True power in an RC series circuit: Is the real power dissipated given by P_R = I^2 * R, with the capacitor contributing zero average real power?

Introduction / Context:
In AC circuits, resistors dissipate real power as heat, while ideal capacitors and inductors exchange reactive power with the source, averaging to zero over a complete cycle. Understanding this distinction is essential for power factor correction and thermal design.

Given Data / Assumptions:

• Sinusoidal steady state with RMS current I.
• Ideal capacitor with no dielectric loss (no ESR for first-order analysis).
• Series RC topology.

Concept / Approach:
Real or true power is P = V_RMS * I_RMS * cos(phi). For an RC series, the phase angle phi satisfies cos(phi) = R / |Z|. Equivalently, the real power equals I^2 * R because only the resistor dissipates energy. The capacitor's voltage and current are 90 degrees out of phase, so its average power over a cycle is zero, though it stores and returns energy within each cycle.

Step-by-Step Solution:

Verification / Alternative check:
Wattmeter readings in lab confirm that power scales with the resistive element; adding series capacitance at fixed current does not increase true power, but changes phase and current at fixed voltage.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing apparent power S = V * I with real power P; ignoring capacitor ESR which introduces small real-loss in practice.

Final Answer:
Correct