In a wye connection, how does the line voltage compare to the phase voltage?

In a wye connection, how does the line voltage compare to the phase voltage?

• A. Line voltage is equal to phase voltage
• B. Line voltage is √3 times phase voltage
• C. Phase voltage is twice the line voltage
• D. Phase voltage is equal to line voltage

Answer: (B)

In a wye (or star) connection, the relationship between line voltage and phase voltage is a fundamental concept in three-phase systems. The line voltage is indeed √3 times the phase voltage. To understand why this is the case, consider a wye connection where each phase is connected to a neutral point. The phase voltages are measured between each phase and the neutral point. On the other hand, the line voltage is measured between any two phases. Using vector representation, the phase voltages can be visualized as vectors in a 2D plane, each separated by 120 degrees. When calculating the line voltage between any two phases, the phase voltages can be thought of as forming a triangle. The geometric relationship of these vectors leads to the result that the line voltage, which is the distance between two vertices (phase voltages), equals the square root of the sum of the squares of the individual phase voltages, multiplied by the sine of the angle (120 degrees between them). This results in the formula: \[ V_{line} = \sqrt{V_{phase}^2 + V_{phase}^2 - 2 \cdot V_{phase} \cdot V_{phase} \cdot cos(

In a wye (or star) connection, the relationship between line voltage and phase voltage is a fundamental concept in three-phase systems. The line voltage is indeed √3 times the phase voltage.

To understand why this is the case, consider a wye connection where each phase is connected to a neutral point. The phase voltages are measured between each phase and the neutral point. On the other hand, the line voltage is measured between any two phases.

Using vector representation, the phase voltages can be visualized as vectors in a 2D plane, each separated by 120 degrees. When calculating the line voltage between any two phases, the phase voltages can be thought of as forming a triangle. The geometric relationship of these vectors leads to the result that the line voltage, which is the distance between two vertices (phase voltages), equals the square root of the sum of the squares of the individual phase voltages, multiplied by the sine of the angle (120 degrees between them).

This results in the formula:

[ V_{line} = \sqrt{V_{phase}^2 + V_{phase}^2 - 2 \cdot V_{phase} \cdot V_{phase} \cdot cos(