For a three-phase wye system, the line-to-line voltage equals the line-to-neutral voltage times the square root of 3.

For a three-phase wye system, the line-to-line voltage equals the line-to-neutral voltage times the square root of 3.

• A. True
• B. False
• C. Only for delta
• D. Only for ungrounded

Answer: (A)

In a balanced three-phase wye system, the three phase voltages share the same magnitude and are 120 degrees apart. The voltage between any two lines is the phasor difference of two phase voltages. If each phase voltage has magnitude Vph, the line-to-line magnitude is |V_LL| = sqrt( Vph^2 + Vph^2 − 2 Vph^2 cos 120°). Since cos 120° = −1/2, this becomes sqrt(3) times Vph. So the line-to-line voltage equals sqrt(3) times the line-to-neutral (phase) voltage. Grounding or ungrounded setups don’t change this geometric relationship in a balanced system. In contrast, in a delta arrangement there isn’t a neutral, and the relationship differs, so the given statement specifically applies to a balanced wye system.

In a balanced three-phase wye system, the three phase voltages share the same magnitude and are 120 degrees apart. The voltage between any two lines is the phasor difference of two phase voltages. If each phase voltage has magnitude Vph, the line-to-line magnitude is |V_LL| = sqrt( Vph^2 + Vph^2 − 2 Vph^2 cos 120°). Since cos 120° = −1/2, this becomes sqrt(3) times Vph. So the line-to-line voltage equals sqrt(3) times the line-to-neutral (phase) voltage. Grounding or ungrounded setups don’t change this geometric relationship in a balanced system. In contrast, in a delta arrangement there isn’t a neutral, and the relationship differs, so the given statement specifically applies to a balanced wye system.