Increasing the distance between the plates of a parallel plate capacitor has a direct impact on its capacitance. The capacitance is inversely proportional to the distance between the plates (C = εA / d). When the distance is increased, the electric field created by the charge on the plates becomes less concentrated. This reduction in field strength leads to a decrease in the ability of the capacitor to store the same amount of charge for a given potential difference, effectively reducing the capacitance. It's analogous to increasing the distance between two magnetic poles; the force of attraction or repulsion decreases as they move apart, similarly, the 'connection' between charges on either plate of the capacitor weakens with increased separation.

Parallel plate capacitors have limitations when used in high-voltage applications, primarily due to dielectric breakdown. Dielectric breakdown occurs when the electric field within the capacitor becomes so strong that it exceeds the dielectric material's ability to insulate, causing it to become conductive. This can lead to a short circuit and potential damage to the capacitor and surrounding circuitry. The breakdown voltage depends on the type and thickness of the dielectric material. In high-voltage situations, the risk of dielectric breakdown necessitates the use of dielectrics with higher breakdown strengths and, often, increasing the distance between the plates, which, however, reduces the capacitance. Hence, designing parallel plate capacitors for high-voltage applications involves balancing the need for high capacitance with the need to prevent dielectric breakdown.

The dielectric constant of a material is not a fixed value and can change under various conditions, such as temperature, frequency of the applied electric field, and the nature of the dielectric material itself. For instance, at higher temperatures, the increased thermal energy can disrupt the alignment of the molecules within the dielectric, leading to a change in its polarization properties and, hence, its dielectric constant. Similarly, at different frequencies, the ability of the dielectric material to polarize in response to the electric field can vary, affecting its dielectric constant. These changes in the dielectric constant directly affect the capacitance of a capacitor, as capacitance is directly proportional to the dielectric constant (C = εA / d). A change in the dielectric constant, therefore, results in a corresponding change in the capacitance.

The dielectric constant of a material, by definition, is a ratio of its permittivity to the permittivity of free space (ε₀). It represents the extent to which a material can polarize in response to an electric field, compared to the vacuum. Since the vacuum (or free space) has the lowest possible permittivity (and hence the lowest possible ability to support an electric field), any material placed in an electric field will polarize more than a vacuum. This means that the dielectric constant, which is a measure of this polarization relative to that in a vacuum, will always be greater than one. The greater the dielectric constant, the more effective the material is at reducing the electric field between the capacitor plates, and thus, the higher the capacitance of the capacitor.

Dielectric materials play a crucial role in enhancing the capacitance of a parallel plate capacitor. When a dielectric is inserted between the plates, it becomes polarized in the presence of the electric field created by the charged plates. This polarization results in the development of induced charges on the dielectric's surface, which effectively reduces the electric field between the plates. The reduction in the field leads to a decrease in the potential difference for the same amount of charge on the plates, thereby increasing the overall capacitance. Dielectrics also have the property of dielectric constant (ε), which is a measure of their ability to reduce the electric field. The higher the dielectric constant, the more the electric field is reduced, and thus, the greater the increase in capacitance.