Temperature dependent dielectric spectroscopy measurements on vanadium dioxide thin films allow us to distinguish between the resistive, capacitive, and inductive contributions to the impedance across the metal-insulator transition (MIT). We developed a single, universal, equivalent circuit model to describe the dielectric behavior above and below the MIT. Our model takes account of phase-coexistence of metallic and insulating regions. We find evidence for the existence at low temperature of ultra-thin threads as described by a resistor-inductor element. A conventional resistor-capacitor element connected in parallel accounts for the insulating phase and the dielectric relaxation.