Assertion–Reason on temperature dependence of dielectric constant Assertion (A): The dielectric constant (relative permittivity, εr) is independent of temperature unless the temperature becomes extremely high. Reason (R): At ordinary temperatures, the number density of atoms (number of atoms per unit volume) remains essentially constant.

Introduction / Context:
Dielectric constant (relative permittivity, εr) characterizes how an insulating material polarizes in response to an electric field. This item uses the Assertion–Reason format to test whether learners know how εr depends on temperature and what microscopic features (number density versus dipole alignment) control that dependence.

Given Data / Assumptions:

• Ordinary solid and liquid dielectrics under moderate fields.
• Macroscopic εr arises from electronic, ionic, and orientation polarization mechanisms.
• Number density of atoms or molecules in a solid changes very little with temperature over modest ranges.

Concept / Approach:

Electronic and ionic polarizations have weak temperature dependence, but orientational polarization in polar dielectrics varies approximately as μp^2/(3kT), meaning it decreases with increasing temperature because thermal agitation randomizes dipole orientations. Even in nonpolar materials, lattice vibrations can modify polarizability, so εr is rarely strictly temperature independent. Hence the assertion is not generally true. The reason statement about number density being nearly constant is broadly correct but does not guarantee temperature independence of εr because other temperature-sensitive mechanisms remain.

Step-by-Step Solution:

Verification / Alternative check:

Empirical datasheets for polar polymers (e.g., PVC, PVDF) show clear variation of dielectric constant with temperature at power and RF frequencies, confirming the temperature sensitivity from orientational polarization and relaxation processes.

Why Other Options Are Wrong:

• A and R both true (with or without explanation): incorrect because A is not generally true.
• A true but R false: contradicts known behavior of εr and number density stability.
• Both false: R is broadly correct.

Common Pitfalls:

Assuming solids never change properties with temperature or equating constant number density with constant permittivity, ignoring dipole dynamics and relaxation phenomena.

Final Answer:

A is false but R is true