A thermocouple-type AC voltmeter indicates which electrical quantity of an applied waveform when properly calibrated?

Introduction / Context:
Thermocouple voltmeters convert electrical energy into heat and then into a temperature-dependent electrical signal. Because heating depends on the mean of the square of the current (or voltage across a fixed resistance), these instruments naturally respond to the root-mean-square (rms) quantity, making them valuable for non-sinusoidal waveforms as true-RMS sensors.

Given Data / Assumptions:

• Thermocouple sensor measures temperature rise due to Joule heating in a heater element.
• Heating power P ∝ I^2R or V^2/R averaged over time.
• Instrument is calibrated in rms volts for a sinusoidal reference and reads true-RMS for arbitrary waveforms within bandwidth.

Concept / Approach:
Since the sensor integrates power over time, its output is proportional to the average of v^2(t). The voltage equivalent is V_rms = sqrt( average{ v^2(t) } ). Therefore, the proper reading is rms value. Peak, average (rectified), or peak-to-peak indications correspond to other measurement principles (diode rectifier, crest detector, or oscilloscope, respectively).

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