In a balanced three-phase system, the line-to-line voltage is what factor times the line-to-neutral voltage?

In a balanced three-phase system, the line-to-line voltage is what factor times the line-to-neutral voltage?

• A. 1.732 times
• B. 0.577 times
• C. 1.0 times
• D. 2.0 times

Answer: (A)

In a balanced three-phase system, the line-to-line voltage is the vector difference between two phase voltages that are 120 degrees apart. The magnitude of that difference is V_LL = sqrt(V_phase^2 + V_phase^2 - 2 V_phase^2 cos 120°). Since cos 120° = -1/2, this becomes sqrt(2 V_phase^2 + V_phase^2) = sqrt(3) V_phase. So the line-to-line voltage is sqrt(3) times the line-to-neutral (phase) voltage. sqrt(3) is about 1.732, so the line-to-line voltage is 1.732 times the line-to-neutral voltage (using RMS values). For example, a 100 V line-to-neutral voltage yields about 173.2 V line-to-line.

In a balanced three-phase system, the line-to-line voltage is the vector difference between two phase voltages that are 120 degrees apart. The magnitude of that difference is V_LL = sqrt(V_phase^2 + V_phase^2 - 2 V_phase^2 cos 120°). Since cos 120° = -1/2, this becomes sqrt(2 V_phase^2 + V_phase^2) = sqrt(3) V_phase. So the line-to-line voltage is sqrt(3) times the line-to-neutral (phase) voltage. sqrt(3) is about 1.732, so the line-to-line voltage is 1.732 times the line-to-neutral voltage (using RMS values). For example, a 100 V line-to-neutral voltage yields about 173.2 V line-to-line.