  We examine theoretically and experimentally the localized %and extended
electrical modes existing in a bi-inductive electrical lattice containing a
bulk or a surface capacitive impurity. By means of the formalism of lattice
Green's functions, we are able to obtain closed-form expressions for the
frequencies of the impurity (bound-state) eigenmodes and for their associated
spatial profiles. This affords us a systematic understanding of how these mode
properties change as a function of the system parameters. We test these
analytical results against experimental measurements, in both the bulk and
surface cases, and find very good agreement. Lastly, we turn to a series of
quench experiments, where either a parameter of the lattice or the lattice
geometry itself is rapidly switched between two values or configurations. In
all cases, we are able to naturally explain the results of such quench
experiments from the larger analytical picture that emerges as a result of the
detailed characterization of the impurity-mode solution branches.
