General: Power Dissipation

Which value of an AC signal results in the same power dissipation as a DC voltage of the same value? [G5B07]

A. The peak-to-peak value
B. The peak value
C. The RMS value
D. The reciprocal of the RMS value

This is, unfortunately a “definition” question, so we’ll just come right out and tell you the answer, then explain a bit….

The correct answer is C. The RMS Value.  RMS stands for Root Mean Square.  Mathematically, when speaking about electrical power, it is the peak voltage of the sine wave, divided by the square root of 2.  So it looks like this, where V is the peak voltage.

RMS = V / √2

The exact derivation of this can be found here on Wikipedia.

Physically, you can think of this as similar to a saw being pulled back and forth through a tree or board.  The voltage increases sharply, levels off, decreases sharply again to negative, levels off, and repeats in the sine wave pattern.  Just as the saw blade stops at the end of each cutting motion, and cuts in both directions.

This is how an AC voltage dissipates the equivalent power of the same RMS DC voltage.

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