Wire Pair Resistance

Wire Pair Resistance

Wire Pair Resistance Resistance Calculators

Wire pair Resistance Model
DC resistance of a wire pair is:
ResistanceFormulaDC
Units: Ohms

AC resistance of a wire pair is:
ResistanceFormulaACLargeSkinDepth

ResistanceFormulaACLargeSkinDepth

ResistanceFormulaACLargeSkinDepth

ResistanceFormulaACLargeSkinDepth
Units: Ohms

Skin Depth is:
SkinDepthFormula

Units: meters

Description
Resistance calculated using this tool includes both dc and ac resistance of the wire pair. At low frequencies, where skin depth is greater than wire radius, ac resistance is approximately the same as the dc resistance. As frequency increases, ac resistance increases.

Assumptions and Limitations
Dimensions are in meters.
Wires are assumed to have uniform circular cross section and to be uniformly spaced over their length. Separation between the wires is assumed to be large enough that proximity effect may be ignored.
Wire relative permeability: Symbol-muR
Wire relative conductivity: Symbol-sigmaR

Constants
Permeability of free space: Formula, Permeability of Free Space H/m
Conductivity of copper: Symbol-sigma0 = 5.98 x 10 7 S/m (Siemens per meter) at 20-degrees C

Reference: “Inductance Loop and Partial”, C.R. Paul, Wiley, 2010.

WirePair-Dimensioned

Inputs

Wire 1 radius
rw1
Wire 2 radius
rw2
Length
l
Frequency
f
Relative Conductivity
Relative Permeability

Outputs:

DC Resistance: R = 
4.258e-2 Ohms
AC Resistance: R = 
6.513e-2 Ohms
Skin Depth:  = 
2.058e-4 m