Coil Resistance Report

The CoilResistanceReport computes the electrical resistance of the coil based on its material properties and geometric configuration. The resistance determines how much voltage is required to drive a given current through a coil, and how much power is dissipated as 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 \(V [{\rm V}]\) is the voltage drop across the coil, \(I [{\rm A}]\) is the electric current through the coil. \(R [{\rm \Omega}]\) is the coil resistance.

In the context of electromagnetic devices, resistance plays a key role as it determines the power losses due to Joule heating by \(P = I^2 R\).

Geometric and Material Dependence

The resistance ( R ) of a coil depends on both its geometry and the electrical conductivity of its material:

\[R = \int_\Omega \frac{1}{\sigma} |\vec{\tau}|^2 \, \mathrm{d}\Omega \quad,\]

here \(\Omega\) is the volume of the conductor, \(\sigma\) is the electrical conductivity, and \(\mathbf{\tau}\) is the unit current density vector along the coil winding.

This expression ensures accurate resistance computation even for complex geometries, spatially varying materials, or non-uniform current distributions.

Usage Example

from mufem.electromagnetics.coil import ResistanceReport

help(ResistanceReport)

Help on class ResistanceReport in module mufem.electromagnetics.coil:

class ResistanceReport(mufem.ReportTrait)
 |  Method resolution order:
 |      ResistanceReport
 |      mufem.ReportTrait
 |      pybind11_builtins.pybind11_object
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __init__(...)
 |      __init__(self: mufem.electromagnetics.coil.ResistanceReport, name: str, coil_index: int) -> None
 |
 |      Constructor with name and coil index.
 |
 |  evaluate(...)
 |      evaluate(self: mufem.electromagnetics.coil.ResistanceReport) -> Value
 |
 |      Returns the resistance.
 |
 |      :remark: Exported to python.
 |
 |  get_name(...)
 |      get_name(self: mufem.electromagnetics.coil.ResistanceReport) -> str
 |
 |      Returns the name of the report.
 |
 |      :remark: Exported to python.
 |
 |  ----------------------------------------------------------------------
 |  Static methods inherited from pybind11_builtins.pybind11_object:
 |
 |  __new__(*args, **kwargs) class method of pybind11_builtins.pybind11_object
 |      Create and return a new object.  See help(type) for accurate signature.