The RMS (Root Mean Square) value is a mathematical concept used to describe the average value of a set of numbers or a continuous waveform. In the case of a set of n values, the RMS is the square root of the arithmetic mean of the squares of the values. For a continuous function or waveform, the RMS value is the square root of the mean (average) value of the squared function of the instantaneous values.
In the context of alternating current (AC) circuits, the RMS value is particularly important. It represents the DC current or voltage that would dissipate the same amount of power as the AC current or voltage. For sinusoidal oscillations, the RMS value equals the peak value divided by the square root of 2. The peak value is the maximum value of the waveform, while the RMS value is the effective value of the waveform.
The RMS value is also used in estimation theory as a measure of the imperfection of the fit of an estimator to the data. In physics, the RMS current value can be defined as the "value of the direct current that dissipates the same power in a resistor".
To calculate the RMS value, there are two methods: the graphical method and the analytical method. The graphical method involves using a waveform to find the RMS value, while the analytical method involves using an integral of the squares of the instantaneous values during a cycle.
