Circular Wire Resistance

Circular Wire Resistance

Circular Wire Resistance Resistance Calculators

Circular Wire Resistance Model
DC resistance of a circular wire is:
ResistanceFormulaDC

Units: Ohms

AC resistance of a circular wire is:
ResistanceFormulaACLargeSkinDepth
ResistanceFormulaACSmallSkinDepth

Units: Ohms

Skin Depth is:
SkinDepthFormula
Units: meters

Description
Resistance calculated using this tool includes both dc and ac resistance of a circular wire. 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.
Wire is assumed to have uniform circular cross section over its length.
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.

Wire, Internal-Dimensioned

Inputs

Wire radius
r
Length
l
Frequency
f
Relative Conductivity
Relative Permeability

Outputs:

DC Resistance: R = 
2.0129e-2 Ohms
AC Resistance: R = 
3.257e-2 Ohms
Skin Depth:  = 
2.058e-4 m