In the text, an efficiency calculation for transformers is given as follows:

Efficiency = [ volts x amps (secondary) x power factor] / [(volts x amps (secondary)) + copper loss + core loss]

Notice that power factor is multiplied by secondary volts and amps in the numerator but not in the denominator. This means that we are considering the output of the transformer as true power only, but we are using apparent power for the input. This also means that according to this formula, a poor power factor can drive down the efficiency of the transformer considerably.

This seems okay to me; however, in the text, the example that follows uses apparent power for both input and output. No explanation is given as to why there is a discrepancy.

So which is correct? Should we use only apparent power or only true power in an efficiency calculation, or should we combine the two by using true power as the output of the transformer while using apparent power as an input?

Are there different "types" of efficiency calculations? Some that include power factor and others that do not?

Thanks for the help!