AC waveform, RMS, frequency, and phase

Read an AC waveform in terms of peak and RMS magnitude, frequency, and phase angle between two waveforms.

Utility power is a sinusoid: the instantaneous voltage swings positive and negative 60 times per second in North America. Because the value is constantly changing, a single number has to be chosen to represent it. That number is RMS — the DC value that would produce the same heating in a resistor. For a sine wave, RMS = peak ÷ √2, so a 120 V RMS circuit peaks at about 170 V.

Frequency is how many complete cycles occur per second; period is its reciprocal (16.67 ms at 60 Hz). Frequency matters because inductive and capacitive reactance both depend on it, and because rotating machine speed is tied to it.

Phase is the angular offset between two sinusoids of the same frequency. When current lags voltage, the load is inductive; when it leads, the load is capacitive. That single angle is the seed of power factor, reactive power, and the whole three-phase relationship in the next two modules.

Predicting before you experiment is what makes the result stick. There is no penalty for being wrong here.

Use the waveform lab to see peak, RMS, and phase behaviour on a clean fundamental before harmonics are introduced.

1. Open the lab and keep only the fundamental (set harmonic magnitudes to zero).
2. Note the peak value and the reported RMS value, and confirm the ratio is about 1.41.
3. Introduce a small third harmonic and watch the peak change while the shape distorts.
4. Return the harmonics to zero and confirm the waveform returns to a clean sine.

Write down where in your work a peak value matters more than an RMS value, and where the reverse is true.