The Root Mean Square (RMS) value of an alternating current (AC) is determined by taking the square root of the average of the squares of the instantaneous values over one complete cycle of the waveform.

To calculate the RMS value of an AC waveform, we follow these steps:

1. Square Each Instantaneous Value: First, we square each instantaneous value of the waveform.
2. Calculate the Mean: Next, we compute the mean of these squared values over one full cycle of the waveform.
3. Take the Square Root: Finally, we take the square root of this mean to obtain the RMS value.

This process can be mathematically expressed as:

In this formula:

• $T$ represents the period of the waveform,
• $f(t)$ denotes the instantaneous value of the waveform at time $t$, and
• the integral is taken over one complete cycle of the waveform.

The significance of the RMS value lies in its ability to represent the equivalent direct current (DC) voltage or current that would produce the same heating effect in a resistor as the given AC waveform. Consequently, the RMS value is crucial for calculating the power dissipated in a resistor when an AC voltage or current is applied.

For instance, the power dissipated in a resistor with resistance $R$ when an AC voltage $V$ is applied can be calculated using the formula:

Here, $V$ is the RMS value of the AC voltage. This relationship highlights the practical utility of the RMS value in electrical engineering and circuit analysis.