Problem 92-3    Source:  Problem developed by the site author.

Based on the previous problem (problem 92-2), suppose we have connected to the secondary of the transformer a load of 40 kVA with FP = 0.85. Find:

a) Joule losses, or copper losses.

b) In this condition, what is the efficiency of the transformer.

Solution of the Problem 92-3

Item a

Initially we will determine the value of the electrical current in the secondary, I₂, of the transformer.

As the transformation ratio in the previous problem was already calculated, we can calculate the current in the transformer primary, that is, I₁. So

As the value of R'_eq has already been calculated, which is the equivalent resistance of the windings of the transformer referenced to the primary, we can calculate the joule losses using the equation eq. 92-19, or

Carrying out the calculation, we find

Note that since we are not we are using the rated power of the transformer and the losses depend on the current, the value found is lower than the losses in the short-circuit test. On the other hand, iron losses do not depend on the current, then its value remains being 900 W.

Item b

Now let's use the equation eq. 92-21 to calculate the transformer efficiency, remembering that R''_eq I₂² = R'_eq I₁². So we have:

Carrying out the calculation, we find