Assertion–Reason (lossy dielectrics in AC): Assertion (A) In imperfect capacitors, the current does not lead the applied AC voltage by exactly 90°. Reason (R) Under AC fields, the dielectric constant is represented by a complex quantity ε* = ε′_r − j ε″_r.

Introduction / Context:Real capacitors and dielectrics exhibit losses due to polarization lag and conduction. In AC analysis, these losses are modeled by a complex permittivity. This produces a current that leads voltage by an angle less than 90°, reflected in a nonzero loss tangent (tan δ = ε″/ε′ or equivalently conductance in parallel with capacitance).

Given Data / Assumptions:

• Slightly lossy linear dielectric with ε* = ε′ − j ε″.
• Sinusoidal steady state at angular frequency ω.
• Negligible magnetic effects and linear response.

Concept / Approach:

For a parallel-plate capacitor with area A and gap d, the current density is J = dD/dt + σE. Using D = ε0 ε* E with ε* complex, the displacement current acquires a component in phase with the electric field. The total current phasor leads voltage by 90° only when ε″ = 0 (perfect dielectric). If ε″ > 0, the lead angle is 90° − δ with tan δ = ε″/ε′, proving the assertion and showing how the complex permittivity explains it.

Step-by-Step Solution:

Verification / Alternative check:

Equivalently, model an imperfect capacitor as an ideal C in parallel with R (or series with ESR); both give a phase angle smaller than 90°, consistent with nonzero ε″.

Why Other Options Are Wrong:

• If R were false, there would be no mechanism to reduce the phase lead from 90°.
• Claiming A false contradicts ubiquitous dielectric loss in real materials.

Common Pitfalls:

• Sign conventions: some texts use ε* = ε′ + jε″ with opposite phasor convention; the physics (loss angle > 0) is the same.

Final Answer:

Both A and R are true and R is correct explanation of A