
I
U
L
U
φ
0
17
tg
1
17
45
L
R
U
U
ϕ
ϕ
=
=
=
=
0
0
0
sin(
45 )
sin(
45 )
sin(
45 )
m
R
Rm
L
Lm
i
I
t
u
U
t
u
U
t
ω
ω
ω
=
−
=
−
=
+
______________________________________________________________________
7.57
Dane:
Szukane:
Wzory:
2
L
x
L
fL
ω
π
=
=
2
tg
L
L
R
U
i x
fL
U
i R
R
π
ϕ
⋅
=
=
=
⋅
U
R
I
U
L
U
φ
U
R
I
U
L
U
φ
______________________________________________________________________
7.58
Dane:
Szukane:
Wzory:
1
1
2
C
x
C
fC
ω
π
=
=
1
tg
2
C
C
R
U
i x
U
i R
fCR
ϕ
π
⋅
=
=
=
⋅
______________________________________________________________________
7.59
Dane:
Szukane:
Wzory:
30
0, 6
50
40
U
V
I
A
f
Hz
R
=
=
=
=
Ω
L
=
1
1
2
2
C
L
x
C
fC
x
L
fL
ω
π
ω
π
=
=
=
=
U
R
I
U
C
U
φ
0
0, 6 40
24
24
cos
0,8
30
36 08 '
sin
sin
30 0, 5897
17, 69
17, 69
29, 485
0, 6
2
29, 485
0, 0939
93, 9
2
2 3,14 50
R
R
L
L
L
L
L
L
U
IR
V
U
U
U
U
U
U
V
U
x
I
x
fL
x
L
H
mH
f
ϕ
ϕ
ϕ
ϕ
π
π
=
=
⋅
=
=
=
=
=
=
=
=
⋅
=
=
=
=
Ω
=
=
=
≈
=
⋅
⋅
______________________________________________________________________
7.60
Dane:
Szukane:
Wzory:
4, 2
0,14
75
50
1,5
U
V
I
A
U
V
f
Hz
I
A
=
=
=
=
=
=
=
L
x
L
=
=
1
1
2
2
C
L
x
C
fC
x
L
fL
ω
π
ω
π
=
=
=
=
0
4, 2
30
0,14
1, 5 30
45
45
cos
0, 6
75
53 52 '
sin
sin
75 0,8077
60, 58
60, 58
40, 38
1, 5
2
40, 38
0,1286
128, 6
2
2 3,14 50
R
R
L
L
L
L
L
L
U
R
I
U
IR
V
U
U
U
U
U
U
V
U
x
I
x
fL
x
L
H
mH
f
ϕ
ϕ
ϕ
ϕ
π
π
=
=
=
=
=
Ω
=
=
⋅
=
=
=
=
=
=
=
=
⋅
=
=
=
=
Ω
=
=
=
≈
=
⋅
⋅
______________________________________________________________________
7.61
Dane:
Szukane:
Wzory:
10
200
75
0,8
R
L
H
U
V
f
MHz
µ
=
Ω
=
=
=
L
x
Q
=
=
1
1
2
2
C
L
x
C
fC
x
L
fL
ω
π
ω
π
=
=
=
=
L
x
Q
R
=
6
3
2
2 3,14 0,8 10 0, 2 10
1005
1005
100, 5
10
L
L
x
fL
x
Q
R
π
−
=
= ⋅
⋅
⋅
⋅
⋅
≈
Ω
=
=
=
______________________________________________________________________
7.62
Dane:
Szukane:
Wzory:
27
0,1146
2
50
' 1, 5
R
L
H
I
A
f
Hz
I
A
=
Ω
=
=
=
=
'
f
=
1
1
2
2
C
L
x
C
fC
x
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
2
2
2
2
2
2
2 3,14 50 0,1146
35, 9844
36
27
36
2023,88
45
2 45
90
90
'
60
'
1, 5
'
60
27
2871
53, 58
53, 58
74, 5
2
2 3,14 0,1146
L
L
L
L
x
fL
Z
R
x
U
I Z
V
U
Z
I
x
Z
R
x
f
Hz
L
π
π
=
= ⋅
⋅ ⋅
=
≈
Ω
=
+
=
+
=
=
Ω
= ⋅ = ⋅
≈
=
=
=
Ω
=
−
=
−
=
≈
Ω
=
=
≈
⋅
⋅
______________________________________________________________________
7.63
Dane:
Szukane:
Wzory:
120
0, 5
100
'
8
4
U
V
I
A
f
Hz
I
A
R
=
=
=
=
= Ω
'
L
L
=
=
1
1
2
2
C
L
x
C
fC
x
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
2
120
240
0, 5
240
4
240
L
U
Z
I
x
Z
R
=
=
=
Ω
=
−
=
−
≈
Ω
240
0, 382
2
2 3,14 100
L
x
L
H
f
π
=
=
=
⋅
⋅
2
2
2
2
120
'
15
'
8
'
15
4
14, 46
L
U
Z
I
x
Z
R
=
=
=
Ω
=
−
=
−
≈
Ω
'
14, 46
0, 023
2
2 3,14 100
L
x
L
H
f
π
=
=
≈
⋅
⋅
______________________________________________________________________
7.64
Dane:
Szukane:
Wzory:
5
240
10
10
50
500
U
V
C
F
F
f
Hz
R
µ
−
=
=
=
=
=
Ω
R
C
Z
I
U
U
ϕ
=
=
=
=
=
1
1
2
2
C
L
x
C
fC
x
L
fL
ω
π
ω
π
=
=
=
=
5
5
2
2
2
2
2
2
1
1
10
318
2
2 3,14 50 10
314
(500
318)
500
318
592, 6
240
240(500
318)
(0, 3418
0, 2147)
500
318
500
318
240
0, 405
592, 6
C
C
C
x
fC
Z
R
jx
j
Z
R
x
U
j
I
j
A
Z
j
U
I
A
Z
π
−
=
=
=
=
Ω
⋅
⋅ ⋅
= −
=
−
Ω
=
+
=
+
=
Ω
+
=
=
=
=
+
−
+
=
=
=
0
0
0
0
0
500(0, 3418
0, 2174)
(170, 9
108, 7)
318(0, 3418
0, 2174)
(69,1
108, 7)
0
tg
0
240
0
0, 2174
tg
0, 636
0, 3418
32 28 '
32 28 ' 0
32 28 '
R
C
C
U
U
I
I
I
U
U
RI
j
j
V
U
jx I
j
j
j
V
ϕ
ϕ
ϕ
ϕ
ϕ ϕ ϕ
=
=
+
=
+
= −
= −
+
=
−
=
=
=
=
=
=
=
−
=
− =
______________________________________________________________________
7.65
Dane:
Szukane:
Wzory:
40
220
380
50
N
P
W
U
V
U
V
f
Hz
=
=
=
=
C
=
1
1
2
2
C
L
x
C
fC
x
L
fL
ω
π
ω
π
=
=
=
=
2
U
P
R
=
2
2
220
48400
1210
40
40
N
U
R
P
=
=
=
=
Ω
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
380
220
96000
309,8
1210
C
R
C
C
R
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
x
fC
U
U
U
U
U
U
V
U
Ix
U
I
x
U
Z
I
Z
R
x
U
R
x
I
U
R
x
U
x
U x
R
x
U
U x
R U
x U
U x
x U
R U
R U
x
U
U
RU
x
U
U
π
=
=
+
=
−
=
−
=
=
=
=
=
=
+
=
+
=
+
=
+
=
+
−
=
=
−
⋅
=
=
−
2
2
6
309,8
374858
1703, 9
220
380
309,8
1
1
1,87 10
1,87
2
2 3,14 50 1703, 9
C
C
F
F
fx
µ
π
−
=
=
Ω
−
=
=
=
⋅
=
⋅
⋅ ⋅
______________________________________________________________________
7.66
Dane:
Szukane:
Wzory:
6
3
1
2
2
2 10
5
5 10
40
50
10000
we
C
F
F
R
k
U
V
f
Hz
f
Hz
µ
−
=
= ⋅
=
Ω = ⋅
Ω
=
=
=
wy
U
=
1
1
2
C
X
C
fC
ω
π
=
=
2
2
2
Z
R
X
=
+
6
6
1
2
2
2
2
1
6
6
2
2
2
2
2
1
1
10
'
1592
2
2 3,14 50 2 10
628
'
'
5000
1592
5247
'
'
40
'
'
5000
38,1
'
5247
1
1
10
''
7, 96
8
2
2 3,14 10000 2 10
125600
''
''
5000
8
5000
''
''
'
C
C
we
we
wy
C
C
we
X
f C
Z
R
X
U
I
Z
U
U
I R
R
V
Z
X
f C
Z
R
X
U
I
Z
U
π
π
−
−
=
=
=
=
Ω
⋅
⋅ ⋅ ⋅
=
+
=
+
=
Ω
=
=
=
=
≈
=
=
=
=
Ω ≈ Ω
⋅
⋅
⋅ ⋅
=
+
=
+
≈
Ω
=
1
40
'
''
5000
40
''
5000
we
wy
U
I R
R
V
Z
=
=
=
≈
______________________________________________________________________
7.67
Dane:
Szukane:
Wzory:
1
3
1
2
3
2
5
1
10
8
3,19
3,19 10
3, 7
500
R
L
mH
H
R
L
mH
H
U
V
f
Hz
−
−
= Ω
=
=
= Ω
=
=
⋅
=
=
1
2
1
2
cos
cos
cos
L
L
Z
U
U
ϕ
ϕ
ϕ
=
=
=
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
2
2
2
2
2
3 2
1
1
1
1
1
1
1
1
2
2
2
2
2
3 2
2
2
2
2
2
2
2
2
(2
)
5
(2 3,14 500 10 )
25 9,86
5, 9
5
cos
0,8475
5, 9
(2
)
8
(2 3,14 500 3,19 10 )
64 100, 33
12,82
8
cos
0, 6240
12,82
L
L
Z
R
X
R
fL
R
Z
Z
R
X
R
fL
R
Z
π
ϕ
π
ϕ
−
−
=
+
=
+
=
+ ⋅
⋅
⋅
=
+
=
Ω
=
=
=
=
+
=
+
=
+ ⋅
⋅
⋅
⋅
=
+
≈
Ω
=
=
=
(
) (
)
(
) (
)
(
)
(
)
(
)
2
2
2
2
2
2
1
2
1
2
2
2
1
2
2
2
1
2
2
3 2
1
2
2
2
2
13
(2 3,14 500 4,19 10 )
169 173, 09
18, 5
5 8
cos
0, 7027
18, 5
L
L
Z
R
R
X
X
R
R
fL
fL
R
R
f L
L
R
R
Z
π
π
π
ϕ
−
=
+
+
+
=
+
+
+
=
+
+
+
=
=
+ ⋅
⋅
⋅
⋅
=
+
≈
Ω
+
+
=
=
=
1
1
2
2
3, 7
0, 2
18, 5
0, 2 5, 9 1,18
0, 2 12,82
2, 56
L
L
U
I
A
Z
U
I Z
V
U
I Z
V
=
=
=
= ⋅ =
⋅
=
= ⋅
=
⋅
=
______________________________________________________________________
7.68
Dane:
Szukane:
Wzory:
6
1
6
2
400
16
16 10
4
4 10
0, 25
50
R
C
F
F
C
F
F
I
A
f
Hz
µ
µ
−
−
=
Ω
=
= ⋅
=
= ⋅
=
=
1
'
'
'
'
C
R
I
U
U
ϕ
=
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
C
Z
R
X
=
+
(
)
(
)
2
2
2
2
1
2
1
2
2
2
2
6
6
2
2
2
2
2
2
2
2
1
6
1
1
1
2
2
1
1
400
160000
199 796
115025
1072
2 3,14 50 16 10
2 3,14 50 4 10
0, 25 1072
268
1
1
'
400
400
199
4
2
2 3,14 50 16 10
C
C
C
Z
R
X
X
R
fC
fC
U
I Z
V
Z
R
X
R
fC
π
π
π
−
−
−
=
+
+
=
+
+
=
=
+
+
=
+
+
=
≈
Ω
⋅
⋅ ⋅ ⋅
⋅
⋅ ⋅ ⋅
= ⋅ =
⋅
≈
=
+
=
+
=
+
=
+
≈
⋅
⋅ ⋅ ⋅
46,8
Ω
1
1
1
0
268
'
0, 6
'
446,8
'
'
0, 6 400
240
'
'
0, 6 199 119, 4
'
119, 4
tg
0, 4975
'
240
26 27 '
R
C
C
C
R
U
I
A
Z
U
I R
V
U
I X
V
U
U
ϕ
ϕ
=
=
≈
= ⋅ =
⋅
=
= ⋅
=
⋅
=
=
=
=
=
______________________________________________________________________
7.69
Dane:
Szukane:
Wzory:
6
60
28, 6
28, 6 10
100
0,1
50
R
C
F
F
L
mH
H
f
Hz
µ
−
=
Ω
=
=
⋅
=
=
=
Z
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
(
)
(
)
6
6
2
2
2
2
2
2 3,14 50 0,1 31, 4
1
1
10
111, 4
2
2 3,14 50 28, 6 10
8980
60
31, 4 111, 4
3600 6400
100
L
C
L
C
X
fL
X
fC
Z
R
X
X
π
π
−
=
= ⋅
⋅ ⋅
=
Ω
=
=
=
≈
Ω
⋅
⋅ ⋅
⋅
=
+
−
=
+
−
=
+
=
Ω
R
X
L
X
C
Z
______________________________________________________________________
7.70
Dane:
Szukane:
Wzory:
6
60
28, 6
28, 6 10
100
0,1
50
50
R
C
F
F
L
mH
H
f
Hz
U
V
µ
−
=
Ω
=
=
⋅
=
=
=
=
R
C
L
I
U
U
U
=
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
(
)
(
)
6
6
2
2
2
2
2
2 3,14 50 0,1 31, 4
1
1
10
111, 4
2
2 3,14 50 28, 6 10
8980
60
31, 4 111, 4
3600 6400
100
L
C
L
C
X
fL
X
fC
Z
R
X
X
π
π
−
=
= ⋅
⋅ ⋅
=
Ω
=
=
=
≈
Ω
⋅
⋅ ⋅
⋅
=
+
−
=
+
−
=
+
=
Ω
50
0, 5
100
0, 5 60
30
0, 5 31, 4 15, 7
0, 5 111, 4
55, 7
R
L
L
C
C
U
I
A
Z
U
IR
V
U
IX
V
U
IX
V
=
=
=
=
=
⋅
=
=
=
⋅
=
=
=
⋅
=
______________________________________________________________________
7.71
U
R
I
U
L
U
C
U
Dane:
Szukane:
Wzory:
6
150
31, 9
31, 9 10
0, 319
50
240
R
C
F
F
L
H
f
Hz
U
V
µ
−
=
Ω
=
=
⋅
=
=
=
C
RL
I
U
U
ϕ
=
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
(
)
(
)
2
2
2
2
6
6
2
2
2
2
2
2 3,14 50 0, 319 100
150
100
180, 3
1
1
10
99,8
2
2 3,14 50 31, 9 10
10017
150
100 99,8
150
L
L
L
C
L
C
X
fL
Z
R
X
X
fC
Z
R
X
X
π
π
−
=
= ⋅
⋅ ⋅
≈
Ω
=
+
=
+
≈
Ω
=
=
=
≈
Ω
⋅
⋅ ⋅
⋅
=
+
−
=
+
−
≈
Ω
240
1, 6
150
1, 6 180, 3
288, 5
1, 6 99,8 159, 7
RL
L
C
C
U
I
A
Z
U
IZ
V
U
IX
V
=
=
=
=
=
⋅
≈
=
=
⋅
≈
0
100 99,8
0, 2
sin
0, 0013
150
150
0 05 '
L
C
X
X
Z
ϕ
ϕ
−
−
=
=
=
=
=
______________________________________________________________________
7.72
Dane:
Szukane:
Wzory:
6
150
31, 9
31, 9 10
0, 319
100
240
R
C
F
F
L
H
f
Hz
U
V
µ
−
=
Ω
=
=
⋅
=
=
=
I
ϕ
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
(
)
(
)
2
2
2
2
6
6
2
2
2
2
2
2 3,14 100 0, 319
200
150
200
250
1
1
10
49, 91
50
2
2 3,14 100 31, 9 10
10017
150
200 50
212,13
L
L
L
C
L
C
X
fL
Z
R
X
X
fC
Z
R
X
X
π
π
−
=
= ⋅
⋅
⋅
≈
Ω
=
+
=
+
=
Ω
=
=
=
≈
Ω ≈
Ω
⋅
⋅
⋅
⋅
=
+
−
=
+
−
≈
Ω
240
1,13
212,13
U
I
A
Z
=
=
=
0
200 50
150
sin
0, 7071
212,13
213,13
45
L
C
X
X
Z
ϕ
ϕ
−
−
=
=
=
=
=
______________________________________________________________________
7.73
Dane:
Szukane:
Wzory:
6
50
6, 37
6, 37 10
0,8
50
200
C
R
C
F
F
L
H
f
Hz
U
V
µ
−
=
Ω
=
=
⋅
=
=
=
U
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
6
2
2 3,14 50 0,8
251
1
1
500
2
2 3,14 50 6, 37 10
200
0, 4
500
L
C
C
C
X
fL
X
fC
U
I
A
X
π
π
−
=
= ⋅
⋅ ⋅
≈
Ω
=
=
≈
Ω
⋅
⋅ ⋅
⋅
=
=
=
2
2
2
2
0, 4 50
20
0, 4 251 100, 4
(
)
20
(100, 4 200)
102
R
L
L
R
L
C
U
IR
V
U
IX
V
U
U
U
U
V
=
=
⋅
=
=
=
⋅
=
=
+
−
=
+
−
≈
______________________________________________________________________
7.74
Dane:
Szukane:
Wzory:
160
50
40
40
50
R
L
R
f
Hz
U
V
U
V
U
V
=
Ω
=
=
=
=
L
C
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
40
0, 25
160
R
U
I
A
R
=
=
=
40
160
0, 25
2
160
160
0, 51
2 3,14 50
314
50
200
0, 25
L
L
L
U
X
I
f
L
H
X
U
Z
I
π
=
=
=
Ω
=
=
=
≈
⋅
⋅
=
=
=
Ω
2
2
2
2
2
2
2
2
2
1
2
2
2
2
1
6
1
1
6
2
2
(
)
160
200
160
160 120
40
160
200
160
160 120
280
1
1
79, 6 10
79, 6
2
314 40
1
1
11, 37 10
11, 37
2
314 280
L
C
C
L
C
L
C
L
C
C
Z
R
X
X
X
X
Z
R
X
X
Z
R
X
X
Z
R
C
F
F
fX
C
F
F
fX
µ
π
µ
π
−
−
=
+
−
=
±
−
=
−
−
=
−
−
=
−
=
Ω
=
+
−
=
+
−
=
+
=
Ω
=
=
=
⋅
=
⋅
=
=
=
⋅
=
⋅
______________________________________________________________________
7.75
Dane:
Szukane:
Wzory:
0, 2
50
40
120
200
L
I
A
f
Hz
U
V
R
X
=
=
=
=
Ω
=
Ω
C
X
C
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
2
2
2
2
2
2
2
2
2
2
1
2
2
1
40
200
0, 2
(
)
(
)
200
200
120
200 160
360
200
200
120
200 160
40
L
C
L
C
C
L
C
C
U
Z
I
Z
R
X
X
X
X
Z
R
X
X
Z
R
X
X
=
=
=
Ω
=
+
−
−
=
−
=
±
−
=
+
−
=
+
=
Ω
=
−
−
=
−
=
Ω
6
1
1
6
2
2
1
1
1
8,85 10
8,85
2
2 3,14 50 360
113040
1
1
1
79, 6 10
79, 6
2
2 3,14 50 40
12560
C
C
C
F
F
fX
C
F
F
fX
µ
π
µ
π
−
−
=
=
=
≈
⋅
=
⋅
⋅ ⋅
=
=
=
≈
⋅
=
⋅
⋅ ⋅
______________________________________________________________________
7.76
Dane:
Szukane:
Wzory:
0
0
0, 2
50
40
120
200
j
L
I
A
f
Hz
U
V
R
X
=
=
=
=
Ω
=
Ω
C
L
R
U
U
U
U
=
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
0
0
0
0
0, 2
0, 2(cos 0
sin 0 )
0, 2(1
0)
0, 2
j
I
e
j
j
A
=
=
+
=
+
=
0
0
0
0
0
0
0
0
0
0
0
0
1
120 0, 2
24
24
200 0, 2
40
0, 2
0, 2
40(cos
sin )
24
40
0, 2
40 cos
40 sin )
24
(40
0, 2)
40 cos
24
24
cos
0, 6
40
53 08 '
sin 53 08 '
0
j
j
j
R
j
L
L
j
C
C
C
C
R
L
C
C
C
e
U
RI
e
e
V
U
jX I
j
e
j
V
U
jX I
jX
e
jX
U
U
U
U
j
j
jX
j
j
X
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
=
=
=
⋅
=
=
=
=
⋅
=
= −
= −
⋅
= −
⋅
=
+
+
±
=
+
−
⋅
±
=
+
−
⋅
=
=
=
=
=
,8
40 sin
(40
0, 2)
40 0,8
(40
0, 2)
32
(40
0, 2)
32
40
0, 2
'
40
C
C
C
C
C
j
j
X
j
j
X
j
j
X
X
X
ϕ
+
=
−
⋅
+
⋅
=
−
⋅
+
=
−
⋅
=
−
⋅
=
40 sin
( 40
0, 2)
40 0,8
( 40
0, 2)
32
( 40
0, 2)
32
40
0, 2
''
360
C
C
C
C
C
j
j
X
j
j
X
j
j
X
X
X
ϕ
−
= − +
⋅
−
⋅
= − − +
⋅
−
= − − +
⋅
= − +
⋅
=
'
0, 2
40 0, 2
8
''
0, 2
360 0, 2
72
C
C
C
C
U
jX
j
j V
U
jX
j
j
V
= −
⋅
= −
⋅
= −
= −
⋅
= −
⋅
= −
(
)
(
)
'
'
24
40
8
24
32
''
''
24
40
72
24
32
R
L
C
R
L
C
U
U
U
U
j
j
j
V
U
U
U
U
j
j
j
V
=
+
+
=
+
−
=
+
=
+
+
=
+
−
=
−
______________________________________________________________________
7.77
Dane:
Szukane:
Wzory:
120
:
:
2 : 3 : 4
R
L
C
U
V
R X
X
=
=
RC
RL
U
U
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
U’’
U’’
C
U
R
U
L
I
y
I
U
R
y
U
L
U’
C
U’
2
2
2
2
2
2
2
2
2
3
3
2
3
3
2
2
9
9
1
120 1,8
216
4
4
2
4
4
2
4
2
2
4
1 4
120 1,8
268
R
R
L
L
R
R
L
L
R
RL
R
L
R
R
C
C
R
C
C
R
RL
R
L
R
R
R
U
R
I
U
I
R
R
X
R
X
U
U
R
U
IX
R
U
U
U
U
U
U
V
R
X
R
X
U
R
U
IX
U
R
U
U
U
U
U
U
V
=
=
=
=
=
=
⋅
=
=
+
=
+
=
+ ≈
⋅
=
=
=
=
=
⋅
=
=
+
=
+
=
+ ≈
⋅
=
______________________________________________________________________
7.78
Dane:
Szukane:
Wzory:
U
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
I
y
U
R
U
L
U
C
U
RC
U
R
1
2
1
2
40
50
80
50
120
5
L
L
C
C
V
R
X
X
X
X
U
V
=
Ω
=
Ω
=
Ω
=
Ω
=
Ω
=
2
2
2
Z
R
X
=
+
2
2
2
2
2
1
1
1
2
2
1
1
2
2
2
2
2
2
1
2
1
2
(
)
40
30
50
5
0,1
50
0,1 50
5
0,1 40
4
0,1 80
8
0,1 50
5
0,1 120 12
(
)
0,1 40
40
5, 66
V
L
C
V
V
L
L
R
L
L
C
C
C
C
L
L
C
C
Z
R
X
X
U
I
A
Z
U
IX
V
U
IR
V
U
IX
V
U
IX
V
U
IX
V
U
IZ
I R
X
X
X
X
V
=
+
−
=
+
=
Ω
=
=
=
=
=
⋅
=
=
=
⋅
=
=
=
⋅ =
=
=
⋅
=
=
=
⋅
=
=
=
+
+
−
−
=
+
≈
______________________________________________________________________
7.79
Dane:
Szukane:
Wzory:
______________________________________________________________________
7.80
Dane:
Szukane:
Wzory:
r
f
=
U
1
U
2
U
3
U
4
U
5
U
6
U
12
160
250
R
L
H
C
pF
µ
=
Ω
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
3
9
6
12
1
1
1
796 10
796
2
2 3,14 10
160 250
2 3,14 160 10
250 10
r
f
kHz
LC
π
−
−
−
=
=
=
=
⋅
=
⋅
⋅
⋅
⋅
⋅
⋅
⋅
______________________________________________________________________
7.81
Dane:
Szukane:
Wzory:
3
9
465
465 10
1000
10
r
f
kHz
Hz
C
pF
F
−
=
=
⋅
=
=
r
f
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
(
)
9
6
2
6
1
10
117 10
117
4 9,86 216225 10
2
r
L
H
H
f
C
µ
π
−
=
=
≈
⋅
=
⋅
⋅
⋅
______________________________________________________________________
7.82
Dane:
Szukane:
Wzory:
6
4
1, 2
1, 2 10
100
10
r
f
MHz
Hz
L
H
H
µ
−
=
=
⋅
=
=
r
f
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
(
)
4
9
9
2
12
1
10
10
0,176 10
176
4 9,86 1, 44 10
5, 679
2
r
C
F
pF
f
L
π
−
−
=
=
=
≈
⋅
=
⋅
⋅
⋅
______________________________________________________________________
7.83
Dane:
Szukane:
Wzory:
9
3
20
20 10
20
20 10
10
0; 20;100
C
nF
F
L
mH
H
U
V
R
−
−
=
=
⋅
=
=
⋅
=
=
Ω
1;2;3
( )
r
f
I
F f
Q
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
C
C
L
L
r
X
U
X
U
Q
R
R
U
U
=
=
=
=
6
3
9
1
1
10
7962
6, 28 20
2
2 3,14 20 10
20 10
r
f
Hz
LC
π
−
−
=
=
=
≈
⋅
⋅
⋅
⋅ ⋅
1
2
2
2
2 3,14 7962 0, 02
0
2
2 3,14 7962 0, 02
50
20
2
2 3,14 7962 0, 02
10
100
L
r
r
L
r
r
L
r
r
X
f L
Q
R
R
X
f L
Q
R
R
X
f L
Q
R
R
π
π
π
⋅
⋅
⋅
=
=
=
≈ ∞
⋅
⋅
⋅
=
=
=
≈
⋅
⋅
⋅
=
=
=
≈
2
2
(
)
L
C
U
I
R
X
X
=
+
−
0
100
200
300
400
500
600
I[mA]
F[Hz]
______________________________________________________________________
7.84
Dane:
Szukane:
Wzory:
200
0, 318
25
50
f
Hz
L
H
U
V
R
=
=
=
=
Ω
;
L
C
R
C L
I
U
U
U
C
U
U
=
=
=
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
C
C
L
L
r
X
U
X
U
Q
R
R
U
U
=
=
=
=
(
)
(
)
6
2
2
1
1
1
2 10
2
501656
2
2 3,14 200
0, 318
C
F
F
f
L
µ
π
−
=
=
=
≈ ⋅
=
⋅
⋅
(
)
(
)
(
)
2
2
2
2
2
2
2
2
2
2
1
2
2
1
2
1
2
2
25
0, 5
50
2
2
2
L
C
U
U
U
I
R
X
X
R
fL
fC
R
fL
f
f
L
U
U
A
R
f
L
R
fL
f
π
π
π
π
π
π
π
π
=
=
=
=
+
−
+
−
+
−
=
=
=
=
+
−
6
6
0, 5
0, 5 10
200
2
2 3,14 200 2 10
2512
2
0, 5 2 3,14 200 0, 318
200
0, 5 50
25
200
8
25
200
8
25
C
C
L
L
R
L
C
I
U
I X
V
fC
U
I X
I
fL
V
U
I R
V
U
U
U
U
π
π
−
⋅
= ⋅
=
=
=
≈
⋅
⋅
⋅ ⋅
= ⋅
=
=
⋅ ⋅
⋅
⋅
≈
= ⋅ =
⋅
=
=
=
=
=
______________________________________________________________________
7.85
Dane:
Szukane:
Wzory:
9
3
40
40 10
3
3 10
N
C
nF
F
f
kHz
Hz
−
=
=
⋅
=
= ⋅
L
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
(
)
(
)
3
2
2
2
6
9
3
9
1
1
1
70, 4 10
70, 4
18,84 10
40 10
2
2 3,14 3 10
40 10
L
H
mH
f
C
π
−
−
−
=
=
=
≈
⋅
=
⋅
⋅ ⋅
⋅
⋅ ⋅
⋅ ⋅
______________________________________________________________________
7.86
Dane:
Szukane:
Wzory:
9
1
9
2
3
1
3
2
8
8 10
2
2 10
1
10
3
3 10
C
nF
F
C
nF
F
L
mH
H
L
mH
H
−
−
−
−
=
= ⋅
=
= ⋅
=
=
=
= ⋅
f
ω
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
1
1
1
2
1
2
1
2
1
2
1
2
2
1
2
1
2
1
2
9
9
9
1
2
9
9
3
3
9
9
3
1
2
1
2
6
12
1
1
1
1
1
(
)
(
)
8 10
2 10
10 10
(
)
8 10
2 10 (10
3 10 )
16 10
10
4 10
10
0, 3952 10
/
64 10
2
L
C
L
L
C
C
X
X
X
X
X
X
L
L
C
C
L
L
C
C
C
C
L
L
C C
C
C
C C L
L
rad s
f
f
ω
ω
ω
ω
ω
ω
ω
ω
ω
π
−
−
−
−
−
−
−
−
−
−
−
=
+
=
+
+
=
+
+
=
+
+
+
=
+
⋅
+ ⋅
⋅
=
=
=
=
+
⋅
⋅ ⋅
+ ⋅
⋅
⋅
⋅ ⋅
=
≈
⋅
⋅
=
=
6
6
0, 3952 10
62, 9 10
63
2
2 3,14
Hz
kHz
ω
π
⋅
=
=
⋅
≈
⋅
______________________________________________________________________
7.87
Dane:
Szukane:
Wzory:
100
0,1
1
z
R
L
H
C
F
=
Ω
=
=
6
1
10
C
F
F
µ
−
=
=
|
|
2
2
L
C
r
X
X
X
R
I
Z
R
I
=
−
=
≤
≥
1
2
r
f
f
f
Q
=
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
W zadaniu jest podana pojemność
1
z
C
F
=
lecz w przykładzie z obliczeniami podstawiana
jest
6
1
10
C
F
F
µ
−
=
=
6
1
1
503
2
2
0,1 10
2
503 0,1
3,16
100
r
r
f
Hz
LC
L
Q
R
π
π
ω
π
−
=
=
=
⋅
⋅
⋅
=
=
=
(
)
|
|
lub
L
C
L
C
L
C
X
X
R
to
X
X
R
X
X
R
−
=
−
=
−
−
=
Rozwiązując jedno równanie:
(
)
2
1
1
1
0
L
C
C
L
r
r
r
r
r
r
r
X
X
R
X
X
R
L
R
C
L
C
R
C
LC
RC
ω
ω
ω ω
ω
ω
ω
−
−
=
−
=
−
=
−
=
−
−
+ =
(
) ( )
( )
(
) ( )
( )
2
2
1
1
2
2
2
2
1
( 4
)
4
2
2
0
( 4
)
4
2702
/
2
2
430
2
r
r
r
r
RC
RC
LC
RC
RC
LC
LC
LC
RC
RC
LC
RC
RC
LC
rad s
LC
LC
f
Hz
ω
ω
ω
ω
π
− −
+
− −
+
+
=
=
−
−
<
− −
−
− −
−
+
=
=
≈
−
−
=
=
Rozwiązując drugie równanie:
2
1
1
1
0
L
C
r
r
r
r
r
r
r
X
X
R
L
R
C
L
C
R
C
LC
RC
ω
ω
ω ω
ω
ω
ω
−
=
−
=
− =
−
− =
(
) ( )
( )
(
) ( )
( )
2
2
1
2
2
2
2
1
2
( 4
)
4
'
3702
/
2
2
( 4
)
4
'
2
2
'
0
'
589
2
r
r
r
r
RC
RC
LC
RC
RC
LC
rad s
LC
LC
RC
RC
LC
RC
RC
LC
LC
LC
f
Hz
ω
ω
ω
ω
π
− −
+
− −
+
+
=
=
≈
− −
−
− −
−
+
=
=
<
=
≈
2
1
589 430 159
B
f
f
Hz
= − =
−
=
______________________________________________________________________
7.88
Dane:
Szukane:
Wzory:
50
5
R
L
mH
=
Ω
=
6
0, 5
0, 5 10
C
F
F
µ
−
=
=
⋅
|
|
2
2
L
C
r
X
X
X
R
I
Z
R
I
=
−
=
≤
≥
1
2
r
f
f
f
=
=
=
1
1
2
2
C
L
X
C
fC
X
L
fL
ω
π
ω
π
=
=
=
=
2
2
2
Z
R
X
=
+
1
2
r
f
LC
π
=
5
5
3
6
1
1
1
10
3184
31, 4
2
2
25 10
2
5 10
0,5 10
r
f
Hz
LC
π
π
π
−
−
−
=
=
=
=
≈
⋅
⋅
⋅
⋅
⋅
(
)
|
|
lub
L
C
L
C
L
C
X
X
R
to
X
X
R
X
X
R
−
=
−
=
−
−
=
Rozwiązując jedno równanie:
(
)
2
1
1
1
0
L
C
C
L
r
r
r
r
r
r
r
X
X
R
X
X
R
L
R
C
L
C
R
C
LC
RC
ω
ω
ω ω
ω
ω
ω
−
−
=
−
=
−
=
−
=
−
−
+ =
(
) ( )
( )
(
) ( )
(
)
2
2
1
1
2
2
6
6
3
6
2
3
6
6
12
12
3
3
9
( 4
)
4
2 (
)
2
0
50 0, 5 10
50 0, 5 10
4 5 10
0, 5 10
( 4
)
2
2 5 10
0, 5 10
25 10
625 10
10000 10
780776 10
15, 616 10
15616
5 10
5
r
r
r
RC
RC
LC
RC
RC
LC
LC
LC
RC
RC
LC
LC
r
ω
ω
ω
−
−
−
−
−
−
−
−
−
−
− −
+
− −
+
+
=
=
⋅ −
−
<
⋅
⋅
−
⋅
⋅
+ ⋅ ⋅
⋅
⋅
− −
−
− −
=
=
=
−
− ⋅ ⋅
⋅
⋅
⋅
−
⋅
+
⋅
−
⋅
=
=
≈
⋅
=
− ⋅
−
1
1
/
58443
2487
2
2 3,14
r
ad s
f
Hz
ω
π
=
=
≈
⋅
Rozwiązując drugie równanie:
2
1
1
1
0
L
C
r
r
r
r
r
r
r
X
X
R
L
R
C
L
C
R
C
LC
RC
ω
ω
ω ω
ω
ω
ω
−
=
−
=
− =
−
− =
(
) ( )
( )
(
)
(
)
2
2
2
6
6
3
6
1
3
6
6
12
9
6
12
3
3
9
9
2
50 0, 5 10
50 0, 5 10
4 5 10
0, 5 10
( 4
)
4
'
2
2
2 5 10
0, 5 10
25 10
625 10
10 10
25 10
10625 10
128, 078 10
25, 616 10
25616
/
5 10
5 10
5
'
r
r
RC
RC
LC
RC
RC
LC
LC
LC
rad s
RC
ω
ω
−
−
−
−
−
−
−
−
−
−
−
−
−
⋅
⋅
+
⋅
⋅
+ ⋅ ⋅
⋅
⋅
− −
+
− −
+
+
=
=
=
=
⋅ ⋅
⋅
⋅
⋅
+
⋅
+ ⋅
⋅
+
⋅
⋅
=
=
=
≈
⋅
=
⋅
⋅
− −
=
( )
( )
2
2
2
1
2
( 4
)
4
2
2
'
0
25616
4079
2
2 3,14
r
r
RC
LC
RC
RC
LC
LC
LC
f
Hz
ω
ω
π
−
− −
−
+
=
<
=
=
≈
⋅
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