In AC circuit terminology, the “effective” value of a periodic voltage—equal to the DC value that would deliver the same average power to a resistor—is called the ______ value.

Introduction:
The effective value of an AC quantity is the figure used for power calculations in resistive loads. Recognizing that this is the RMS value is fundamental to using meters and datasheets correctly.

Given Data / Assumptions:

• Resistive load for definition of equivalence.
• Periodic waveform; for pure sine, Vrms = Vpeak / sqrt(2).
• Average power equivalence to DC is the reference concept.

Concept / Approach:
RMS (root mean square) is computed by squaring the instantaneous value, averaging over a period, and taking the square root. This process yields the DC-equivalent heating effect in a resistor and is why most AC meters report RMS or RMS-calibrated values.

Step-by-Step Explanation:
1) Define effective requirement: same average power as a DC source.2) Use RMS definition to translate any periodic waveform to an equivalent DC magnitude.3) For a sine wave: Vrms = Vpeak / 1.414 and Irms = Ipeak / 1.414.4) Use RMS values in power formulas: P = Vrms * Irms for resistive loads.

Verification / Alternative check:
For a purely resistive load, Pavg = (1/T) * ∫ v^2(t)/R dt = Vrms^2 / R, identical in form to DC, confirming RMS as the effective value.

Why Other Options Are Wrong:
Average: for a pure sine, the algebraic average over a cycle is zero.

Peak or peak-to-peak: helpful for headroom, not for power equivalence.

Crest: refers to crest factor (Vpeak/Vrms), not an absolute value definition.

Common Pitfalls:
Using peak values in power calculations or confusing RMS with average responding meters calibrated for sine waves.

Final Answer:
root mean square