In a Y connection, how do the line voltages compare to the phase voltages?

In a Y (or star) connection, the line voltages and phase voltages have a specific relationship defined by the geometry of the system and the balanced nature of three-phase power. In this configuration, the line voltage, which is measured between any two of the three phases, is 1.732 times higher than the corresponding phase voltage. This ratio comes from the properties of a three-phase voltage system and can be derived from the formula used to calculate the relationship between line and phase values.

Specifically, if the phase voltages are represented as V_phase, the line voltages (V_line) can be expressed mathematically as:

V_line = √3 * V_phase

The √3 (approx. 1.732) factor arises from the 120-degree phase shift between the voltages in a three-phase system. This geometric relationship illustrates how much higher the voltage measured between the lines is compared to the voltage measured across a single phase. Understanding this concept is crucial in the field of electrical engineering, particularly when dealing with the design and analysis of three-phase systems.