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Peak, peak-to-peak and RMS

AC circuits and filters · Intermediate · about 15 minutes · part of Zen’s Electronics Design Mastery

An AC voltage swings between +V_pk and −V_pk. Its RMS value is the DC voltage that would heat a resistor equally: for a sine, V_rms = V_pk / √2. Mains “220 V” is an RMS value; its peaks reach 311 V.

Peak, peak-to-peak and RMS: the circuit on the simulator's bench

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How it works

Crest factor for a sine: V_pk = √2 · V_rms

Vpk = 1.414 × 11.94 V = 16.89 V, Vpp = 2·Vpk = 33.77 V

P = Vrms² / R = 1.43 W, the same heat as 11.94 V DC.

The average over a whole cycle is 0 V, so a DC meter would read nothing useful. That is why AC is quoted in RMS.

Try it on the bench

  1. Select the AC source and switch the wave to square: now the peak equals the RMS value.
  2. Try triangle: the peak is √3 = 1.73× the RMS value.
  3. Set 220 V and a 2.2 kΩ 50 W resistor to see the 311 V mains peaks.

Parts on the bench

In the course

Zen’s Electronics Design Mastery, module “AC & Reactance”.

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