What is the relationship between effective value and peak value?

The correct relationship between effective value and peak value is that effective value is 0.707 times the peak value, which arises from the principles of alternating current (AC) voltage and current signals. In electrical engineering, especially in the context of AC circuits, the peak value represents the maximum instantaneous value of the signal, while the effective value (also known as the root mean square, or RMS value) represents a measure that equates how much work can be done by the AC signal compared to a direct current (DC) signal.

To derive the effective value, the peak value of a sinusoidal waveform is divided by the square root of 2, which approximately equals 0.707. This is particularly important because the effective value provides a practical means to assess the voltage or current that produces the same heating effect as a DC value. Understanding this relationship is crucial for applications involving power calculations and the safe design of electrical systems.