To solve the problem of determining the voltage between any leg of a 480 V wye transformer and ground, we should follow these steps:
1. Understand the terminology:
- Wye transformer: In a wye (or star) configuration, three windings are connected such that one end of each winding is connected to a common point (neutral), and the other ends are connected to the power lines.
- Line voltage: The voltage measured between any two lines (commonly denoted as [tex]\( V_{LL} \)[/tex]).
- Phase voltage: The voltage measured between any one line and the neutral point (commonly denoted as [tex]\( V_{LN} \)[/tex]).
2. Given data:
- The line voltage ([tex]\( V_{LL} \)[/tex]) is 480 V.
3. Determine the formula needed:
- In a wye transformer, the relationship between line voltage ([tex]\( V_{LL} \)[/tex]) and phase voltage ([tex]\( V_{LN} \)[/tex]) can be expressed as:
[tex]\[
V_{LN} = \frac{V_{LL}}{\sqrt{3}}
\][/tex]
4. Apply the relationship:
- Substituting the given line voltage (480 V) into the formula, we get:
[tex]\[
V_{LN} = \frac{480}{\sqrt{3}}
\][/tex]
- Calculate the value:
[tex]\[
V_{LN} \approx 277.1281292110204 \, \text{V}
\][/tex]
5. Match the closest value to the given options:
- The options are:
[tex]\[
\text{A. 208 V} \\
\text{B. 277 V} \\
\text{C. 120 V} \\
\text{D. 240 V}
\][/tex]
- The calculated voltage of approximately 277.128 V is closest to the option 277 V, making it the most accurate and reasonable choice.
Therefore, the voltage between any leg of a 480 V wye transformer and ground is:
B. 277 V.
