What does the RMS value represent for an AC voltage or current, and how is it used in power calculations?

• A. Vpeak
• B. Vrms = Vpeak / sqrt(2)
• C. Vpeak * sqrt(2)
• D. Vpeak^2

Answer: (B)

RMS is the effective value of an AC quantity—the DC level that would produce the same average heating in a resistor as the AC signal does over time. For a sinusoidal voltage or current, the instantaneous value is v(t) = Vpeak sin(ωt). The average of v^2 over one cycle is Vpeak^2/2, so the RMS value is sqrt(Vpeak^2/2) = Vpeak/√2. That’s why power calculations use Vrms and Irms: P = Vrms × Irms. For a purely resistive load, Irms = Vrms / R, so P = Vrms^2 / R (or P = Irms^2 × R). This RMS concept isn’t the peak or the peak-to-peak value, but the heating-equivalent value that lets you apply DC power formulas to AC signals. For example, if Vpeak is 100 V, Vrms is about 70.7 V; with a 50 Ω resistor, the average power is about 100 W.