How is RMS voltage defined?

How is RMS voltage defined?

• A. The square root of the mean of the squares of all the voltage values in one cycle
• B. The arithmetic mean of the voltage over a cycle
• C. The maximum instantaneous voltage
• D. The peak-to-peak voltage

Answer: (A)

RMS voltage represents the effective value that would produce the same heating in a resistor as a DC voltage of that magnitude. It is found by squaring the instantaneous voltage, averaging those squares over one complete cycle, and then taking the square root. In continuous form this is V_rms = sqrt( (1/T) ∫ v(t)^2 dt ); in a discrete sense over one cycle, V_rms = sqrt( (1/N) ∑ v_i^2 ). This is precisely the idea of the square root of the mean of the squares of all the voltage values in one cycle. This value is what you use to compute power: P = V_rms^2 / R (or P = I_rms^2 R). For a sine wave, V_rms is V_peak / √2. The other options describe the average value, the maximum instantaneous value, or the peak-to-peak amplitude, none of which capture the heating effect the RMS value measures.

RMS voltage represents the effective value that would produce the same heating in a resistor as a DC voltage of that magnitude. It is found by squaring the instantaneous voltage, averaging those squares over one complete cycle, and then taking the square root. In continuous form this is V_rms = sqrt( (1/T) ∫ v(t)^2 dt ); in a discrete sense over one cycle, V_rms = sqrt( (1/N) ∑ v_i^2 ). This is precisely the idea of the square root of the mean of the squares of all the voltage values in one cycle.

This value is what you use to compute power: P = V_rms^2 / R (or P = I_rms^2 R). For a sine wave, V_rms is V_peak / √2. The other options describe the average value, the maximum instantaneous value, or the peak-to-peak amplitude, none of which capture the heating effect the RMS value measures.