Formulas of Electric Engineering and Electronic
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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
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q = Cross-section in mm²
D = Conductor diameter in mm
d = Single wire diameter in mm
n = Number of wires |
Conductor resistance
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 |
|
l |
= |
Conductor length in m |
|
Materials |
Conductivity
|
Spec. Resistance
|
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 |
|
|
|
|
|
|
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
for communication cable
at low frequencies
Z = √ |
R |
(Ω) x tan φ = 1, φ = 45° |
ωC |
at high frequencies
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D |
= |
Diameter over insulation |
d |
= |
Conductor diameter |
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|
R |
= |
Resistance (Ω/km) |
L |
= |
Inductance (mH/km) |
C |
= |
Capacitance (nF/km) |
ω |
= |
2 π f |
|
Wave Length
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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