When a dielectric fills only part of the gap between parallel plates, model it as capacitors in series or parallel. Dielectric of thickness t (t < d) filling the full area: two capacitors in series — $C_{eq}$ = $epsilon_0$A / (d - t + t/K). Dielectric filling half the area (full thickness): two capacitors in parallel — $C_{eq}$ = $epsilon_0$A$\frac{1 + K}{(2d)}$. Multiple layers of different dielectrics: series if layers are perpendicular to E (stacked), parallel if they divide the area. For a conducting slab of thickness t: K -> infinity, so C = $epsilon_0$$\frac{A}{d-t}$. A conducting slab of thickness t is equivalent to reducing the gap by t.