An air-gap capacitor with parallel-plate area A discharges by the electrical breakdown of the air between its parallel plates (separation d) when the voltage between its plates exceeds V₀. Lay a slab with dielectric constant κ and thickness t < d on the surface of the lower plate and maintain a potential difference V between the plates.

(a) Find the capacitance of this structure with the dielectric slab present.
(b) Show that the value of V where electric breakdown occurs in the air portion of the capacitor gap is

Transcribed Image Text:

V² = Vo [1 -/- (1 - 1)]. V' d K