# Concepts of solid conductor and stranded conductor

## Two types of conductors

The conductors related to the field – A.C. circuit coupling are of two types:

• solid conductors with the shape of bars, plates, … are characterized by a value of the skin depth comparable to or smaller than the dimensions of the conductor cross-section. The density of supplied or induced (eddy) currents is non-uniform in the cross-section of such conductors;
• stranded conductors are characterized by a value of the skin depth much greater than the dimensions of the conductor cross-section and, as a consequence, by an almost uniform distribution of the current in the conductor cross-section.

The difference between these two conductor types is presented in the following blocks.

## A solid conductor …

Within a solid conductor, there is a coupling between the electric and the magnetic A.C. fields ; eddy currents occur in the volume of such a conductor.

The current density J in a solid conductor can be considered as a superposition between the density of the supplied current (if such a current exists) and the density of the induced current.

The electrical potential V at the terminals of a solid conductor is due to the applied voltage, but also to the effect of the A.C. magnetic field on this conductor.

## A stranded conductor …

Within a stranded conductor, the value of skin depth is much larger than the dimensions of the conductor cross-section.

In this case, the induced current within the conductor is negligible in comparison with the supplied current, if such a current exists. The space distribution of the magnetic field is practically not affected by the induced currents that allow the partial decoupling of the magnetic and electric field equation.

The current density can be considered constant over the conductor cross-section.

## … in practice, in the software

The conductors concerned by the field - circuit coupling are represented twice:

• once in the electrical circuit, under the form of components :
• of stranded conductor type
• of solid conductor type
• once in the finite elements domain, under the form of regions :
• of stranded conductor type (or of non-meshed coils in 3D)
• of solid conductor type