What Is Root Mean Square (RMS) of Alternating Current?

The electrical power supply we receive at our homes, workplaces, and industries is generally in the form of Alternating Current (AC). In India, the nominal single-phase supply voltage is 230 V AC, while the nominal three-phase supply voltage is 400 V AC, with a standard frequency of 50 Hz.

When we mention an AC voltage such as 230 V, we are referring to its RMS (Root Mean Square) value, not its instantaneous or peak value. Since a sinusoidal AC voltage continuously changes with time, the question naturally arises: how can a continuously varying voltage be represented by a single value?

This is where RMS becomes important. In this article, we will understand what RMS means, why it is used for AC voltage and current, and how its value is calculated for a sinusoidal waveform.

Note: The AC waveform considered in this article is sinusoidal.

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 of AC(sinusoidal) waveform 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

AC voltage/current changes every instant → ordinary average can become misleading → square the instantaneous values → take their mean → take the square root → obtain RMS.

• 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 !