Electricity 2 — AC Circuits

Peak vs RMS

ELI5: the "120 V" on the wall is not the peak the voltage actually reaches — it's the RMS value, the equivalent steady DC voltage that would heat a toaster just as much. Because the sine wave spends most of its time below the peak, RMS = peak / √2.

V_{pk} := 170 V

= 170 V what the wall voltage actually peaks at

V_{rms} = \frac{V_{pk}}{\sqrt{2}}

= 120.21 V the "120 V" printed on the label

Real-world hook: RMS is why your multimeter reads 120 V (not 170), how audio power is rated, and why an AC motor's nameplate voltage is the RMS figure.

Try it yourself: an AC supply peaks at 340 V. What is its RMS voltage? (RMS = peak/√2.)

Vrms_{you} := 340 V / sqrt(2)

= 240.42 V ✏️ Your turn: divide the 340 V peak by √2. (This is European 240 V mains, in fact.)

✓ pass

abs(Vrms_{you} - 340 V / sqrt(2)) < 0.1 V

green when your RMS voltage is correct