 # RMS Value of AC Signal

In mathematics and its applications, the RMS Value of AC Signal is define as the square root of the mean square (the arithmetic mean of the squares of a set of numbers). The RMS (Root Mean Square) Value of AC Signal is also call as the quadratic mean and is a particular case of the generalized mean with exponent 2. RMS can also be define for a continuously varying function in terms of an integral of the squares of the instantaneous values during a cycle.

For alternating electric current, RMS Value of AC Signal is equal to the value of the direct current that would produce the same average power dissipation in a resistive load.

Suppose, we have a simple DC circuit (figure – 1) and we want to replicate it in an AC circuit. We got every thing same, except supply voltage which is now to be an AC supply voltage. Now, the question is what should be the value of AC supply voltage so that our circuit works exactly same as that of DC.

Let us put same value of AC supply voltage (AC Vpeak = 10 volt) which is in our DC circuit. By doing that we can see (figure 3) for a half cycle. How the AC voltage signal is not covering up the whole area (blue area) of constant DC voltage. Which means our AC signal can not supply the same amount of power as our DC supply.

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 call 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, that AC voltage is supply 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.

Moreover, 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 (Root Mean Square) Value of AC Signal.

We are always concerned about how much power is flowing through our circuits irrespective. 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.

### Conclusion

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.