Tool Box

Rectangular Wire Resistance

Rectangular Wire Resistance

Rectangular Wire Resistance Model
DC resistance of a rectangular wire is:
ResistanceFormulaDC

Units: Ohms

AC resistance of a 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 rectangular conductor. At low frequencies, where skin depth is greater than conductor width and thickness, 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

Constant
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: “Analysis of Multiconductor Transmission Lines,” 2nd Ed., Clayton R. Paul, 2008.

Inputs

Width
w
Thickness
t
Length
l
Frequency
f
Relative Conductivity
Relative Permeability

Outputs:

DC Resistance: R = 
3.344e-2 Ohms
AC Resistance: R = 
3.992e-2 Ohms
Skin Depth:  = 
2.058e-4 m