Why this rms voltage is 0.707 times peak voltage?

The root mean square (RMS) voltage is 0.707 times the peak voltage for a sinusoidal waveform because of the mathematical relationship between peak and RMS values. The RMS value is calculated as the peak value divided by the square root of 2 for a sinusoidal waveform. This factor of 0.707 ensures that the average power delivered by the AC voltage is the same as the equivalent DC voltage for resistive loads. This relationship is crucial for accurately representing and analyzing AC voltage in electrical systems.