What is the phase to neutral value of a 13,800 volt 3-phase 4-wire system?

In a 13,800 volt 3-phase system, the phase to neutral voltage can be calculated using the formula for converting line-to-line voltage to phase voltage in a three-phase system. The relationship is given by:

[ V_{phase} = \frac{V_{line-to-line}}{\sqrt{3}} ]

Here, the line-to-line voltage is 13,800 volts. By performing the calculation:

[ V_{phase} = \frac{13,800}{\sqrt{3}} \approx \frac{13,800}{1.732} \approx 7,961 \text{ volts} ]

This result rounds to approximately 7,960 volts, which aligns with the first option.

The other options do not match this calculation; for instance, 7,200 volts does not correctly reflect the phase voltage for a 13,800 volt system, 13,200 volts represents a value that is the line-to-line voltage, and 12,470 volts is also incorrect as it does not correspond to the proper calculation for phase to neutral voltage in this scenario. Hence, the correct answer highlights the crucial conversion process between line-to-line and phase voltages in a three-phase system.