To find the system voltage in a Wye system, which formula is correct?

To find the system voltage in a Wye system, which formula is correct?

• 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 (star) connection, the line-to-line (system) voltage is √3 times the phase (coil) voltage because the three phase voltages add vectorially at 120-degree angles. This geometric relationship gives the line voltage as v_line = v_phase × √3. Using the common approximation 1.732, the formula is system voltage = coil voltage × 1.732. For example, with a 120 V phase voltage, the line voltage is about 208 V (120 × 1.732). The other options don’t reflect this phasor addition: 0.5 yields too small a voltage, 2 doubles it (not the correct line-to-line relationship for a Wye), and adding 1.732 has no basis in the voltage relationship.

In a Wye (star) connection, the line-to-line (system) voltage is √3 times the phase (coil) voltage because the three phase voltages add vectorially at 120-degree angles. This geometric relationship gives the line voltage as v_line = v_phase × √3. Using the common approximation 1.732, the formula is system voltage = coil voltage × 1.732. For example, with a 120 V phase voltage, the line voltage is about 208 V (120 × 1.732). The other options don’t reflect this phasor addition: 0.5 yields too small a voltage, 2 doubles it (not the correct line-to-line relationship for a Wye), and adding 1.732 has no basis in the voltage relationship.