  We report results from an in--plane and out--of--plane impedance study on
SmB$_6$ single crystals, performed at low temperatures and over a wide
frequency range. A universal equivalent circuit describes the dielectric
behavior of this system across the transition, from surface to bulk dominated
electrical conduction between 2 and 10 K. We identify the resistive,
capacitive, and inductive contributions to the impedance. The equivalent
inductance, obtained from fits to experimental data, drops drastically as the
bulk starts to control electrical conduction upon increasing temperature.
SmB$_6$ single crystals also show current--controlled negative differential
resistance at low temperatures, which is brought about by Joule heating. This
feature, in addition to inductive and capacitive contributions to the
impedance, can give rise to the self--sustained voltage oscillations observed
below 5 K (Stern {\it et al.}, Phys. Rev. Lett. {\bf 116}, 166603 (2016)).
