Download T096 Formulas of the electrotechnic and - Hi

Formulas of electrotechnic and electronic
Ohm’s Law
The current intensity (I) is proportional to voltage (U) and inversely proportional to resistance (R)
d p
? n or d2 ? 0,7854 ? n
4
Diameter for
single wires cross-section
2
q =
qffiffiffiffiffiffiffiffiffi
q4
p
D =
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q 1; 2732
or
Diameter for bunched wires
D =
q
D
d
n
=
=
=
=
pffi
1; 34 n d
cross-section (mm2)
conductor diameter (mm)
single wire diameter (mm)
number of wires
Conductor Resistance
l
=
or
R
kq
RLoop
=
2l
kq
R
RLoop
q
k (Kappa)
r (Rho)
l
=
=
=
=
=
=
Electrical direct-current resistant (Ohm)
Resistance of a complete circuit
cross-section (mm2 or q mm)
Conductivity
Specific resistance (r = k1 )
Conductor length (m)
Conductivity
Spec. resistance
m
W mm2
W mm2
m
Copper
58,00
0,01724
Aluminium
33,00
0,0303
Silver
62,00
0,1613
Materials
Iron
7,70
0,1299
Constantan
2,00
0,50
Serial connection
Resistance:
R ¼ R1 þ R2 þ R3 þ ::: þ Rn
þ C11 þ C12 þ C13 þ ::: þ C1n
Capacitance:
1
C
Inductance:
L ¼ L1 þ L2 þ L3 þ ::: þ Ln
Parallel connection
Resistance:
R = R1
1
Capacitance:
þ R12 þ R13 þ ::: R1n
C ¼ C1 þ C2 þ C3 þ :::Cn
L = L1 þ L1 þ L1 þ ::: L1
n
1
3
2
Equivalent resistance of 2 parallel connected resistance
Inductance:
R R
R = R 1 þ R2
1
2
Mutual capacity (C)
r 103
* coaxial cable
C=
(nF/km)
18 In Da
d
*
parallel core
C=
r 103
(nF/km)
36 In Da
d
*
shielded twisted pair
r 103
CB =
(nF/km)
ðDa2 a2 Þ
36 In 2a
2 2
d
Da =
Ds =
d =
a =
=
T 96
=
=
=
=
U
R
R = UI
U = I ? R
current intensity (Amps – A)
electrical resistance (W)
electrical voltage (V)
Conductance
1
=
G = 1R
1S = 11W
or 1 mS
1MW
S (Siemens) = reziprocal value of a resistance
is used as conductance
1 Siemens = 1/Ohm
G = electrical conductance
Capacitance
Single core against earth
r 103
CB =
(nF/km or pF/m)
18 In Di
d
* Unshielded symmetrical twisted pair
r 103
CB =
(nF/km or pF/m)
36 In 2a
d
* Coaxial pair
r 103
(nF/km or pF/m)
CB =
18 In Di
d
* Shielded symmetrical twistet pair
r 103
(nF/km or pF/m)
CB =
ðDa2 a2 Þ
36 In 2a
2 2
d
*
rl
q
2l p
q
or
I
I
R
U
R
Cross-section for single wire round
D2 p
q =
or D2 ? 0,7854
4
Cross-section for bunched wire
ðDa þa Þ
Outer diameter over insulation
diameter over shield
diameter of conductor
distance – mid to mid of both conductors
dielectric constant
Di =
Da =
d =
a =
ðDa þa Þ
outer diameter over single core (mm)
outer diameter of multicores (mm))
conductor diameter (mm)
distance between two conductors –
mid to mid of both conductors
Inductance of parallel cores
at low frequencies
L = 0,4 (In Da
r + 0,25) mH/km
at high frequencies
L = 0,4 (In Da
r + 0) mH/km
Inductance of coaxial cable
at high frequencies
L = 0,2 (In Da
r + 0) mH/km
Da = distance between two conductors –
mid to mid of both conductors
r = radius of a conductor
r = dielectric constant
Impedance (Z)
for coaxial cable
D =
d =
60
D
Z = pffiffiffi ? In
d (W)
r
diameter over insulation
conductor diameter
for communication cable
at low frequencies
Z=
at
R
L
C
w
high frequencies
Z=
= Resistance (W/km)
= Inductance (mH/km)
= Capacitance (nF/km)
= 2pf
qffiffiffiffiffiffi
R
=
=
w C (W) ? tan j 1, j 458
qffiffiffiffi
L
C
(W)
Wave length l = vf
l = wave length
v = propagation velocity (velocity of light: 300 000 km/s)
f = frequency
units of attenuation – Neper (N), decibel (dB) and Bel (B)
1 Np = 8,686 dB
1
Bel
1 dB = 0,1151 Np = 10
1 Bel = 10 dB = 1,1513 Np