In a Wye system, which formula gives the line voltage from the phase voltage?

In a Wye system, which formula gives the line voltage from the phase voltage?

• A. System voltage = coil voltage x 1.732
• B. System voltage = coil voltage x 0.5
• C. System voltage = coil voltage x 2
• D. System voltage = coil voltage + 1.732

Answer: (A)

In a Wye connection, the voltage from a line to neutral (phase voltage) and the voltage between two lines (line voltage) relate through the geometry of three-phase phasors. The line-to-line voltage is the vector difference of two phase voltages that are 120 degrees apart, which gives VL = VP × sqrt(3). Since sqrt(3) is about 1.732, the line voltage is 1.732 times the phase voltage. That’s why the correct relation is System voltage = coil voltage × 1.732. The other options don’t reflect the actual vector relationship between line and phase voltages.

In a Wye connection, the voltage from a line to neutral (phase voltage) and the voltage between two lines (line voltage) relate through the geometry of three-phase phasors. The line-to-line voltage is the vector difference of two phase voltages that are 120 degrees apart, which gives VL = VP × sqrt(3). Since sqrt(3) is about 1.732, the line voltage is 1.732 times the phase voltage. That’s why the correct relation is System voltage = coil voltage × 1.732. The other options don’t reflect the actual vector relationship between line and phase voltages.