Dielectric Constant of an Insulator

The dielectric constant, also known as the relative permittivity, is a property of a material that determines its ability to store electrical energy in an electric field. It is denoted by the symbol K. The dielectric constant of an insulator can have different values, but in this case, the correct answer is option 'D', which is 5.

Explanation:
Insulators are materials that do not conduct electricity easily. They have high resistivity and low conductivity. When an insulator is placed in an electric field, the electric field induces polarization in the material. The atoms or molecules in the material rearrange themselves, creating positive and negative charges that oppose the external electric field.

The dielectric constant is a measure of how effectively an insulator can store electrical energy in this polarized state. It represents the ratio of the electric field in a vacuum to the electric field in the insulator. Mathematically, it can be defined as:

K = E(insulator) / E(vacuum)

Where E(insulator) is the electric field in the insulator and E(vacuum) is the electric field in a vacuum.

Significance of the Dielectric Constant:
The dielectric constant determines the capacitance of a capacitor with the insulator as the dielectric material. The capacitance is directly proportional to the dielectric constant, so a higher dielectric constant leads to a higher capacitance.

The dielectric constant also affects the speed at which electrical signals propagate through the material. A higher dielectric constant slows down the signal propagation speed, while a lower dielectric constant allows for faster signal transmission.

Options a), b), and c):
Option 'a' (-1), option 'b' (0), and option 'c' (0.5) are incorrect answers for the dielectric constant of an insulator. A dielectric constant cannot be negative or zero. Negative values would imply a reversal of electric field direction, which is not physically possible. A dielectric constant of 0 or 0.5 would indicate that the material has no ability to store electrical energy in an electric field, which is not true for insulators.

Option d) 5:
Option 'd' (5) is the correct answer for the dielectric constant of an insulator. A dielectric constant of 5 indicates that the insulator can store electrical energy in an electric field effectively. It implies that the electric field in the insulator is five times weaker than the electric field in a vacuum.

In summary, the dielectric constant of an insulator can have different values, but a dielectric constant of 5 is a reasonable value that represents the ability of the insulator to store electrical energy in an electric field.