The efficiency of a transformer is a measure of how well the transformer can convert electrical power from the primary coil to the secondary coil. It is defined as the ratio of the power output in the secondary coil to the power input in the primary coil, expressed as a percentage.
The correct option for the efficiency of a transformer is "Efficiency of a transformer = (power developed in the secondary coil ÷ power supplied to the primary coil) × 100%". This equation takes into account the losses that occur during the transformation process, such as heat and electromagnetic radiation. The power developed in the secondary coil is the output power, which is the power delivered to the load. The power supplied to the primary coil is the input power, which is the power delivered to the transformer.
The other options given in the question are not correct because they do not take into account the losses that occur during the transformation process. The first option calculates the voltage ratio between the secondary and primary coils, which is not the same as efficiency. The second option calculates the mechanical advantage and velocity ratio, which are relevant to mechanical systems, not transformers. The third option calculates the turns ratio between the secondary and primary coils, which is related to the voltage ratio, but not to efficiency.
Therefore, the correct answer is "Efficiency of a transformer = (power developed in the secondary coil ÷ power supplied to the primary coil) × 100%".