| Deutsche Version |
1-Wire online tutorial. This tutorial will give you an overview of the 1-wire protocol, it's device operation and application solutions. In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + is an elementary example of a geometric series that converges absolutely. First six summands drawn as portions of a square. The geometric series on the real line. In this sense 1 + 1 + 1 + 1 + ⋯ = ζ(0) = − 1 / 2. Emilio Elizalde presents a comment from others about the series: In a short period of less than a year, two distinguished physicists, A. Yndurain, gave seminars in Barcelona, about different subjects.
Conversion and calculation − cross section < > diameter
● Cable diameter to circle cross-sectional areaand vice versa ●
Round electric cable, conductor, wire, cord, string,wiring, and rope
| 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 = 2 × r to the circle cross section surface or the cross-section area A (slice plane) to the cable diameter d? Why is the diameter value greater than the area value? Because that's not the same. Resistance varies inversely with the cross-sectional area of a wire. The required cross-section of an electrical line depends on the following factors: 1) Rated voltage. Net form. (Three-phase (DS) / AC (WS)) 2) Fuse - Upstream backup = Maximum permissible current (Amp) 3) On schedule to be transmittedpower (kVA) 4) Cable length in meters (m) 5) Permissible voltage drop (% of the rated voltage) 6) Line material. Copper (Cu) or aluminum (Al) |
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The 'unit' is usually millimeters but it can also be inches, feet, yards, meters (metres),
or centimeters, when you take for the area the square of that measure.
Litz wire (stranded wire) consisting of many thin wires need a 14 % larger diameter compared to a solid wire.
Cross section is an area. Diameter is a linear measure. That cannot be the same. The cable diameter in millimeters is not the cable cross-section in square millimeters. |
| The cross section or the cross sectional area is the area of such a cut. It need not necessarily have to be a circle. Commercially available wire (cable) size as cross sectional area: 0.75 mm2, 1.5 mm2, 2.5 mm2, 4 mm2, 6 mm2, 10 mm2, 16 mm2. |
r = radius of the wire or cable
d = 2 r = diameter of the wire or cable
| There are four factors that affect the resistance of a conductor: 1) the cross sectional area of a conductor A, calculated from the diameter d 2) the length of the conductor 3) the temperature in the conductor 4) the material constituting the conductor |
| 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 placed under the ground. Also, it depends on the ambient temperature, the allowable current density, and the allowable voltage 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 Δ V
The voltage drop formula with the specific resistance (resistivity) ρ (rho) is:
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 volume resistivity) of copper = 0.01724 ohm×mm2/m (also Ω×m) (Ohms for l = 1 m length and A = 1 mm2 cross section area of the wire)ρ = 1 / σ A = Cross section area in mm2 σ = sigma, electrical conductivity (electrical conductance) of copper = 58 S·m/mm2 |
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The derived SI unit of electrical resistivity ρ is Ω ×m, shortened from the clear Ω ×mm² / m.
The reciprocal of electrical resistivity is electrical conductivity.
Electrical conductance and electrical resistance ρ = 1/κ = 1/σ
| Electrical conductor | Electrical conductivity Electrical conductance | Electrical resistivity Specific resistance |
| silver | σ = 62 S·m/mm² | ρ = 0.0161 Ohm∙mm²/m |
| copper | σ = 58 S·m/mm² | ρ = 0.0172 Ohm∙mm²/m |
| gold | σ= 41 S·m/mm² | ρ = 0.0244 Ohm∙mm²/m |
| aluminium | σ = 36 S·m/mm² | ρ = 0.0277 Ohm∙mm²/m |
| constantan | σ= 2.0 S·m/mm² | ρ = 0.5000 Ohm∙mm²/m |
Difference between electrical resistivity and electrical conductivity
| The conductance in siemens is the reciprocal of the resistance in ohms. |
| To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
| The 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 / area
| The 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, such as T0 = 293.15 K = 20°C at which the electrical resistivity ρ (T0) is known. |
Convert resistance to electrical conductance
Conversion of reciprocal siemens to ohms
1 ohm [Ω] = 1 / siemens [1/S]
1 siemens [S] = 1 / ohm [1/Ω]
| To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
1 millisiemens = 0.001 mho = 1000 ohms
| Mathematically, conductance is the reciprocal, or inverse, of resistance: The symbol for conductance is the capital letter 'G' and the unit is the mho, which is 'ohm' spelled backwards. Later, the unit mho was replaced by the unit Siemens − abbreviated with the letter 'S'. |
Table of typical loudspeaker cables
