Which means we must increase the AC voltage to cover the same area and see if it is supplying the same amount of power or not.
We found that (figure 4) by increasing the peak voltage Vpeak up to (π/2) times of DC supply voltage we can actually cover the whole area of DC in AC. When the AC voltage signal completely represents the DC voltage signal then that value of DC signal is called the "average value" of AC signal.
Now our AC voltage should supply the same amount of power. But when we switched-on the supply surprisingly, we found that AC voltage is supplying more power than the DC. Because an average value of AC supplies same amount of charges but not the same amount of power. So, to get same amount of power from our AC supply we must decrease our AC supply voltage.
We found that by decreasing the peak voltage Vpeak up to √2 times DC voltage we get same amount of power flowing in both the circuits. When the AC voltage signal supply same amount of power as in DC then that value of DC voltage is called root mean square or rms value of AC.
We are always concerned about how much power is flowing through our circuits irrespective of how much electrons are needed to supply that power and that is the reason why we always use the rms value of AC supply instead of average value everywhere in AC system.
Average value of an AC current represent the equal amount of charges in DC current. RMS value of an AC current represent the equal amount of power in DC current AC current takes less amount of charges to supply the same amount of DC power.