Problem 55-13    Source:   Problem 1 - List of RLC Problems - Discipline Electrical Circuits of the School of Engineering - UFRGS - 2011 - Prof. Dr. Valner Brusamarello.

Determine the impedance Z, in the circuit show in the Figure 55-13.1, so that we have I₂ = 10 ∠0°.

Solution of the Problem 55-13   

Note that the current source is in parallel with the voltage source. Then we can eliminate it. Determining the Thévenin equivalent for the points b-c.

And the impedance of Thévenin will be the parallel between the two inductors, or:

The Figure 55-13.2 shows the new configuration of the circuit after calculating the equivalent of Thévenin.

By the statement of the problem, it is known that I₂ = 10∠0°. So, this allows us to calculate Z_in, that is, the total impedance that the circuit offers to the voltage source.

Since all the components that are part of the circuit are in series, adding all of them must be obtained Z_in. So:

Performing the calculation:

That is, the impedance Z must be composed of a resistor of 5 ohms in series with an reactance inductive that has a 0.8 ohms, to achieve the value of I₂ requested in the problem statement.