How is line-to-neutral voltage calculated in a 3-phase system?

In a 3-phase system, line-to-neutral voltage is calculated by dividing the line-to-line voltage by the square root of 3. This relationship arises due to the geometry of the voltage vectors in a three-phase system.

In a balanced three-phase system, the line-to-line voltages represent the voltage difference between two phases, while the line-to-neutral voltage corresponds to the voltage between any phase and the neutral point (usually the ground). Since the phases are 120 degrees apart from each other, the relationship between the line-to-neutral voltage (often denoted as V_phase) and the line-to-line voltage (denoted as V_line) is derived from the following relationship:

[ V_{line} = \sqrt{3} \times V_{phase} ]

Rearranging this relationship to solve for the line-to-neutral voltage gives us:

[ V_{phase} = \frac{V_{line}}{\sqrt{3}} ]

This mathematical formulation is pivotal for electrical engineers and technicians when designing and troubleshooting three-phase systems, allowing them to understand the conversion between line-to-line and line-to-neutral voltages accurately.