is dielectric constant k dimensionless or not? and why?

Answer 1

The formula for a parallel plate capacitor is C = k ε_o A/d where k is the dielectric constant, ε_o is a constant = 8.85 x 10^-12F/m, A us area in m², d is plate separation in m, C is capacitance in Farads (F).

If you solve for k, you get k = C x d /(ε_o x A). Substitute the units F x m / F/m x m². The units cancel, so the dielectric constant is dimensionless.