D

Step 1: Understand the basic working principle of a transformer. A transformer operates on the principle of electromagnetic induction and the relationship can be described using the equation: $$ V_s = V_p \times \frac{N_s}{N_p} $$ Where:

• $V_s$ = secondary voltage
• $V_p$ = primary voltage
• $N_s$ = number of turns in the secondary coil
• $N_p$ = number of turns in the primary coil

Step 2: Analyze the options provided:

• Option A: Voltage in the primary coil - The secondary voltage is directly proportional to the primary voltage due to the transformer relation.
• Option B: Ratio of number of turns in the two coils - The secondary voltage is determined by the turns ratio, thus it directly affects the secondary voltage.
• Option C: Frequency of the source - For an ideal transformer, the operating frequency does not affect the voltage ratio, however, in real transformers, it can affect losses but not the direct relationship of voltage to turns ratio.
• Option D: Both (C and frequency) - Considering that frequency can affect efficiency but not the basic principle relating voltage to turns ratio.

Conclusion: Voltage in the secondary coil is dependent on both the voltage in the primary coil and the turns ratio. Therefore, the correct response should indicate that the secondary voltage does not depend on Option C if considering ideal conditions. Thus, the answer is D, as Option C represents a factor that does not change the ideal relationship.
Therefore, the correct answer is D.