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Coil Resistance Report

The ResistanceReport computes the electrical resistance of the coil from its material properties and geometric configuration. The resistance sets how much voltage you need to drive a given current, and how much power the coil dissipates as Joule heat.

What Is Resistance?

Electrical resistance quantifies how strongly a material opposes the flow of electric current. Ohm's law defines it:

\[ V = R I, \]

where \(V\) [V] is the voltage drop, \(I\) [A] is the current, and \(R\) [\(\Omega\)] is the coil resistance. In electromagnetic devices, resistance determines the Joule losses through \(P = I^2 R\).

Geometric and Material Dependence

The resistance depends on both the coil geometry and the electrical conductivity of its material:

\[ R = \int_\Omega \frac{|\boldsymbol{\tau}|^2}{n_f \, \sigma} \, d\Omega, \]

where:

  • \(R\) is the DC resistance of the coil (\(\Omega\)).
  • \(\Omega\) is the coil volume (m³).
  • \(\sigma\) is the electric conductivity of the coil material (S/m). For an anisotropic material, mufem uses the mean of the diagonal entries.
  • \(\boldsymbol{\tau}\) is the unit current density vector along the winding (1/m²). It contains the number of turns.
  • \(n_f\) is the fill factor (dimensionless). For a stranded coil it comes from the wire specification. For a solid coil, or a stranded coil without a wire specification, \(n_f = 1\).

This integral form gives a consistent resistance even for complex geometries, spatially varying materials, and non-uniform current distributions.

Usage

from mufem.electromagnetics.coil import ResistanceReport

coil_resistance_report = ResistanceReport(
    name="Coil Resistance",
    coil_index=0,
)

resistance = coil_resistance_report.evaluate()
print(f"Coil resistance: {resistance}")

When to use this

  • Thermal coupling. Combine with the Time-Domain or Time-Harmonic Magnetic model to estimate Joule heating for transformer / motor thermal-management studies.
  • Winding-design trade-offs — compare resistance vs. weight or vs. number of turns at fixed cross-section.
  • DC-loss verification at the start of any AC analysis.