In a transformer with a wye connection, how does line voltage relate to phase voltage?

In a transformer with a wye connection, how does line voltage relate to phase voltage?

• A. In a wye connection, line voltage equals phase voltage.
• B. In a wye connection, line voltage equals √3 times phase voltage; in delta, line voltage equals phase voltage.
• C. In a wye connection, line voltage is half the phase voltage.
• D. In a wye connection, line voltage equals phase voltage divided by √3.

Answer: (B)

In a three-phase system, line voltage is the voltage between two lines, while phase voltage is the voltage from a line to neutral. In a wye (star) connection, each winding connects from a line to neutral, giving three phase voltages that are 120 degrees apart. The line-to-line voltage is the vector difference between two of these phase voltages, and because of the 120-degree phasor arrangement, its magnitude ends up being √3 times a single phase voltage. So line voltage = √3 × phase voltage for a wye connection. In a delta connection, each winding is connected directly between two lines, so the voltage across a winding is already the line-to-line voltage. That means line voltage equals phase (winding) voltage in delta. Thus the relation is that line voltage is √3 times the phase voltage in a wye system, and line voltage equals phase voltage in a delta system.

In a three-phase system, line voltage is the voltage between two lines, while phase voltage is the voltage from a line to neutral. In a wye (star) connection, each winding connects from a line to neutral, giving three phase voltages that are 120 degrees apart. The line-to-line voltage is the vector difference between two of these phase voltages, and because of the 120-degree phasor arrangement, its magnitude ends up being √3 times a single phase voltage. So line voltage = √3 × phase voltage for a wye connection.

In a delta connection, each winding is connected directly between two lines, so the voltage across a winding is already the line-to-line voltage. That means line voltage equals phase (winding) voltage in delta.

Thus the relation is that line voltage is √3 times the phase voltage in a wye system, and line voltage equals phase voltage in a delta system.