AC Waveform
Prerequisites
A U.S. wall outlet delivers 120 volts of alternating current at 60 Hz. But 120 V is not the peak voltage; it is the RMS (root-mean-square) voltage. The actual voltage swings from +170 V to -170 V, sixty times per second. The "120 V" label describes the effective heating power of this oscillating wave.
Alternating current follows a sinusoidal waveform: voltage rises smoothly to a positive peak, drops through zero to a negative peak, and returns to zero. One complete cycle (positive peak to negative peak and back) is one period. At 60 Hz, this happens 60 times per second, so one period lasts about 16.7 milliseconds.
Three numbers describe any AC waveform. Frequency (Hz) is cycles per second. Peak voltage is the maximum instantaneous value. RMS voltage is peak divided by √2 (about 1.414), and it equals the DC voltage that would deliver the same average power. For a U.S. outlet: peak is 170 V, RMS is 170/√2 = 120 V. For a European outlet: peak is 325 V, RMS is 230 V.
Worked Example
A device is rated for 120 V RMS, 60 Hz.
- Find peak voltage. V_peak = V_RMS x √2 = 120 x 1.414 = 170 V.
- Find the period. T = 1/f = 1/60 = 0.0167 seconds = 16.7 ms.
If you measured the voltage at a random instant, what range of values might you see?
Anywhere from -170 V to +170 V. The instantaneous voltage varies continuously. The "120 V" rating is an average-power equivalent, not a constant.
A voltmeter reading "120 V" is quietly doing calculus, averaging a wave that never sits still. Every transformer and generator downstream is built to work with that average, not the peak.
Japan's residential grid runs at 100 V RMS, lower than the U.S. standard of 120 V RMS. What is the peak voltage of a Japanese wall outlet?
Peak = RMS x √2 regardless of the country's standard: 100 x 1.414 = 141 V, the same relationship that converts 230 V RMS to 325 V peak in Europe.
The answer is ALesson complete
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