### RoHS Compliant Cable & Wire Technical Information

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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
Items For Quote

 Technical Information Copper & Alu Price Calculation Reference to DIN VDE Standards Harmonized Identification Code Designations Conductor Diameters and Resistance Strand Make-up acc. to DIN VDE 0295, IEC 60228 & HD 383 Nominal & Operating Voltage Current Carrying Capacity for Power Cables & Wires Installation Methods & Operating Conditions Laying Conditions for Power Cables Current Ratings for Installation Color Codes Bending Radius & Chemical Resistance Heat Resistance & Caloric Load Values Installation Instructions for UL and CSA Cables AWG Wires & AWG Stranded Conductors US and British Units - Conversions Current Ratings for UL-CSA Cables List of UL-Styles Index British Standard International Abbreviations Characteristics of Insulating and Jacket Materials Definitions: Classes of Stress in Flexible Cables and Insulated Wires Safety Requirements Glossary of Terms: Cables & Wires International Certification Marks & Testing Institute Formulas of Electronic & Power Engineering Cable-Drums - Capacity & Cable Lengths Notes on CE-Marking European Directives
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