Derive an expression for capacitance of a parallel plate capacitor when a dielectric slab of thickness t is inserted between the plates separated by a distance d. What will be the capacitance if:
a) The dielectric constant kappa is greater than 1 and the dielectric slab completely fills the space between the plates.
b) The dielectric constant kappa is less than 1 and the dielectric slab completely fills the space between the plates.
c) The dielectric constant kappa is equal to 1 and the dielectric slab completely fills the space between the plates.
d) The dielectric constant kappa is equal to 1 and the dielectric slab is partially inserted between the plates, covering only a fraction of the plate area.