Which expression defines the relationship between peak voltage and effective voltage?

The relationship between peak voltage (Vpk) and effective voltage, also known as root mean square voltage (Vrms), is defined by the formula Vrms = Vpk / √2. This equation arises from the understanding of how electrical energy is distributed in alternating current (AC) systems.

Peak voltage refers to the maximum voltage level reached during the AC cycle, while effective voltage is a measure of the overall power delivered by that voltage. The factor of √2 (approximately 1.414) comes into play because, within one complete cycle of a sinusoidal waveform, the average power delivered is effectively represented by the Vrms value, which accounts for how the voltage varies over time.

To derive this relationship, the Vrms value is obtained through integrating the square of the voltage function over a full cycle, then averaging it, and finally taking the square root. This ensures that the effective voltage correctly reflects the ability of the AC voltage to perform work, which is crucial for calculating power in electrical systems. Thus, using this formula allows engineers and technicians to effectively relate peak voltage to the more practically useful effective voltage in various applications.