What is the relationship of the turns ratio for a wye-delta transformer with a ratio of 2:1?

In a wye-delta transformer with a turns ratio of 2:1, the relationship concerning voltage can be understood through the fundamental principles of transformer operation. The turns ratio directly influences the transformation of voltage between the primary and secondary sides.

When the turns ratio is 2:1, it indicates that for every 2 turns on the primary winding, there is 1 turn on the secondary winding. This means that the voltage across the secondary is reduced in relation to the primary. Consequently, with this 2:1 turns ratio, the secondary voltage will indeed be half of the primary voltage. This is derived from the transformer voltage ratio formula, which states that the primary voltage divided by the secondary voltage equals the turns ratio. Thus, a higher number of turns on the primary winding results in a higher voltage, while a lower number of turns on the secondary leads to a lower voltage.

This relationship clearly establishes that with a 2:1 turns ratio, the secondary voltage cannot be greater than or equal to the primary voltage, thereby making the assertion that the secondary voltage is half of the primary voltage correct. The other options do not align with the transformations dictated by the turns ratio in this scenario.