The square root of three factor in a three-phase generator is derived from the geometry of the voltage phases, which are arranged in a 120-degree separation, forming equilateral triangles. When analyzing the relationship between the side lengths of a right triangle that bisects this equilateral triangle, the ratio leads to the square root of three. This geometric relationship is crucial for understanding phase voltage and line voltage in three-phase systems. The derivation emphasizes the importance of spatial arrangement in electrical engineering. Understanding this concept is essential for effective three-phase generator design and analysis.
