In the real world, various factors contribute to non-idealities within inductors.
Nonzero Resistance edit
Nearly all common components have wire leads. Inductors specifically have this drawback in addition to the fact that they are typically made from a length of wire which is coiled around some form of material. This wire typically does not have zero resistance. While small lengths of wire made of typical conductive materials, such as copper, larger coils will have a relatively large amount of this wire, leading to an added resistance which may not be neglected. This also becomes true when the potential applied across the inductor increases.
To account for this added resistivity, a non-ideal inductor may be modeled as an ideal inductor in series with a resistor. This resistance may be measured under DC steady-state conditions.
High-frequency considerations edit
Although quite small, lead wires do have some amount of self-inductance. This will usually be neglectable except in the case of very small values for inductive components as well as for high frequency design. To account for the inductance added by these wires, one may model such a non-ideal inductor by including series inductors on for each of the two (or more) leading wires coming from the component.