What primarily determines the voltage transformation in a transformer?

The voltage transformation in a transformer is primarily determined by the number of turns in the coils, which directly influences the ratio between the primary and secondary voltages. This principle is based on Faraday's law of electromagnetic induction, which states that the induced voltage in a coil is proportional to the rate of change of magnetic flux through that coil.

When a transformer is designed, if the primary coil has more turns than the secondary coil, the transformer steps down the voltage, resulting in a lower secondary voltage compared to the primary voltage. Conversely, if the secondary coil has more turns, it steps up the voltage. This ratio of turns—known as the turns ratio—plays a crucial role in determining how much the voltage will change as it passes through the transformer, making the number of turns the key factor in the transformation process.

The other aspects, such as frequency, winding length, and material, do affect the efficiency and performance of the transformer but do not directly determine the voltage transformation. For instance, while frequency can influence the transformer's behavior regarding inductance and loss, it does not dictate the voltage change ratio like the turns do. Thus, the correct choice reflects the fundamental operation and design principle of transformers.