Dielectrics — determining relative permittivity from capacitor measurements (assertion–reason) Assertion (A): The relative permittivity εr of a dielectric can be found experimentally by measuring the capacitance of a parallel-plate capacitor with and without the dielectric inserted. Reason (R): For a parallel-plate capacitor, the capacitance is C = ε A / d = ε0 εr A / d, where A is plate area and d is plate spacing.

Introduction / Context:Relative permittivity (dielectric constant) quantifies how much a dielectric increases the capacitance of a given geometry over its vacuum value. Laboratory measurements often use a parallel-plate capacitor to determine εr by direct comparison.

Given Data / Assumptions:

• Parallel-plate geometry with plate area A and separation d.
• Uniform dielectric fully filling the gap.
• Fringing fields neglected (large plate approximation).

Concept / Approach:For a parallel-plate capacitor, C = ε A / d = ε0 εr A / d. With the same A and d, the vacuum capacitance is C0 = ε0 A / d and the filled capacitance is Cd = ε0 εr A / d. Therefore, εr = Cd / C0. Measuring C with and without the dielectric gives εr directly, making R an explanation for A.

Step-by-Step Solution:Measure C0 (air or vacuum) for known A, d.Insert the dielectric and measure Cd.Compute εr = Cd / C0 using the formula C = ε0 εr A / d.

Verification / Alternative check:Bridge methods (e.g., Schering bridge) also determine εr consistently with the same relationship for capacitive reactance; fringing corrections can be applied if high precision is needed.

Why Other Options Are Wrong:Any option denying the formula or its explanatory role contradicts the standard capacitance expression for uniform dielectrics.

Common Pitfalls:

• Neglecting to fully fill the gap with dielectric, which introduces series air layers and reduces measured εr.
• Ignoring fringing in small or thin samples; guard-ring electrodes mitigate this.

Final Answer:Both A and R are true and R is correct explanation of A