RMS Value of AC Wave

Direct current has constant direction and usually constant magnitude with respect to time. Thus, a description of its magnitude is relatively straightforward. On the other hand, Alternate Current changes its direction and magnitude with time. So, a description of its magnitude for a long period poses difficulty. Some other values, such as peak and average values, provide useful information. But they also have limitations when we have to compare Alternate Current with Direct Current. To solve the above problems, the RMS value of the AC wave is quite useful.

Meaning of RMS value of AC Wave

RMS value stands for root-mean-square value. Thus, the RMS value of any quantity is denoted by first squaring the values of the quantity taken over some time, then finding their mean, and finally calculating the square root of the above mean. For the AC wave, this RMS value equals that amount of Direct Current, which produces the same heating effect if passed through the same resistance for an equal period. For example – an AC wave of RMS value of 10A will produce the same heating effect as will be produced by 10A Direct Current if the resistance and period are the same.

Significance

In addition to making Alternating Current comparable to Direct Current, the RMS value of AC wave is also useful in practically denoting the Alternating Current and Voltage. For example – the household supply of 230V Alternating Current means the RMS voltage of AC supply is 230V. RMS value is also the value that is being measured by AC ammeters and voltmeters.

Related Concepts

• Peak Value refers to the maximum value attained by the Alternating Current during a complete cycle. A sinusoidal AC wave attains peak values at 90° and 270°.
• Average Value refers to the average of all instantaneous values of the Alternating Current over a time period. The average value of the Alternating Current transfers the same charge as transferred by the Direct Current of the same value over the same time across any circuit. The average value of the sinusoidal AC wave is zero because the positive half of the cycle is equal to the negative half of the cycle. Thus, the average value of only half cycle is considered.
• Form Factor refers to the ratio of the RMS value to the average value of the Alternating Current. This factor shows the peakiness of the waveform. 
• Peak Factor refers to the ratio of the peak value to the RMS value of the Alternating Current. It is useful for dielectric insulation testing. Because the dielectric stress on the insulator depends upon the peak value of the applied voltage. It is also relevant for measuring iron losses because iron losses depend on the peak flux value.

RMS Value of AC Wave Problems

• The relationship between the peak value and RMS value for a sinusoidal AC wave – the peak value is 1.414 times the RMS value of the sinusoidal AC wave. Thus, 1.414 is also the peak factor for sinusoidal AC waves.
• The relationship between the RMS value and the average value for a half cycle of a sinusoidal AC wave – the RMS value is 1.11 times the average value of the sinusoidal AC wave for a half cycle. Thus, 1.11 is also the form factor for sinusoidal AC waves.
• The relationship between the average value and the peak value for a half cycle of a sinusoidal AC wave – the average value is 0.637 times the peak value of the sinusoidal AC wave for a half cycle.
• The form factor is higher for a triangular waveform or a sinusoidal waveform. As the peakiness of a triangular waveform is greater than the sinusoidal waveform, the form factor for a triangular waveform is higher than a sinusoidal waveform.
• The form factor for a square wave – The RMS and average values are the same for a square wave. The form factor for a square wave is 1.00.