1.1
Dane: Szukane: Wzory:
t =1 s
I = Q
I =
t
i = 5Å"1018 e
e = -1,6Å"10-19 C
Q i Å"e 5Å"1018 Å"1,6 Å"10-19
I = = = = 0,8 A
t t 1
______________________________________________________________________
1.2
Dane: Szukane: Wzory:
I =
Q
S = 6 mm2
I =
t
J =
i = 4Å"1020 e
I
e = -1,6Å"10-19 C
J =
S
t = 2 s
Q = i Å"e
Q 4Å"1020 Å"1,6Å"10-19
I = = = 32 A
t 2
I 32
J = = H" 5,33 A/ mm2
S 6
______________________________________________________________________
1.3
Dane: Szukane: Wzory:
I =150 A t ' =
Q
I =
I '= 6 A
t
t = 2 s
Q = I Å"t = 300 C
Q
t'= = 50 s
I'
______________________________________________________________________
1.4
Dane: Szukane: Wzory:
I = 0 ÷8 A Q =
Q
I =
t = 30 s
t
0 + 8
Iśr = = 4 A
2
Q = IÅ›r Å"t =120 C
______________________________________________________________________
1.5
Dane: Szukane: Wzory:
Q = 30 Ah
I1 = Q
I =
t = 8 h
t
I2 =
t1 = 2 h
I3 =
I2 = I1 / 2
I4 =
I3 = I2 / 2 = I1 / 4
I4 = I3 / 2 = I1 /8
I1 Å"t1 + I2 Å"t1 + I3 Å"t1 + I4 Å"t1 = Q
I1 I1 I1
I1 Å"t1 + Å"t1 + Å"t1 + Å"t1 = Q
2 4 8
15I1
Å"t1 = Q
8
8Å"Q
I1 = = 8 A
15Å"t1
I2 = 4 A
I3 = 2 A
I4 =1 A
______________________________________________________________________
1.6
Dane: Szukane: Wzory:
U = 3,6 V
R = U
I =
G =
I = 0,2 A
R
1
G =
R
U
R = =18 &!
I
1
G = H" 0,0556 S
R
______________________________________________________________________
1.7
Dane: Szukane: Wzory:
U =10 V
I = U
I =
R
Rv = 200 k&! = 200000 &! = 2Å"105 &!
U
I = = 5Å"10-5 A = 50 µA
R
______________________________________________________________________
1.8
Dane: Szukane: Wzory:
I = 4 A U =
U
I =
R = 55 &!
R
U = I Å" R = 220 V
______________________________________________________________________
1.9
Dane: Szukane: Wzory:
I = 0,25 A U =
U
I =
Ra = 0,12 &! R
U = I Å" R = 0,03V
______________________________________________________________________
1.10
Dane: Szukane: Wzory:
U =
Idop = 24 mA = 0,024 A U
I =
R
R =1 k&! = 1000 &!
U = I Å" R = 24 V
______________________________________________________________________
1.11
Dane: Szukane: Wzory:
U = 24V
I1 = U
I =
R = 5 &! ÷100 &!
R
I2 =
24
I1 = = 4,8 A
5
24
I2 = = 0,24 A
100
______________________________________________________________________
1.12
Dane: Szukane: Wzory:
U = 220 V
I = U
I =
J =
R =100 &!
R
2
d = 0,5 mm
Ä„ Å" d
S =
4
I
J =
S
220
I = = 2,2 A
100
2
Ä„ Å" d
S = = 0,19625 mm2
4
2,2
J = H"11,2 A / mm2
0,19625
______________________________________________________________________
1.13
Dane: Szukane: Wzory:
IAB = 1,5 A VB = U
I =
R
RAB = 0,8 &! VB ' =
VA = 3,8V
UAB =1,5Å"0,8 = 1,2 V
VA -UAB = VB
VB = 3,8 -1,2 = 2,6 V
VA +U = VB '
AB
VB ' = 3,8 +1,2 = 5V
______________________________________________________________________
1.14
Dane: Szukane: Wzory:
I = 0 ÷8 A
VB = U
I =
R = 2 &!
R
VB ' =
"Umax = I Å" R = 8Å" 2 = 16 V
dU [V]
20
15
10 dU=f(I)
5
0
0 8 I [A]
______________________________________________________________________
1.15
Dane: Szukane: Wzory:
U = Ux ÷ 30V R = U
I =
Ux =
R
I = 0,6 ÷ 5 A
U 30
R = = = 6 &!
I 5
Ux = 0,6Å"6 = 3,6V
______________________________________________________________________
1.16
Dane: Szukane: Wzory:
1
ÁCu =17,25Å"10-9 &!m
Á =
Å‚
&!m2 106 &!mm2 &!mm2 &!mm2
ÁCu =17,25Å"10-9 =17,25Å"10-9 Å" = 17,25Å"10-3 = 0,01725
m 1 m m m
1 S 1 m m
H" 57,97 Å"106 = 57,97 Å"106 Å" = 57,97
Å‚ =
Cu
17,25Å"10-9 m 106 &!mm2 &!mm2
______________________________________________________________________
1.17
Dane: Szukane: Wzory:
R = l
ÁCu = 18,25Å"10-9 &!m
R = Á
S
S = 0,12 mm2 = 0,12Å"10-6 m2
l = 500 m
l 500
R = ÁCu = 18, 2Å"10-9 Å" H" 75,8 &!
S 0,12Å"10-6
______________________________________________________________________
1.18
Dane: Szukane: Wzory:
R = 1
Å‚ = 35Å"106 S / m
Al
Á =
Å‚
l = 150 m
l
d = 1,6 mm
R =
Å‚ Å" S
Al
2
Ä„ d
S =
4
3,14Å" 2,56Å"10-6
S = H" 2,01Å"10-6 m2
4
150
R = H" 2,13 &!
35Å"106 Å" 2,01Å"10-6
______________________________________________________________________
1.19
Dane: Szukane: Wzory:
N = ? l
Å‚ = 2, 23Å"106 S / m
R =
Å‚ Å" S
D = 12 mm
2
d = 0,05 mm = 0,05Å"10-3 m Ä„ d
S =
4
R = 1,5 k&! = 1500 &!
O = Ä„ d
2
Ä„ d 3,14Å"(0,05Å"10-6)2
S = = H" 1,96Å"10-9 m2
4 4
l = R Å"Å‚ Å" S = 1500Å" 2,32Å"106 Å"1,96Å"10-9 H" 6,82 m
l 6,82
N = = H" 180
Ä„ Å"(D + d) 3,14Å"0,01205
______________________________________________________________________
1.20
Dane: Szukane: Wzory:
R = ? l
Å‚ = 55Å"106 S / m
Cu
R =
Å‚ Å" S
m = ?
l = 1 km = 1000 m
Cu
m = ´Cu Å"V
d = ?
S = 10 mm2 = 10Å"10-6 m2
V = S Å"l
´Cu = 8,9Å"103 kg / m3
2
Ä„ d
S =
4
1000
R = H" 1,82 &!
55Å"106 Å"10Å"10-6
m = ´Cu Å"V = ´Cu Å" S Å"l = 8,9Å"103 Å"10Å"10-6 Å"1000 = 89 kg
4S 4Å"10 mm2
d = = H" 3,57 mm
Ä„ 3,14
______________________________________________________________________
1.21
Dane: Szukane: Wzory:
l
SAl =
Å‚ = 55Å"106 S / m
Cu
R =
Å‚ Å" S
Å‚ = 35Å"106 S / m
Al
lCu = lAl = l
RCu = RAl
SCu = 6 mm2
RCu = RAl
l l
=
Å‚Cu Å" SCu Å‚ Å" SAl
Al
Å‚Cu Å" SCu
SAl = H" 9, 43 mm2
Å‚ Å"
Al
______________________________________________________________________
1.22
Dane: Szukane: Wzory:
l
dAl =
Å‚ = 55Å"106 S / m
Cu
R =
Å‚ Å" S
Å‚ = 35Å"106 S / m
Al
mCu
m = ´ Å"V = ´ Å" S Å"l
´Cu = 8,9Å"103 kg / m3 =
2
mAl Ä„ d
S =
´Al = 2,7 Å"103 kg / m3
4
lCu = lAl = l
RCu = RAl
dCu = 2 mm
2
Ä„ d
SCu = = 3,14 mm
4
RCu = RAl
l l
=
Å‚Cu Å" SCu Å‚ Å" SAl
Al
Å‚Cu Å" SCu
SAl = H" 4,93 mm2
Å‚ Å"
Al
4S 4Å" 4,93
d = = H" 2,51 mm
Ä„ 3,14
mCu ´Cu Å" SCu Å"l ´Cu Å" SCu
= = H" 2,1
mAl ´ Å" SAl Å"l ´Al Å" SAl
Al
______________________________________________________________________
1.23
Dane: Szukane: Wzory:
U = l
Å‚ = 50Å"106 S / m
R =
Å‚ Å" S
S = 100 mm2 = 100Å"10-6 m2
U = I Å" R
l = 1 km = 1000 m
I = 400 A
l 1000
R = = = 0, 2 &!
Å‚ Å" S 50Å"106 Å"100Å"10-6
U = I Å" R = 400Å"0, 2 = 80 V
______________________________________________________________________
1.24
Dane: Szukane: Wzory:
Á =
l
d = 0,3 mm = 0,3Å"10-6 m
R = Á
S
l = 2, 4 m
2
Ä„ Å" d
R = 17 &!
S =
4
l
R = Á
S
2
Ä„ Å"d
R Å"
2
R Å" S R Å"Ä„ Å"d
4
Á = = = = 0,5Å"10-6 &!m
l l 4l
______________________________________________________________________
1.25
Dane: Szukane: Wzory:
Á =
l
Å‚ = 55Å"106 S / m
Cu
R =
Å‚ S
U = 12 V
U
I = 2,5 A
I =
R
SCu = 25 mm2 = 25Å"106 m2
U
R = = 4,8 &!
I
2Å"l
R =
Å‚ S
RÅ‚ S
l = = 3300 m
2
______________________________________________________________________
1.26
Dane: Szukane: Wzory:
I = l
Å‚ = 35Å"106 S / m
Al
R =
J =
Å‚ S
U = 0,3V
U
SAl = 1 cm Å"6 cm = 6 cm2 = 6Å"10-4 m2
I =
R
l = 30 m
I
J =
S
l 30
R = = = 0,1428Å"10-2 &! = 1, 428 m&!
Å‚ S 35Å"106 Å"6Å"10-4
U 0,3
I = = = 210 A
R 0,001428
I
J = = 35 A / cm2 = 0,35 A / mm2 = 0,35Å"106 A / m2
S
______________________________________________________________________
1.27
Dane: Szukane: Wzory:
U = l
Å‚ = 55Å"106 S / m
Cu
R =
Å‚ S
J = 2Å"106 A / m2 = 2 A / mm2
U
l = 200 m
I =
R
I
J =
S
l 2Å"106 Å"200
U = I Å" R = J Å" S Å" = H" 7,27 V
Å‚ Å" S 55Å"106
______________________________________________________________________
1.28
Dane: Szukane: Wzory:
o
R2 =
Å1 = 20 C
R = R1 îÅ‚1+Ä… ( -½1 Å‚Å‚
½
)ûÅ‚
2
ðÅ‚
o
Å2 = 70 C
R1 = 45 &!
1
Ä…Cu = 0,004
o
C
R = R1 îÅ‚1+Ä… ( -½1 Å‚Å‚ = 45(1+ 0, 2) = 54 &!
½2
)ûÅ‚
ðÅ‚
______________________________________________________________________
1.29
Dane: Szukane: Wzory:
o
Å2 =
Å1 = 18 C
R = R1 îÅ‚1+Ä… ( -½1 Å‚Å‚
½
)ûÅ‚
2
ðÅ‚
R1 = 0,8 &!
R2 = 0,9 &!
1
Ä…Cu = 0,004
o
C
R2 = R1 îÅ‚1+Ä… ( -½1 Å‚Å‚
½2
)ûÅ‚
ðÅ‚
R2
-1
R1
o
½2 = +½1 = 49, 25 C
Ä…
______________________________________________________________________
1.30
Dane: Szukane: Wzory:
U = 14 V
Å2 =
R = R1 îÅ‚1+Ä… ( -½1 Å‚Å‚
½
)ûÅ‚
2
ðÅ‚
I = 0, 25 A
U
I =
l = 550 m
R
d = 0,5 mm = 0,5Å"10-3 m l
R =
Å‚ Å" S
Å‚ = 55Å"106 S / m
Cu
2
Ä„ d
1
S =
Ä…Cu = 0,004
o
4
C
o
Za temperaturÄ™ poczÄ…tkowÄ… przyjmujemy Å1 = 20 C dlatego że współczynnik rezystancyjny
odnosi siÄ™ do tej temperatury.
2
Ä„ d 3,14(0,5Å"10-3)2
S = = = 0,196Å"10-6 m2
4 4
l 550
R1 = = = 51 &!
Å‚Cu Å" S 55Å"106 Å"0,196Å"10-6
U 14
R2 = = = 56 &!
I 0, 25
R2
-1
R1
o
½2 = +½1 = 44,5 C
Ä…Cu
______________________________________________________________________
1.31
Dane: Szukane: Wzory:
o
Ä… =
Å1 = 20 C
R = R1 îÅ‚1+Ä… ( -½1 Å‚Å‚
½
)ûÅ‚
2
ðÅ‚
o
Å2 = 60 C
R1 = 100 &!
R2 = 116 &!
R2 = R1 îÅ‚1+Ä… ( -½1 Å‚Å‚
½2
)ûÅ‚
ðÅ‚
R2
-1
R1 1
Ä… = = 0,004
o
½2 -½1 C
______________________________________________________________________
1.32
Dane: Szukane: Wzory:
o
I2 = R = R1[1+Ä… (½2 -½1)]
Å1 = 10 C
o
U
Å2 = 60 C
I =
R
I1 = 3,5 A
1
Ä…Cu = 0,004
o
C
U = const
U U
= îÅ‚1+Ä… ( -½1 Å‚Å‚
½2
)ûÅ‚
I2 I1 ðÅ‚
I1U 3,5
I2 = = H" 2,92 A
U îÅ‚1+Ä… ( -½1 Å‚Å‚ 1,2
½
)ûÅ‚
2
ðÅ‚
______________________________________________________________________
1.33
Dane: Szukane: Wzory:
o
Ä… =
R = R1[1+Ä… (½2 -½1)]
Å1 = 20 C
o
U
Å2 = 30 C
I =
R
R1 = 100 &!
R2 = 85 &!
R2 = R1[1+Ä… (½ -½1)]
2
R2
-1
R1 -0,15 1
Ä… = = = -0,015
o
½2 -½1 10 C
______________________________________________________________________
1.34
Dane: Szukane: Wzory:
1
Å2 -Å2 = R = R1[1+Ä… (½2 -½1)]
Ä…Cu = 0,004
o
C
R2 = R1 +1 %Å" R1
R2 = R1 +1 %Å" R1 = R1 Å"1,01
R2 = R1[1+Ä… (½ -½1)]
2
1,01Å" R1 = R1[1+Ä… (½ -½1)]
2
1,01-1 0,01
o
½2 -½1 = = = 2,5 C
Ä… 0,004
______________________________________________________________________
1.35
Dane: Szukane: Wzory:
1
Ä…CuMn = R = R1[1+Ä… (½2 -½1)]
Ä…Cu = 0,004
o
C
R2 - R1
xÅ 2 = 100%
RMn = 4RCu
R1
Å2 -Å1 = 1oC
RCu _Å 2 - RCu
xCu = 100%
RCu
R1 = RMN + RCu = 5RCu
R2 = RMN + RCu[1+Ä… (½ -½1)] = 4RCu + RCu (1+ 0,004) = 5,004RCu
2
R2 - R1 5,004RCu - 5RCu
x = 100% = 100% = 0,08%
R1 5RCu
RCu _Å 2 - RCu
RCu[1+Ä… (½2 -½1)] - RCu 0,004
xCu = 100% = 100% = 100% = 0,398%
RCu RCu[1+Ä… (½2 -½1)] 1,004
R2
-1
R1 1,0008 -1 1
Ä… = = = 0,0008
o
½2 -½1 1 C
______________________________________________________________________
1.36
Dane: Szukane: Wzory:
1
Å2 = R = R1[1+Ä… (½2 -½1)]
Ä…W = 0,0046
o
C
R1 = 40 &!
R2 = 32 &!
o
Å1 = 0 C
R2 = R1[1+Ä… (½ -½1)] ~
2
R2
-1
R1 -0, 2
o
½2 = +½1 = H" -43, 48 C
Ä… 0,0046
______________________________________________________________________
1.37
Dane: Szukane: Wzory:
R =
R1 = 20 &! R = R1 + R2
U1 = U = I Å" R
R2 = 40 &!
U = 12 V U2 =
R = R1 + R2 = 60 &!
I = U / R = 0, 2 A
U1 = I Å" R1 = 0, 2Å" 20 = 4 V
U2 = I Å" R2 = 0, 2Å" 40 = 8V
______________________________________________________________________
1.38
Dane: Szukane: Wzory:
R =
R1 = 8 &! R = R1 + R2 + ...
U1 = U = I Å" R
R2 = 16 &!
U2 =
R3 = 10 &!
R4 = 21 &!
U = 220 V
R = R1 + R2 + R3 + R4 = 8 +16 +10 + 21 = 55 &!
I = U / R = 220 / 55 = 4 A
U1 = I Å" R1 = 4Å"8 = 32 V
U2 = I Å" R2 = 4Å"16 = 64 V
U2 = I Å" R3 = 4Å"10 = 40 V
U2 = I Å" R4 = 4Å" 21 = 84 V
______________________________________________________________________
1.39
Dane: Szukane: Wzory:
R = 20 &!
Io = R = R1 + R2
RN = 0 ÷100 &!
U = I Å" R
Uo =
U = 120 V
Rz = R + RN = 120 &!
Io1 = U / R = 6 A
Io2 = U / Rz = 1 A
Uo1 = U - I Å" RN = 120 -1Å"100 = 20 V
Uo2 = U - I Å" RN = 120 - 6Å"0 = 120 V
______________________________________________________________________
1.40
Dane: Szukane: Wzory:
R = 20 &!
Rx = R = R1 + R2
UN = 6 V
U = I Å" R
U = 15V
I = UN / R = 0,3 A
Ux = U -UN = 9 V
Ux
Rx = = 30 &!
I
______________________________________________________________________
1.41
Dane: Szukane: Wzory:
R = 1 &!
Rx = R = R1 + R2
Ux = 0,8V
U = I Å" R
UN = 0,32 V
I = UN / RN = 0,32 A
Ux
Rx = = 2,5 &!
I
______________________________________________________________________
1.42
Dane: Szukane: Wzory:
S = U = I Å" R
IN = 20 A
l
l = 200 m
R =
Å‚ S
Å‚ = 35Å"106 S / m
Al
U = 230 V
UN = 220 V
U = U -UN = 10 V
p
U
p
Rp = = 0,5 &!
IN
2Å"l 2Å" 200
S = = = 22,857 Å"10-6 m2 = 22,857 mm2
Å‚ R 35Å"106 Å"0,5
______________________________________________________________________
1.43
Dane: Szukane: Wzory:
R = 44 &! I = U = I Å" R
l
l = 275 m Uo =
R =
Å‚ S
Å‚ = 55Å"106 S / m Ul =
Cu
U = 225V
S = 10 mm2
2Å"l 2Å" 275
Rl = = = 1 &!
Å‚ S 55Å"106 Å"10Å"10-6
U 225
I = = = 5 A
Rp + R 45
Ul = I Å" Rl = 5V
Uo = U -Ul = 220 V
______________________________________________________________________
1.44
Dane: Szukane: Wzory:
U = I Å" R
RV = 30 k&! = 30000 &! R =
U = 60 V
UV = 6 V
UV 6
I = = = 0, 2 mA
RV 30 k&!
Uo = U -UV = 54 V
Uo
R = = 270 k&!
I
______________________________________________________________________
1.45
Dane: Szukane: Wzory:
U = I Å" R
R1 =
Ia = 500 µ A = 0,5Å"10-3 A
R2 =
Ra =100 &!
R3 =
U1 = 5V
U2 = 20 V
U3 = 100 V
Ua = Ia Å" Ra = 0,5Å"10-3 Å"100 = 0,05V
U1 -Ua 5 - 0,05
R1 = = = 9,9 k&!
I 0,5Å"10-3
U2 -U1 20 - 5
R2 = = = 30 k&!
I 0,5Å"10-3
U3 -U2 100 - 20
R3 = = = 160 k&!
I 0,5Å"10-3
______________________________________________________________________
1.46
Dane: Szukane: Wzory:
I = 2 A U = I Å" R
R1 =
R1 2
R2 =
=
R2 3
R3 =
R2 3
=
R3 5
R1 2
=
R3 5
U = 70 V
3
R2 = R1 Å"
2
5
R3 = R1 Å"
2
3 5 10
R = R1 + R2 + R3 = R1 + R1 Å" + R1 Å" = R1 Å" = R1 Å"5
2 2 2
U
R =
I
U
5R1 =
I
U 70
R1 = = = 7 &!
5I 10
3
R2 = R1 Å" = 10,5 &!
2
5
R3 = R1 Å" = 17,5 &!
2
______________________________________________________________________
1.47
Dane: Szukane: Wzory:
U = I Å" R
R1 = 360 &! U2 =
R2 = 40 &!
U = 200 V
U
I = = 0,5 A
R1 + R2
U2 = R2 Å" I = 20 V
______________________________________________________________________
1.48
Dane: Szukane: Wzory:
U = I Å" R
R1 = 750 &! R2 =
U
U2 =
4
U = U1 +U2
U
U = U1 +
4
3
U = U1
4
3
I Å" R = I Å" R1
4
4
R = Å" R1 = 1000 &!
3
R2 = R - R1 = 250 &!
______________________________________________________________________
1.49
Dane: Szukane: Wzory:
U = U = I Å" R
R1 = 10 &!
R2 = 30 &!
R3 = 60 &!
U = 300 V
U 300
I = = = 3 A
R1 + R2 + R3 100
UR1 = I Å" R1 = 30 V
UR2 = I Å" R2 = 90 V
UR3 = I Å" R3 = 180 V
UR12 = UR1 +UR2 = 120 V
UR23 = UR2 +UR3 = 270 V
U = UR1 +UR2 +UR3 = 300 V
______________________________________________________________________
1.50
Dane: Szukane: Wzory:
R = 5 k&! U = I Å" R
Rx =
I = 1 mA
U = 600 V
U
I =
R + Rx
U 600
Rx = - R = - 5000 = 595 k&!
I 10-3
Rx e" 595 k&!
______________________________________________________________________
1.51
Dane: Szukane: Wzory:
U = I Å" R
Rwzb = 400 &! Rx =
R = R1 + R2 +&
I5 = 0,25 A
I4 = 0,3 A
I3 = 0,35 A
I2 = 0, 4 A
I1 = 0,45 A
Iwzb = 0,5 A
U = 200 V
U U 200
I1 = R1 = - Rwzb = - 400 = 44, 44 &!
R1 + Rwzb I1 0, 45
U U 200
I2 = R2 = - (Rwzb + R1) = - 444, 44 = 55,56 &!
R1 + R2 + Rwzb I2 0, 4
U U 200
I3 = R3 = - (Rwzb + R1 + R2) = - 500 = 71, 43 &!
R1 + R2 + R3 + Rwzb I3 0,35
U U 200
I4 = R4 = - (Rwzb + R1 + R2 + R3) = - 571, 43 = 95, 24 &!
R1 + R2 + R3 + R4 + Rwzb I4 0,3
U
I5 =
R1 + R2 + R3 + R4 + R4 + Rwzb
U 200
R5 = - (Rwzb + R1 + R2 + R3 + R4) = - 666,67 = 133,33 &!
I5 0, 25
______________________________________________________________________
1.52
Dane: Szukane: Wzory:
U = I Å" R
R1 = 9 &! Ix =
1 1 1
R2 = 18 &! Rz =
= + +&
R R1 R2
R3 = 12 &! Gz =
I1 = 2 A
U = I1 Å" R1 = 2Å"9 = 18V
U 18
I2 = = = 1 A
R2 18
U 18
I3 = = = 1,5 A
R3 12
I = I1 + I2 + I3 = 2 +1+1,5 = 4,5 A
1 1 1 1 1 1 1 9
= + + = + + =
Rz R1 R2 R3 9 18 12 36
Rz = 4 &!
lub
U 18
Rz = = = 4 &!
I 4,5
1 1
Gz = = = 0, 25 S
Rz 4
______________________________________________________________________
1.53
Dane: Szukane: Wzory:
R = 200 &!
1 1 1
R2 =
= +
R1 = 250 &! R R1 R2
R Å" R1 50000
R2 = = = 1000 &!
R1 - R 50
______________________________________________________________________
1.54
Dane: Szukane: Wzory:
R =
R1 = 4 &! 1 1 1 1
= + +
R R1 R2 R3
G =
R2 = 6 &!
1
I1 =
R2 = 8 &!
G =
R
U = 12 V I2 =
U
I3 = I =
R
1 1 1 1 1 1 1 6 + 4 + 3 13
= + + = + + = =
R R1 R2 R3 4 6 8 24 24
24
R = H" 1,846 &!
13
1
G = H" 0,542 S
R
U 12
I1 = = = 3 A
R1 4
U 12
I2 = = = 2 A
R2 6
U 12
I3 = = = 1,5 A
R3 8
______________________________________________________________________
1.55
Dane: Szukane: Wzory:
R1 = 60 &! I1 = 1 1 1
= +
R R1 R2
R2 = 90 &! I2 =
U
I = 1 A
I =
R
1 1 1 3 + 2 5
= + = =
R 60 90 180 180
180
R = = 36 &!
5
U = I Å" R = 36 V
U 36
I1 = = = 0,6 A
R1 60
U 36
I2 = = = 0,4 A
R2 90
______________________________________________________________________
1.56
Dane: Szukane: Wzory:
R1 = 8 &! I1 = 1 1 1 1 1
= + + +
R R1 R2 R3 R4
R2 = 10 &! I2 =
U
R3 = 20 &! I3 =
I =
R
R4 = 15 &! I4 =
I = 41 A
1 1 1 1 1
= + + + = 0,125 + 0,1+ 0,05 + 0,06667 = 0,34167
R 8 10 20 15
1 1 1 1 1 15 +12 + 6 + 8 41
= + + + = = = 0,34167
R 8 10 20 15 120 120
120
R = H" 2,9268 &!
41
U = I Å" R = 120 V
U 120
I1 = = = 15 A
R1 8
U 120
I2 = = = 12 A
R2 10
U 120
I3 = = = 6 A
R3 20
U 120
I4 = = = 8 A
R4 15
______________________________________________________________________
1.57
Dane: Szukane: Wzory:
1 1 1
Ra = 0,18 &! RB =
= +
R R1 R2
I = 5 A
U
Ia = 0,5 A
I =
R
I = I1 + I2
U = Ia Å" Ra = 0,09 V
IB = I - Ia = 4,5 A
U 0,09
RB = = = 0,02 &!
IB 4,5
______________________________________________________________________
1.58
Dane: Szukane: Wzory:
1 1 1
Rb = 0,5 &! Rp =
= +
R R1 R2
Ia = 2 mA = 0,002 A
'
U
Ia = 0,04 A
I =
R
U = 20 V
I = I1 + I2
'
Ib = Ia - Ia = 0,04 - 0,002 = 0,038 A
Ua = Ib Å" Rb = 0,019 V : napiÄ™cie na ukÅ‚adzie amperomierz / bocznik
Ua 0,019
Ra = = = 9,5 &!
Ia 0,002
U = U -Ua = 20 - 0,019 = 19,981V
p
U
19,981
p
Rp = = = 9990,5 &! :odłączony bocznik, a do amperomierza dołączony posobnik
'
Ia 0,002
______________________________________________________________________
1.59
Dane: Szukane: Wzory:
1 1 1
Ra = 0,02 &! Iodb =
= +
R R1 R2
d = 2 mm = 2Å"10-3 m
U
l = 20 cm = 0, 2 m
I =
R
Ia = 0,8 A
I = I1 + I2
Å‚ = 55Å"106 S / m
Cu
l
R =
Å‚ S
2
Ä„ d
S =
4
3,14Å" 4Å"10-6
S = = 3,14Å"10-6 mm2
4
0, 2
Rb = = 1,158Å"10-3 &!
55Å"106 Å"3,14Å"10-6
Ub = Ib Å" Rb
Ua = Ia Å" Ra
Ub = Ua
Ib Å" Rb = Ia Å" Ra
Ia Å" Ra 0,8Å"0,02
Ib = = = 13,82 A
Rb 1,158Å"10-3
Iodb = Ia + Ib = 14,62 A
______________________________________________________________________
1.60
Dane: Szukane: Wzory:
R = 1000 M &!
R1
Rx =
R =
szt n
i = 20
km
l = 5km
n = i Å"l = 100
R1 1000
R = = = 10M &!
n 100
______________________________________________________________________
1.61
Dane: Szukane: Wzory:
Rs = 50 &! R1 = R1 Å" R2
Rr =
R1 + R2
Rr = 12 &! R2 =
Rs = R1 + R2
R1 = Rs - R2
R1 Å" R2
Rr =
R1 + R2
(Rs - R2) Å" R2
Rr =
Rs - R2 + R2
Rr Å" Rs = (Rs - R2) Å" R2
Rr Å" Rs = Rs Å" R2 - R2 Å" R2
R22 - Rs Å" R2 + Rr Å" Rs = 0
R22 - R2 Å"50 + 600 = 0
" = b2 - 4ac = 2500 - 2400 = 100
-b - " 50 -10
x1 = = = 20
2a 2
-b + " 50 +10
x2 = = = 30
2a 2
R2 = 30 &!
R1 = Rs - R2 = 50 - 30 = 20 &!
______________________________________________________________________
1.62
Dane: Szukane: Wzory:
U = 240V R1 Å" R2
R1 =
Rr =
R1 + R2
Ir =16 A
R2 =
Rs = R1 + R2
Is = 3 A
U
R =
I
U 240
Rs = = = 80 &!
Is 3
U 240
Rr = = = 15 &!
IR 16
R1 = Rs - R2
R1 Å" R2
Rr =
R1 + R2
(Rs - R2) Å" R2
Rr =
Rs - R2 + R2
Rr Å" Rs = (Rs - R2) Å" R2
Rr Å" Rs = Rs Å" R2 - R2 Å" R2
R22 - Rs Å" R2 + Rr Å" Rs = 0
R22 - R2 Å"80 +1200 = 0
" = b2 - 4ac = 6400 - 4800 = 1600
-b - " 80 - 40
x1 = = = 20
2a 2
-b + " 80 + 40
x2 = = = 60
2a 2
R2 = 60 &!
R1 = Rs - R2 = 80 - 60 = 20 &!
______________________________________________________________________
1.63
Dane: Szukane: Wzory:
U = 8V "% = U
R =
I
I = 0,4 A
1 1 1
Rv =1000 &!
= +
R Rv Ro
U 8
R = = = 20 &!
I 0, 4
1 1 1
= +
R Rv Ro
1 1 1
= -
Ro R Rv
R Å" Rv 20000
Ro = = H" 20, 408 &!
Rv - R 980
Ro - R 0, 408
"% = 100% = 100% = 2%
Ro 20, 408
______________________________________________________________________
1.64
Dane: Szukane: Wzory:
"% = U
UvA =100,5V
R =
I
Ia = 0,5 A
UvB =100V
Ib = 0,505 A
Rv = 20000 &!
Ra =1&!
UvA 100,5
RA = = = 201&!
Ia 0,5
UvA = Ua +Uo
UvA = Ia Å" Ra + Ia Å" RoA
UvA
Ra + RoA =
Ia
UvA 100,5
RoA = - Ra = -1 = 200 &!
Ia 0,5
RoA - RA -1
"% = Å"100% = Å"100% = -0,5%
RoA 200
Ub 100
RB = = = 198,0198 &!
Ib 0,505
Ub 100
Iv = = = 0,005 A
Rv 20000
Ib = Iv + Io
Ub
Rob =
Io
Ub 100
Rob = = = 200 &!
Ib - Iv 0,505 - 0,005
Rob - RB 200 -198,0198
"% = 100% = 100% = 0,99%
Rob 200
______________________________________________________________________