What is the RMS value in relation to the peak value?

The RMS (Root Mean Square) value is a statistical measure used primarily in the context of alternating current (AC) electrical systems to represent the effective value of an AC waveform. For a sinusoidal waveform, the RMS value is an important concept because it allows for the comparison of AC signals to direct current (DC) values in terms of power delivery.

For a sinusoidal wave, the relationship between the RMS value and the peak value is defined as approximately 0.707 times the peak value. This means that if one knows the peak value of an AC signal, multiplying it by 0.707 gives the RMS value. This factor arises because the RMS calculation considers the square of the instantaneous values over one complete cycle, thus averaging out the variations of the sinusoidal signal.

Understanding this relationship is critical for anyone working with electrical systems, especially when calculating power and sizing components to ensure they can handle the effective current. The other options reflect incorrect multiplications of the peak value, which do not represent the well-established relationship between the peak and RMS values for a sinusoidal waveform.