Which formula is correct?

In a standard three-phase wye (star) connected electrical system, common in data centers, the phase-to-phase voltage (also known as line voltage) is greater than the phase-to-neutral voltage (or phase voltage) by a factor of the square root of 3 (√3 ≈ 1.732). The relationship is defined as: Phase-to-Phase Voltage = Phase-to-Neutral Voltage 1.732. To find the Phase-to-Neutral Voltage, this formula is rearranged, making the correct formula: Phase-to-Neutral Voltage = Phase-to-Phase Voltage / 1.732. For example, in a common 208/120V system, 208V (phase-to-phase) divided by 1.732 equals 120V (phase-to-neutral).

A. This formula incorrectly calculates the phase-to-phase voltage, not the phase-to-neutral voltage. It reverses the correct relationship.
C. This option is mathematically illogical, stating a value is equal to itself multiplied by 1.732, which is only true if the voltage is zero.
D. This is a nonsensical and dimensionally incorrect formula that does not represent any standard electrical principle for voltage calculation.

1. Hale, P. T., & Unruh, T. D. (2007). NIST Technical Note 1482: Power Quality and the U.S. Economy. National Institute of Standards and Technology. In Appendix A, Section A.1.1, the document describes three-phase wye systems, stating, "The line-to-neutral voltage is the line-to-line voltage divided by the square root of three." (Page 43).

2. Kirtley, J. L. (2007). Lecture 4: Three-Phase Systems. MIT OpenCourseWare, Course 6.061: Introduction to Electric Power Systems, Spring 2007. On page 4-6, it is shown that for a wye connection, the magnitude of the line-to-line voltage is √3 times the magnitude of the phase voltage (VL-L = √3 Vph), which rearranges to Vph = VL-L / √3.

3. IEEE Std 1100-2005, IEEE Recommended Practice for Powering and Grounding Electronic Equipment ("Emerald Book"). In Section 4.2.2, "208Y/120-V three-phase, four-wire plus ground," the standard describes this common data center power system, where the relationship 208 V (line-to-line) / 1.732 = 120 V (line-to-neutral) is fundamental to its definition.