What is the root mean square voltage of an alternating current?

Since the voltage of alternating current, by definition, changes over time, it is helpful for physics to describe it using a sinusoidal curve. In this case, the amplitude of that sine curve becomes is what we would call peak voltage. But exactly due to the way the potential changes over time, it can be cumbersome to make calculations with this function.This is where the rms voltage comes in: if we were to find the direct current with the same performance as our A.C. can give us, what would its potential be? We can derive this using some simple integration, and the result for a sinusoidal curve will be U_peak/sqrt(2).