In AC circuits, what does RMS (root-mean-square) represent?

• A. The average value of the waveform
• B. The peak value of the waveform
• C. The effective DC value that delivers the same power
• D. The instantaneous value at a moment in time

Answer: (C)

RMS stands for root-mean-square and is the effective DC value that delivers the same power to a resistor as the AC waveform. Power in a resistor depends on the square of the instantaneous voltage, so you average v(t)² over time and then take the square root. This gives you V_rms, the value you’d use to calculate heating or power: P = V_rms² / R. For a sinusoidal voltage, V_rms equals the peak voltage divided by √2, and the same idea applies to current with I_rms = I_peak / √2. This RMS value isn’t the average value (which can be zero for a symmetric AC signal) and it isn’t the peak value (the maximum instantaneous value), but the steady DC-equivalent that produces the same heating effect.