[1] In its most common form, an equivalent circuit is made up of linear, passive elements.
[2] One of linear circuit theory's most surprising properties relates to the ability to treat any two-terminal circuit no matter how complex as behaving as only a source and an impedance, which have either of two simple equivalent circuit forms:[1][3] However, the single impedance can be of arbitrary complexity (as a function of frequency) and may be irreducible to a simpler form.
Linear four-terminal circuits in which a signal is applied to one pair of terminals and an output is taken from another, are often modeled as two-port networks.
The electrical behavior of a Lithium-ion battery cell is often approximated by an equivalent circuit model.
Equivalent circuits can be used to electrically describe and model either a) continuous materials or biological systems in which current does not actually flow in defined circuits or b) distributed reactances, such as found in electrical lines or windings, that do not represent actual discrete components.