In a wye connected system, how does line voltage relate to phase voltage?

In a wye connected system, how does line voltage relate to phase voltage?

• A. It is equal to the phase voltage
• B. It is half of the phase voltage
• C. It is 1.73 times the phase voltage
• D. It is double the phase voltage

Answer: (C)

In a wye connected system, line voltage is indeed 1.73 times the phase voltage. This relationship arises from the geometry of the system and the way voltages are measured. In a wye configuration, each phase is connected to a common neutral point, and the line voltage is the voltage measured between any two of the three lines. The phase voltage, on the other hand, is the voltage measured across each individual phase winding to the neutral point. The mathematical derivation of this relationship is based on the principles of phasor addition, specifically using the properties of a 120-degree phase shift between the voltages in a three-phase system. When you apply the Pythagorean theorem to the three-phase system, considering that the line voltages can be viewed as vectors due to their 120-degree separation, the resulting relationship can be expressed as: Line Voltage = √3 × Phase Voltage This simplifies to approximately 1.732 times the phase voltage, which is commonly rounded to 1.73 in practical calculations. Understanding this relationship helps in analyzing and designing electrical systems, ensuring that the proper voltages are considered for equipment and conductors. Thus, the correct answer reflects an important aspect of three-phase electrical systems.

In a wye connected system, line voltage is indeed 1.73 times the phase voltage. This relationship arises from the geometry of the system and the way voltages are measured.

In a wye configuration, each phase is connected to a common neutral point, and the line voltage is the voltage measured between any two of the three lines. The phase voltage, on the other hand, is the voltage measured across each individual phase winding to the neutral point. The mathematical derivation of this relationship is based on the principles of phasor addition, specifically using the properties of a 120-degree phase shift between the voltages in a three-phase system.

When you apply the Pythagorean theorem to the three-phase system, considering that the line voltages can be viewed as vectors due to their 120-degree separation, the resulting relationship can be expressed as:

Line Voltage = √3 × Phase Voltage

This simplifies to approximately 1.732 times the phase voltage, which is commonly rounded to 1.73 in practical calculations. Understanding this relationship helps in analyzing and designing electrical systems, ensuring that the proper voltages are considered for equipment and conductors. Thus, the correct answer reflects an important aspect of three-phase electrical systems.