In a Y connected load, how is the line voltage calculated?

In a Y-connected (or star-connected) load, the relationship between line voltage and phase voltage is defined by the formula:

Line Voltage (EL) = √3 × Phase Voltage (Ep).

This relationship arises from the geometric arrangement of the phases in a Y connection. In such a system, the line voltage is the voltage measured between two line conductors, while the phase voltage is the voltage across each individual load in the Y configuration.

To visualize this, imagine a balanced three-phase system with each of the phases equally spaced at 120 degrees. When calculating the line voltage using vector addition of the phase voltages, the √3 factor emerges from the sine of the angles involved. Hence, the line voltage is larger than the phase voltage by a factor of √3.

This understanding is crucial for working with three-phase electrical systems, as it helps in determining the appropriate voltage levels for equipment, ensuring compatibility and safety in electrical installations.