The dielectric constant (K) of a medium significantly affects the capacitance of a capacitor, particularly in parallel plate configurations. As the dielectric constant increases, the electric field between the plates is reduced, requiring more charge to achieve the same voltage. This relationship indicates that the presence of a dielectric effectively increases the capacitance by allowing for greater charge storage. Dielectrics are materials that can be polarized, which enhances their ability to influence capacitance. Overall, higher dielectric constants lead to increased capacitance in capacitors.