When measuring a 50/60 Hz sine wave with a standard AC voltmeter designed for sinusoidal inputs, which value does the instrument display by default?

Introduction:AC voltmeters and multimeters commonly report a single representative value of a periodic voltage. For sinusoidal inputs, the conventional measure is the rms value, because it directly reflects the heating (power) equivalent of a DC voltage across a resistive load.

Given Data / Assumptions:

• Input is a sinusoidal voltage at power-line frequency.
• Meter is a standard AC voltmeter or averaging-rectifier meter calibrated for sine waves, or a true-RMS meter.
• No significant waveform distortion.

Concept / Approach:RMS (root-mean-square) is defined such that a voltage Vrms produces the same power in a resistor as a DC voltage of the same magnitude. Traditional analog meters measure average of the rectified sine and scale it to rms; modern DMMs compute true rms directly. In either case, the displayed value for a pure sine is Vrms.

Step-by-Step Solution:For sine: Vrms = Vp / √2 and Vavg(rectified) = (2/π) * Vp.Meters calibrated for sine use the known ratio between Vrms and rectified average.Thus, the reading presented corresponds to Vrms.For non-sinusoidal waveforms, only a true-RMS meter reports correct rms.

Verification / Alternative check:Compare measurements with an oscilloscope: compute Vrms from measured Vp as Vp/√2; values should match the meter reading within accuracy specs for a sine wave.

Why Other Options Are Wrong:

• Average: Some meters measure this internally but display rms for sine calibration.
• Peak / peak-to-peak: Not displayed by standard voltmeters; these are oscilloscope quantities.
• Crest factor: A ratio, not a voltage magnitude.

Common Pitfalls:

• Using an averaging meter on non-sinusoidal waveforms; readings will be in error.
• Confusing rms with peak values when sizing components.

Final Answer:rms