Root Mean Square(Alternating Current)

The input power supply we are getting at our premises whether it is home or workplace, is a type of  Alternating Current(AC). In India, Single phase voltage standard is 230V AC While three phase voltage standard is 400V AC with frequency rating of 50Hz. Note: The alternating current which is considered in this post; is sinusoidal.

All the AC voltage standards are measured in RMS. At starting, RMS term seems difficult to understand. But as we process further, This post totally explains the concept of RMS.

RMS(ROOT MEAN SQUARE)

RMS DEFINITION : “RMS is the square Root of mean value of the instantaneous squared values of a cycle of the waveform.”

Get confused again ?? Just flow through the post, it will be easier next !

If we consider the DC waveform as shown above which remains constant throughout the time. It is easy to consider the level of the waveform which is Vmax because it is not changing.

On the other hand, AC waveform Which is continuously moving with respect to time & changing its direction at fixed intervals. The question is, What do we consider in AC waveform. & the answer is ROOT MEAN SQUARE.

RMS :

1. RMS value is lowered than Maximum value but greater than average value.
2. RMS value of an AC waveform produces the same power output as do produced by the DC of same magnitude. For example, DC voltage of 100 Volts produces the same power output as do produced by AC rms voltage of 100.
3. In AC, RMS value been considered as a overall magnitude of the waveform.
4. RMS is the square Root of mean value of the instantaneous squared values of a cycle of the waveform.

“The four points discussed above; Explain all about the RMS value. At first sight, It is difficult to understand all these point but do not bother our next explanation through the graph make it easy to understand.”

POINT 1 : As per graph, RMS value is lowered than maximum value while it is greater than average value.

RMS FORMULA & ITS EXPLANATION

• General RMS formula for n values,  Vrms=√[(x1²+x2² . .xn²)/n]
• For 8 instantaneous values, Vrms=√[(x1²+x2²+x3² . . . .x8²)/8]
• 8 instantaneous voltage levels Which we considered are 325,295,266,236,207,177,148,118
• After putting all these values in the formula, RMS value we get 231.599.

FUN FACT : “Vmax voltage of DC is a RMS value !”

To prove this, We are next considering the a DC power supply of 24V DC. Waveform is shown below:

 

Now let suppose, we are taking 10 instantaneous value on 24V DC waveform. All the values will be 24.

• 10 values : 24,24,24,24,24,24,24,24,24,24
• Squared values : 576,576,576,576,576,576,576,576,576,576
• Mean of value : 576
• Square root value : 24

 

AC Formulas

• V(maximum)=  V(rms)*√2
• V(maximum)= [V(average)*π]/2
• V(rms)= [V(average)*π]/2√2

 

 SUMMARY

AC Voltage standards are expressed in RMS, particularly pertinent due to the sinusoidal nature of AC. The RMS value represents the effective voltage, equating to the DC output, with RMS lower than maximum and higher than average values. It reflects the overall magnitude of the waveform. The article explains how to compute RMS using a formula derived from instantaneous squared values while emphasizing its significance in providing comparable power outputs to DC systems.

Hope, You like the post. If you have any doubt, suggestion or query please do comments !