RMS Value in AC Circuit

An alternating current's half-cycles are equal and opposite in directions. So, the average value of an alternating current for one cycle is zero.

As a result, the average value of an alternating current is calculated for a half-cycle, and is the ratio of the enclosed area to the length of the base of the half-cycle.

Consider a small section of an alternating current waveform. Recall the value of instantaneous current, and by integrating it for the half-cycle, the area enclosed by the half-cycle can be determined. Dividing it by the base length of the half-cycle, the average value of an alternating current can be obtained.

Consider a small section of a squared alternating current waveform.

By integrating the area of the section, the area of the half-cycle of the squared wave can be determined. By dividing it by the base length, the average value of the squared alternating current waveform can be obtained.

The root-mean-square value is defined as the square root of the average of the square of the alternating current, which is greater than the average value.