RMS voltage enables power dissipation calculations in AC circuits that are comparable with DC circuits.

• A. True
• B. False
• C. Only for pure resistive
• D. Only at high frequency

Answer: (A)

RMS voltage gives you an effective, DC-like value for power calculations in AC circuits, which lets you compute average (real) power in a way that aligns with how you do it in DC. For a resistor, the instantaneous power is p(t) = v(t)^2 / R. If the voltage is v(t) = Vp sin(ωt), then p(t) = (Vp^2/R) sin^2(ωt). Averaging over a full cycle gives P_avg = (Vp^2)/(2R). Since the RMS voltage is Vrms = Vp/√2, this becomes P_avg = Vrms^2 / R. So the same resistor dissipates power in an AC circuit as a DC source with voltage equal to the RMS value across the resistor.

When the circuit includes reactance, the situation changes subtly: real power is still P = V_rms I_rms cos φ, where φ is the phase angle between voltage and current. The RMS framework remains useful, but you must include the cos φ factor because not all the current contributes to heating; some is stored and returned by reactive elements. The key idea is that RMS values let you translate AC behavior into an equivalent DC-like power calculation for the dissipative portion, making power comparisons with DC meaningful.