Near the qualitative behavior depends upon whether or not
there is a ``resonance'' there. If there is, then
can begin with a complex component that
attenuates the propagation of EM energy in a (nearly static) applied
electric field. This (as we shall see) accurately describes *conduction* and *resistance*. If there isn't, then is
nearly all real and the material is a dielectric insulator.

Suppose there are both ``free'' electrons (counted by ) that are
``resonant'' at zero frequency, and ``bound'' electrons (counted by
). Then if we start out with:

(9.125) |

where is now

We can understand this from

(9.126) |

(9.127) |

If we assume a harmonic time dependence and a ``normal'' dielectric
constant , we get:

(9.128) |

On the other hand, we can instead set the static current to *zero*
and consider all ``currents'' present to be the *result* of the
polarization response
to the field
. In this case:

(9.129) |

Equating the two latter terms in the brackets and simplifying, we
obtain the following relation for the conductivity:

(9.130) |

We conclude that the distinction between dielectrics and conductors is a matter of perspective away from the purely static case. Away from the static case, ``conductivity'' is simply a feature of resonant amplitudes. It is a matter of taste whether a description is better made in terms of dielectric constants and conductivity or complex dielectric.