Problem 91-3    Source:  Problem developed by the site author.

Be an ideal single-phase transformer powered by voltage ratings 13200/660 volts . On the secondary a load is connected whose value is Z_L = 10 + j6 ohms.

a) Calculate the current at the secondary and primary of the transformer.

b) Calculate the real and reactive power the load consumes.

c) Calculate the module of the impedance that is seen by the network.

Solution of the Problem 91-3

Item a

Using the load impedance in polar form, that is, Z_L = 10 + j6 = 11.66∠31°. Furthermore, taking as a reference the voltage in the primary, where we can write V₁ = 13 200∠0° and therefore V₂ = 660∠0°. Therefore, the current in the secondary will be:

Knowing the voltages in the primary and secondary, it is possible to calculate the transformation ratio, or:

Therefore, the current in the primary will be:

Item b

To calculate the powers requested in the problem, the following equations are used:

Item c

And, of course, the impedance that the network "sees" is given by:

Note that, in this particular case, we can obtain this impedance by reflecting the load to the primary, or: