If line-to-neutral voltage is 120 V in a three-phase system, what is the line-to-line voltage?

If line-to-neutral voltage is 120 V in a three-phase system, what is the line-to-line voltage?

• A. 120 V
• B. 207.84 V
• C. 346.4 V
• D. 60 V

Answer: (B)

Line-to-line voltage in a balanced three-phase system equals the line-to-neutral voltage multiplied by the square root of 3. This comes from the phasors for the three phases being 120 degrees apart; the voltage difference between two phases is the vector difference of two 120-degree-apart voltages, whose magnitude is sqrt(3) times a single phase (line-to-neutral) voltage. So with 120 V line-to-neutral, the line-to-line voltage is 120 × sqrt(3) ≈ 207.84 V. This matches the common 120/208 V three-phase configuration.

Line-to-line voltage in a balanced three-phase system equals the line-to-neutral voltage multiplied by the square root of 3. This comes from the phasors for the three phases being 120 degrees apart; the voltage difference between two phases is the vector difference of two 120-degree-apart voltages, whose magnitude is sqrt(3) times a single phase (line-to-neutral) voltage. So with 120 V line-to-neutral, the line-to-line voltage is 120 × sqrt(3) ≈ 207.84 V. This matches the common 120/208 V three-phase configuration.