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Formulas of Electric Engineering and Electronic

Cross-section for single wires round
q = D² x π  or   D² x 0.7854
4

Cross-section for bunched wires
q = d² x π x n   or   d² x 0.7854 x n
4

Diameter for single wires
D = √ q x 4    or   √q x 1.2732
π

Diameter for bunched wires
D = √  1.34 x n x d

q = Cross-section in mm²
D = Conductor diameter in mm
d = Single wire diameter in mm
n = Number of wires
Conductor resistance
R =    l       or    ρ x l
κ x q q

RCircuit = 2 x l    or    2 x l x p
κ x q q

R = Electrical direct current resistance Ohm
RCircuit = Resistance of complete circuit
q = Cross-section in mm²
κ (Kappa) = Conductivity
ρ (Rho) = Specific resistance
(p =  1  )
κ
l = Conductor length in m
Materials Conductivity
     m     
Ω x mm²
Spec. Resistance
Ω x mm²
m
Copper 58.00 0.01724
Aluminum 33.00 0.0303
Silver 62.00 0.1613
Iron 7.70 0.1299
Constantan 2.00 0.50

Serial Connection
Resistance: R = R1 + R2 + R3 + ... + Rn
   
Capacitance:
C =  1  +  1  +  1  + ... +  1 
C1 C2 C3 Cn
   
Inductance: L = L1 + L2 + L3 + ... + Ln
   
Parallel connection
Resistance:
R =  1  +  1  +  1  + ... +  1 
R1 R2 R3 Rn
   
Capacitance: C = C1 + C2 + C3 + ... + Cn
   
Inductance:
L =  1  +  1  +  1  + ... +  1 
L1 L2 L3 Ln
   
Equivalent resistance of 2 parallel connections
   
 
R = R1 x R2
R1 + R2
   
Mutual capacity
Coaxial cable:
C =    ξr x 10³    (nF/km)
18 x ln Da
d
   
Parallel conductor:
C =    ξr x 10³    (nF/km)
36 x ln Da
d
   
Shielded twisted pair:
CB =         ξr x 10³         (nF/km)
36 ln 2a x (Da²-a²)
d x (Da²-a²)
   
Da = Outer diameter over insulation
Ds = Diameter over shield
d = Diameter of conductor
a = Distance - mid to mid of both conductors
ξ = dielectric constant
Ohm's Law
The current intensity (I) is proportional to Voltage (U) and universaly proportional to Resistance (R)

I =  U    I =  U    U = I x R
R   R  
I = Current intensity (in Ampere - A)
R = Electrical resistance (in Ohm - Ω)
U = Electrical Voltage (in V)
Conductance

G =  1    S =  1    1μS =    1   
R   1Ω   1MΩ
S (Siemens) = Reziprocal value of a resistance is used as conductance
S Siemens = 1/Ohm
G = Electrical conductance
Capacitance
Single conductor against ground
 
CB =    ξr x 10³    (nF/km or pF/m)
18 x ln Di
d
   
Unshielded symmetrical twisted pair
 
CB =    ξr x 10³    (nF/km or pF/m)
36 x ln 2a
d
   
Coaxial pair
 
CB =    ξr x 10³    (nF/km or pF/m)
18 x ln Di
d
   
Shielded symmetrical twisted pair
 
CB =         ξr x 10³         (nF/km or pF/m)
36 ln 2a x (Da²-a²)
d x (Da²-a²)
Di = Outer diameter over single conductor
Da = Outer diameter of multi conductors (mm)
d = Diameter of conductor
a = Distance - mid to mid of both conductors
Inductance of parallel conductors
at low frequencies

L = 0.4 (In Da + 0.25) mH/km
r

at high frequencies
L = 0.4 (In Da + 0) mH/km
r

Inductance of coaxial cable
at high frequencies

L = 0.2 (In Da + 0) mH/km
r
Da = Distance - mid to mid of both conductors
r = Radius of conductor
ξr = dielectric constant
Impedance (Z)
for coaxial cable

Z =  60  x In D  (Ω)
√ξr d

for communication cable
at low frequencies

Z = √  R  (Ω) x tan φ = 1, φ = 45°
ωC

at high frequencies
Z = √  L  (Ω)
C
     
     
D = Diameter over insulation
d = Conductor diameter
     
     
     
R = Resistance (Ω/km)
L = Inductance (mH/km)
C = Capacitance (nF/km)
ω = 2 π f
Wave Length
λ =  V 
f


Units of attenuation - Neper (Np), Decibel (dB) and Bel (B)
1 Np = 8.686 dB
1 dB - 0.1151 Np = 1/10 Bel
1 Bel = 10 dB = 1.1513 Np
λ = Wave length
V = Propagation velocity
f = Frequency
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