Conversion• Round electric cable, wire, and wiring• Cable diameter to circle cross-sectional areaand vice versa •Cross section is just a two-dimensional view of a slice through an object. An often asked question: How can you convert the diameter of a round wire d to the circle cross section surface or the cross-section area A (slice plane) to the cable diameter d?Resistance varies inversely with the cross-sectional area of a wire.Litz wire consisting of many thin wires need a 14 % larger diameter compared to a massive wire.Cross section is an area. Diameter is a linear measure.That cannot be the same.Calculation of the cross section A, entering the diameter d:r = radius of the wire or cable d = diameter of the wire or cableCalculation of the diameter r, entering the cross section A:There is no exact formula for the minimum wire size from the maximum amperage.It depends on many circumstances, such as for example, if the calculation is for DC,AC or even for three-phase current, whether the cable is released freely, or is placedunder the ground. Also, it depends on the allowable current density and the allowablevoltage drop, and whether solid or litz wire is present. And there is always the nice but unsatisfactory advice to use for security reasons a thicker and hence more expensive cable. Common questions are about the voltage drop on wires.Voltage drop VThe voltage drop formula with the specific resistance (resistivity) rho ρ ist: V = I·R = I · (2 · l · ρ/A)
I = Current in ampere l = Wire (cable) length in meters (times 2, because there is always a return wire) ρ = rho, electrical resistivity (also known as specific electrical resistance or volumeresistivity) of copper = 0.01724 ohm·mm²/m (Ohms for l = 1 m length and A = 1 mm2 cross section area of the wire)ρ = 1 / σA = Cross section area in mm2σ = sigma, electrical conductivity (electrical conductance) of copper = 58 S·m/mm2Quantity of resistanceR = resistance Ωρ = specific resistance Ω·ml = length of the cable mA = cross sectionm2metalElectrical conductivityElectrical conductanceElectrical resistivitySpecific resistancecopperσ = 58ρ = 0.0172aluminiumσ = 36ρ = 0.0277silberσ = 62ρ = 0.0161Electrical conductivity σ:58 S · m / mm²↔Specific elec. resistance ρ:0.017241 Ohm mm² / mσ = 1/ρρ = 1/σThe value of the electrical conductivity (conductance) and the specific electrical resistance (resistivity) is a temperature dependent material constant. Mostly it is given at 20 or 25°C.Resistance = resistivity x length / areaThe specific resistivity of conductors changes with temperature.In a limited temperature range it is approximately linear: where α is the temperature coefficient, T is the temperature and T0 is any temperature,