What value of an AC signal produces the same power dissipation in a resistor as a DC voltage of the same value?
Why RMS stands for root-mean-square, and it is defined precisely so that an AC waveform delivers the same average heating power to a resistor as a DC voltage of that numeric value. If 120 V RMS AC and 120 V DC are each applied to the same resistor, both dissipate identical average power, since P = V(RMS)^2 / R. For a sine wave, RMS is about 0.707 times the peak value, or peak divided by the square root of 2.
Watch out The peak value is the highest instantaneous voltage of the waveform, and it is about 1.414 times the RMS value, so a sine wave with a peak equal to a DC voltage delivers only half the power. Peak-to-peak is double the peak and describes the total swing, not the heating value.
RMS = the 'DC equivalent' value. Heating power always works in RMS; peak and peak-to-peak just describe the waveform's size.