Introduction:
Dielectric loss is a phenomenon that occurs in dielectric materials when they are subjected to an electric field. It refers to the energy dissipation in the dielectric due to various mechanisms, such as molecular rotation, electronic polarization, and ion conduction. The dielectric loss is characterized by a loss factor called the dielectric loss tangent, which is the ratio of the dielectric loss to the dielectric constant.

Explanation:
The dielectric loss in a dielectric material is proportional to the square of the voltage impressed on the dielectric. This can be explained by considering the behavior of the dielectric under an electric field.

Dielectric Polarization:
When a dielectric material is subjected to an electric field, the electric dipoles present in the material align themselves with the field. This alignment process, known as dielectric polarization, leads to the accumulation of charges on the surface of the dielectric. These charges create an electric field that opposes the applied field, resulting in a decrease in the effective electric field inside the dielectric.

Dielectric Loss:
During the process of dielectric polarization, the electric dipoles in the material undergo movement and rotation. This movement and rotation of dipoles result in energy dissipation in the dielectric, leading to dielectric loss. The amount of energy dissipated as dielectric loss depends on the strength of the electric field and the ability of the dielectric material to resist the movement of dipoles.

Proportional Relationship:
The dielectric loss is directly proportional to the square of the voltage impressed on the dielectric. This is because the voltage is directly related to the strength of the electric field applied to the dielectric. As the voltage increases, the electric field strength increases, leading to a higher dielectric loss.

Mathematical Expression:
Mathematically, the dielectric loss (P) can be expressed as:
P ∝ V²
Where P is the dielectric loss and V is the voltage impressed on the dielectric.

Conclusion:
In conclusion, the dielectric loss in a dielectric material is directly proportional to the square of the voltage impressed on the dielectric. This relationship is due to the energy dissipation that occurs during the dielectric polarization process. Understanding the proportional relationship between dielectric loss and voltage is important in the design and analysis of electrical systems involving dielectric materials.