Line-to-line vs line-to-neutral voltages in a three-phase system are related how in a Y system?

• A. V_LL is the voltage between a line and neutral
• B. V_LL is the voltage between two lines; V_LN is line-to-neutral; In a Y system V_LL = √3 × V_LN
• C. V_LL equals V_LN
• D. V_LL is twice V_LN

Answer: (B)

In a balanced three-phase Y system, the line-to-line voltage is the vector difference between two line-to-neutral voltages. Each phase-to-neutral voltage has the same magnitude V and the phasors are 120 degrees apart. When you subtract two such phasors, the resulting line-to-line magnitude is √3 times the phase (line-to-neutral) magnitude: |V_LL| = √(V^2 + V^2 − 2V^2 cos 120°) = √3 · V. The line-to-line voltage also leads the corresponding phase voltage by about 30 degrees for a given pair. This geometric relationship explains why line-to-line voltage is √3 times the line-to-neutral voltage in a Y-connected system. For example, a 230 V line-to-neutral yields about 400 V line-to-line (230 × √3 ≈ 400).