Capacitors and current flow: which statement best explains how current appears in a capacitor circuit with an ideal dielectric?

Introduction / Context:
Capacitors block direct conduction through their dielectric yet still allow AC current to flow in the external circuit. Grasping this apparent paradox is crucial for understanding filtering, coupling, and reactive power.

Given Data / Assumptions:

• Ideal capacitor with insulating dielectric (no DC conduction).
• Time-varying voltage applied (AC or transient).
• Focus on the physical path of charge and the concept of displacement current.

Concept / Approach:
In an ideal capacitor, no charge carriers cross the dielectric. Instead, electrons accumulate on one plate and are removed from the other, establishing an electric field across the dielectric. The changing electric field gives rise to displacement current, allowing current to appear in the external circuit even though the dielectric itself does not conduct.

Step-by-Step Solution:
Apply a time-varying voltage to the plates.Charges move onto one plate and off the other, changing the electric field.The external circuit sees current i_C = C * dv/dt.Since the dielectric is insulating, conduction through it does not occur; the current is due to field changes (displacement current), not electron flow through the dielectric.

Verification / Alternative check:
For sinusoidal excitation v(t) = V_m sin(ωt), capacitor current i(t) = C * dv/dt = ωC V_m cos(ωt), confirming nonzero AC current with no dielectric conduction.

Why Other Options Are Wrong:
A/B: Imply ionic or electronic conduction through the dielectric, which contradicts the ideal capacitor model. D: Misstates power behavior; capacitors alternately store and release energy with zero average real power in the ideal case.

Common Pitfalls:
Confusing displacement current with actual charge transport through the dielectric; assuming capacitors pass DC—ideal capacitors block DC steady-state.

Final Answer:
Current can flow in a capacitor circuit, but not through the dielectric material itself