Step 1 :Given the frequencies $f_{AC1} = 50 Hz$ and $f_{AC2} = 60 Hz$, we need to find the frequencies $f_{DC1}$ and $f_{DC2}$ and then order all four frequencies from largest to smallest.
Step 2 :We know that the frequency of a transformer is related to the number of turns in the primary and secondary coils. The relationship is given by: $$\frac{f_{primary}}{f_{secondary}} = \frac{N_{primary}}{N_{secondary}}$$
Step 3 :For $f_{DC1}$, we have: $$\frac{f_{AC1}}{f_{DC1}} = \frac{N_{AC1}}{N_{DC1}}$$
Step 4 :For $f_{DC2}$, we have: $$\frac{f_{AC2}}{f_{DC2}} = \frac{N_{AC2}}{N_{DC2}}$$
Step 5 :Given the number of turns: $N_{AC1} = 100$, $N_{DC1} = 200$, $N_{AC2} = 100$, and $N_{DC2} = 150$, we can solve these equations for $f_{DC1}$ and $f_{DC2}$.
Step 6 :Calculating $f_{DC1}$: $$f_{DC1} = \frac{f_{AC1} \times N_{DC1}}{N_{AC1}} = \frac{50 \times 200}{100} = 100 Hz$$
Step 7 :Calculating $f_{DC2}$: $$f_{DC2} = \frac{f_{AC2} \times N_{DC2}}{N_{AC2}} = \frac{60 \times 150}{100} = 90 Hz$$
Step 8 :Final Answer: The correct order of frequencies is $f_{AC2} > f_{DC2} > f_{AC1} > f_{DC1}$, which corresponds to option a. \(\boxed{f_{AC2}>f_{AC1}>f_{DC2}>f_{DC1}}\)