When connecting a transformer in a delta configuration, what is the relationship between line and phase voltages?

In a delta configuration, the relationship between the line and phase voltages is established by how the transformer windings connect. Each phase winding is connected end-to-end to form a closed loop, which creates a situation where the line voltage (the voltage measured between any two lines in the system) is greater than the phase voltage (the voltage across each winding).

The correct answer indicates that the line voltage is √3 times the phase voltage because of the geometry of the delta connection. This can be derived from the fundamental principle of three-phase systems. In a delta configuration, the phase voltage remains equal to the voltage across each winding, while the line voltage is calculated by taking into account the vector sum of the phase voltages. The mathematical relationship can be expressed as:

Line Voltage = √3 × Phase Voltage

This relationship arises from the 120-degree phase difference in a three-phase system, where the line voltage between two phases is effectively the hypotenuse of a right triangle formed by the phase voltages in a vector representation. The result is the voltage across any two lines (line voltage) is √3 times greater than the voltage across one phase winding (phase voltage).

This understanding is essential for calculating voltage levels in a delta-connected transformer system and is