Explanation:

When two single-phase transformers are connected in parallel, the total impedance is a combination of the individual transformer impedances. The impedance of a transformer is represented by its equivalent series impedance (Z) which consists of a resistive component (R) and a reactive component (X). The X/R ratio is the ratio of the reactive component to the resistive component.

Given:
- Transformers A and B are operating in parallel.
- Transformer A has a higher impedance than transformer B.
- The X/R ratio of both transformers is identical.

Implication of identical X/R ratio:
The identical X/R ratio means that the reactive component of the impedance is proportional to the resistive component for both transformers. This implies that the impedance of both transformers has the same phase angle, and hence the power factor is the same.

Implication of higher impedance for transformer A:
Since transformer A has a higher impedance than transformer B, it means that the magnitude of the impedance (Za) for transformer A is greater than the magnitude of the impedance (Zb) for transformer B.

Relationship between impedance and apparent power:
The apparent power (S) is the product of the voltage (V) and current (I) in an AC circuit. The apparent power is also equal to the product of the magnitude of the impedance (Z) and the magnitude of the current (I). Mathematically, S = V * I = |Z| * |I|.

Derivation:
Let's consider the ratio of the impedance of transformer A to the impedance of transformer B.

Za/Zb = |Za| / |Zb|

Since the X/R ratio is identical for both transformers, the power factor is the same. Therefore, we can write the current in terms of the apparent power and the impedance.

I = S / |Z|

Substituting this expression for current in the equation for impedance ratio:

Za/Zb = |Za| / |Zb| = (Sa / |Ia|) / (Sb / |Ib|)

Since the power factor is the same for both transformers, the magnitudes of the currents are equal (|Ia| = |Ib|).

Za/Zb = (Sa / |Ia|) / (Sb / |Ib|) = Sa / Sb

Therefore, the ratio of the impedance of transformer A to the impedance of transformer B is equal to the ratio of the apparent power of transformer A to the apparent power of transformer B.

Za/Zb = Sa / Sb

Conclusion:
Hence, the correct answer is option A: Za/Zb = Sb/Sa.