In AC circuit theory, consider an ideal (pure) capacitor with no series resistance: what is the correct statement about its average real power dissipation as operating frequency changes?

Introduction / Context:
When studying AC circuits, it is essential to distinguish between energy storage in reactive components and true (average) power dissipation. An ideal capacitor stores energy in an electric field and exchanges this energy with the source each cycle. This question tests your understanding of why a pure capacitor does not dissipate average real power and why this conclusion holds regardless of frequency, provided the capacitor is ideal (no resistance).

Given Data / Assumptions:

• The component is an ideal capacitor with zero series resistance and zero dielectric loss (no ESR, no leakage).
• The source is sinusoidal with any frequency f.
• Average real power refers to the time-average over one or more cycles of v(t) * i(t).

Concept / Approach:
For an ideal capacitor, current leads voltage by 90 degrees. With i(t) = C * dv/dt for a sinusoid, the instantaneous power p(t) = v(t) * i(t) alternates positive and negative. The energy taken from the source in part of the cycle is returned in another part. The average over a complete cycle is zero. This is true at all frequencies; frequency changes the magnitude of reactive current (I = 2 * pi * f * C * V_rms) and reactive power, but not the average real power of an ideal capacitor.

Step-by-Step Solution:
Note the phase relationship: current leads voltage by 90 degrees in a pure capacitor.Write p(t) = v(t) * i(t). Positive and negative lobes are equal and opposite over a cycle.Average real power P_avg = (1/T) * ∫ p(t) dt over one period = 0.Since the ideal model is frequency-independent for losses, P_avg = 0 for any f.

Verification / Alternative check:
Compute with phasors: P = V_rms * I_rms * cos(phi). For an ideal capacitor, phi = −90 degrees, so cos(phi) = 0 and P = 0 at all frequencies. Only reactive power Q = V_rms * I_rms * sin(phi) is nonzero in magnitude.

Why Other Options Are Wrong:
Power increasing or decreasing with frequency (B or C) describes nonideal ESR loss, not a pure capacitor. “No definable relationship” (D) is incorrect because the relationship is precisely defined: average real power is zero. “None” is invalid because the correct statement is given in option A.

Common Pitfalls:
Confusing reactive current growth with real power dissipation; forgetting ESR and dielectric losses belong to nonideal models only; assuming “pulsating power” implies nonzero average—here the average is zero.

Final Answer:
Average real power dissipation is zero and does not depend on frequency