What percentage of the amplitude does the RMS value represent?

The RMS (Root Mean Square) value is a statistical measure used to express the effective value of a varying quantity, especially in electrical engineering and physics. When dealing with sinusoidal waveforms, the RMS value is calculated as the square root of the average of the squares of the values over one cycle of the waveform.

For a pure sine wave, the RMS value is approximately 0.707 times the peak amplitude. This translates to about 70.7% of the peak amplitude of the waveform. The significance of this value lies in its ability to represent the amount of work or heating effect that an AC current can produce, which is crucial for the proper sizing and safety of electrical equipment.

Understanding that the RMS value gives us the equivalent DC value that would produce the same heating effect in a resistive load elucidates why it is essential in power calculations. Calculating the power in AC circuits typically relies on using RMS values for current and voltage, confirming that 70.7% representation is not just a numerical value but a standard in electrical theory.

Thus, the RMS value's relationship to the amplitude of a sine wave, specifically as approximately 70.7%, highlights its importance in making calculations related to electrical systems accurate and practical.