Visualizing RMS of a Rectified AC Signal

Visualizing RMS of a Rectified AC Signal
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2021-01-06 10:35
This example demonstrates how an AC waveform is rectified (effectively taking its absolute-value form) and then summarized by its root-mean-square (RMS) value, interpreted as an equivalent magnitude. It highlights the geometric/graphical behavior of the rectification process over one or multiple periods. Key concepts include trigonometric modeling (e.g., cosine/periodic functions), rectification, and the RMS statistic defined via the square, time averaging over a period, and a final square root. Construction uses GeoGebra objects from the summary: omega, T, and t to represent angular frequency, period, and time; I_O and function components f, g for the original waveform; additional parameters/auxiliaries (b, c, d, e, h, p, c_1, a, i) to build the rectified expression, compute squared values and the averaging step, and obtain the RMS result. Suitable for high school through early undergraduate teaching, especially in math modeling, probability & statistics (mean-square ideas), and signals/electrical engineering demonstrations.

GeoGebra Commands & Parameters

  1. Numeric omega(0.936)
  2. (2 * π / omega)
  3. Numeric I_O(1.4)
  4. f(x) = If[x ≥ 0 ∧ sin((omega * x)) ≥ 0, (I_O * sin((omega * x)))]
  5. g(x) = f(x)^(2)
  6. Boolean b(false)
  7. Numeric c_1(0)
  8. Integral[g, 0, (2 * π)] / ((2 * π))
  9. h(x) = Integral[g(x), 0, (0.5 * T)] / T
  10. p(x) = sqrt(h(x))
  11. 0
  12. Boolean c(true)
  13. Boolean d(false)
  14. Boolean e(false)
  15. Boolean i(false)

AI Drawing Prompt Reference

Visualize an AC signal by plotting its original sine wave and its rectified version (absolute value). Show the squared rectified waveform, then compute and plot its average value over one period through integration, and finally take the square root to obtain the RMS value. Use a slider to adjust the frequency and observe the changes in rectification and RMS.
The prompt above was compiled from the original drawing commands and is for reference only.