The correct answer is D. both (b) and (c)

The efficiency of a transformer depends on several factors, including the load current and the power factor of the load.

A. supply frequency: The frequency of the supply voltage does not affect the transformer efficiency. It should be noted that, the transformer is designed to work efficiently within a specific frequency range, which is usually 50 or 60Hz.

B. load current: The load current is directly proportional to the core loss and copper loss of the transformer. The core loss is caused by the magnetic excitation of the core and the copper loss is caused by the resistance of the windings. As the load current increases, the core and copper losses also increase, which in turn decreases the transformer efficiency.

C. power factor of load: Power factor is the ratio of real power (active power) to apparent power (real power + reactive power). Low power factor loads cause more current to flow through the transformer than necessary, which increases the core and copper losses and decreases the transformer efficiency.

D. both (b) and (c): When the load current and power factor of load increase, the core and copper losses of the transformer also increase, which in turn decreases the transformer efficiency. Therefore, the efficiency of a transformer is directly related to the load current and the power factor of the load.