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 is required to drive a given current and how much power is dissipated as Joule heat.

What Is Resistance?¶

Electrical resistance quantifies how strongly a material opposes the flow of electric current. It is defined by Ohm's law:

\[ V = R I, \]

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:

\[ R = \int_\Omega \sigma^{-1} |\boldsymbol{\tau}|^2 \, d\Omega, \]

where \(\Omega\) is the coil volume, \(\sigma\) is the electric conductivity, and \(\boldsymbol{\tau}\) is the unit current density vector along the winding.

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.