Question E8A05:
What is the benefit of making voltage measurements with a true-RMS calculating meter?  

Choices:  
A: An inverse Fourier transform can be used  
B: The signal’s RMS noise factor is also calculated  
C: The calculated RMS value can be converted directly into phasor form  
D: RMS is measured for both sinusoidal and non-sinusoidal signals    

Correct Answer is  D: RMS is measured for both sinusoidal and non-sinusoidal signals  

To measure RMS correctly, a true-RMS meter computes the heating-equivalent value by squaring the instantaneous voltage, averaging, and taking the square root. This works for any waveform within the meter’s bandwidth and crest-factor limits.

Why D is correct (RMS is measured for both sinusoidal and non-sinusoidal signals):
- RMS is defined by:
  $$V_{RMS}=\sqrt{\frac{1}{T}\int_0^T v^2(t)\,dt}$$
- A true-RMS meter performs this calculation (digitally or via thermal methods), so it reads correctly for sine waves, square waves, pulses, distorted audio, and noise.
- This yields the correct heating power in a resistor: $$P=\frac{V_{RMS}^2}{R}$$

Why the other choices are incorrect:
- A: “An inverse Fourier transform can be used”  
  RMS measurement does not require an inverse Fourier transform; true-RMS meters implement time-domain square–average–square-root or equivalent methods.
- B: “The signal’s RMS noise factor is also calculated”  
  “RMS noise factor” is not what the meter reports; while a true-RMS meter can include noise in its RMS reading (within bandwidth), it does not separately calculate a noise factor.
- C: “The calculated RMS value can be converted directly into phasor form”  
  A phasor applies to a single-frequency sinusoid and requires magnitude and phase. RMS alone has no phase information and non-sinusoidal signals cannot be represented by a single phasor.

Useful formulas and rules of thumb:
- For a sinusoid:
  $$V_{RMS}=\frac{V_{pk}}{\sqrt{2}}=\frac{V_{pp}}{2\sqrt{2}}$$
- Average-responding (non–true-RMS) meters assume a sine wave:  
  Rectified average for a sine is $$V_{avg,rect}=\frac{2V_{pk}}{\pi}$$  
  So they scale by $$\frac{\pi}{2\sqrt{2}}\approx 1.1107$$ to display “RMS.” This is wrong for non-sinusoids.
- Use a true-RMS meter for PWM, pulsed RF, distorted audio, or noise. Check the meter’s bandwidth and crest-factor capability for accurate readings.