RMS Value of AC Signal

rms value featured image

Why is RMS value used in AC systems?

What does it means and mean?

Why aren’t all AC system ratings average in RMS?

What is the difference between RMS and average?

These are the questions that come to mind every time we look at alternate circuits.

rms value 1

Suppose we have a simple continuous circuit (Figure 1) and want to play them in a switch circuit.

We all have the same characteristics, except for the supply voltage, which now has to be an alternative supply voltage.

Now the question arises, what should be the AC voltage so that our circuit works the same as that of the DC.

rms value 2

Take the same value for the AC supply voltage (AC Vpeak = 10 volts) as in our DC circuit.

In this way, we can see for half a cycle (Figure 3) that the AC signal does not cover the entire range (blue range) of the constant DC voltage,

which means that our AC signal can not deliver the same power as our DC power supply.

This means that we need to increase the AC voltage to cover the same

range and see if it delivers the same amount of energy or not.

rms value 3

We have found that (Figure 4), by increasing the peak Vpeak voltage to

(p / 2) times the DC supply voltage, the entire AC-DC voltage range can

be covered.

When the AC signal completely represents the DC signal, this DC signal

value is referred to as the average value of the AC signal. Root Mean Square

Red Area of AC = Blue Area of DC

Our AC voltage should now deliver the same amount of energy. However, when we turned on the power supply surprisingly, we found

that the AC voltage supplied more power than the DC voltage.

Because an average AC value provides the same amount of charge, but not the same amount of energy.

To get the same amount of energy from our AC power supply, we need to reduce our AC supply voltage. Root Mean Square or RMS value

Red Area of AC < Blue Area of DC

We have found that by reducing the Vpeak peak voltage to 2 times the

DC voltage in both circuits, the same current flows.

If the AC signal supplies the same amount of energy as DC, this DC

value will be referred to as RMS or AC. Root Mean Square or RMS value

We are always concerned about the amount of energy that flows

through our circuits, no matter how many electrons are needed to drive them.

For this reason, the AC RMS value is always used in the whole AC

the system instead of the average or RMS value.

Conclusion of RMS value

The average value of an alternating current represents the same number of DC loads.

rms value of square wave

The rms value of an alternating current corresponds to the direct current quantity

rms velocity

AC requires less load to deliver the same amount of DC power.

root mean square velocity

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