(ii) A slab (area $A$ and thickness $d_1$) of a linear dielectric of dielectric constant $K$ is inserted between charged plates (charge density $\sigma$) of a parallel plate capacitor [plate area $A$ and plate separation $d$ ($> d_1$)] and opposite charges with charge density of magnitude $\sigma_p$ appear on the faces of the slab. The dielectric constant $K$ is given by : (A) $\frac{\sigma + \sigma_p}{\sigma}$ (B) $\frac{\sigma}{\sigma - \sigma_p}$ (C) $\frac{\sigma + \sigma_p}{\sigma_p}$ (D) $\frac{\sigma}{\sigma_p}$