The correct answer is: $\frac{{{\text{R}}_2^2}}{{{{\text{K}}^2}}}$
The equivalent secondary resistance referred to primary is the resistance of a resistor that, when connected to the primary winding of the transformer, would dissipate the same power as the actual secondary resistance when connected to the secondary winding.
The transformation ratio is the ratio of the number of turns in the primary winding to the number of turns in the secondary winding.
The equivalent secondary resistance referred to primary is given by:
$$R_{eq} = \frac{{{R_2}^2}}{{K^2}}$$
where:
- $R_{eq}$ is the equivalent secondary resistance referred to primary
- $R_2$ is the resistance of the secondary winding
- $K$ is the transformation ratio
Option A is incorrect because it does not take into account the transformation ratio.
Option B is incorrect because it divides the resistance of the secondary winding by the square of the transformation ratio. This would be the correct answer if the resistance of the secondary winding were in parallel with the resistance of the primary winding. However, in this case, the resistance of the secondary winding is in series with the resistance of the primary winding.
Option C is incorrect because it squares the resistance of the secondary winding. This would be the correct answer if the resistance of the secondary winding were in series with the resistance of the primary winding. However, in this case, the resistance of the secondary winding is in parallel with the resistance of the primary winding.
Option D is incorrect because it divides the resistance of the secondary winding by the transformation ratio. This would be the correct answer if the resistance of the secondary winding were in series with the resistance of the primary winding. However, in this case, the resistance of the secondary winding is in parallel with the resistance of the primary winding.