Final answer:
The question relates to determining the primary current and power factor for an ideal transformer given turn ratios, no-load current, and secondary current. However, without additional information such as voltages or power, these cannot be calculated directly.
Step-by-step explanation:
The student is asking about currents and power factors in an ideal transformer. An ideal transformer has a certain number of turns on the primary (Np) and secondary (Ns) coils and operates without energy losses typically associated with a real transformer. For an ideal transformer, the primary to secondary voltage ratio equals the turns ratio (Np/Ns), and the primary current (Ip) times primary voltage (Vp) equals the secondary current (Is) times secondary voltage (Vs), assuming no losses and 100% efficiency.
In this case, given that the no-load current is 2 A with a power factor of 0.2 lagging and the secondary current is 100 A at a 0.8 power factor lagging, you would use the transformer's voltage ratio and power relationships to calculate the primary current (Ip) and its power factor. However, since the question doesn't provide voltages or power, and only turn ratios with current values are given, these cannot be directly calculated without additional information. Normally, the calculation of the primary current would include the effects of the secondary current and the magnetizing current due to the no-load condition (with the mentioned power factor).
In practice, the power factor of the primary can be influenced by the magnetizing current and the current drawn by the secondary load. For an ideal transformer, the power factor could be determined considering the phase difference between the primary voltage and the total current taking into account both the magnetizing and load currents. The actual calculation would depend on the complex phasor sum of the no-load and load currents reflected back to the primary.