Problem + Hard 52-4    Source:   Adapted from Problem 3 of the 1st Exam of 2019 - Discipline Electric Circuits of Engineering School - PUCRS - 2019.

As a complement to the previous problem (see previous problem by clicking here!) determine:

a) The current I₁.

b) The values ​​of R_A , R_C and X_C .

c) A phasor diagram of the currents and voltages involved in the circuit.

Solution of the Problem + Hard 52-4

Item a

In the previous problem it was determined that S_A + S_C = V I^*₁ = 300 + j200 = 360.56∠33.7° VA. Then, one can calculate I^*₁ using the following relation:

Carrying out the calculation, we obtain:

So the value of I₁ will be:

Item b

With this data, you can calculate R_A, since it is known that P_A = 100 W, so :

Carrying out the calculation, we obtain:

Using the same procedure, the value of R_C can be calculated, since it is known that P_C = 200 W, soon:

Carrying out the calculation, we obtain:

And from the previous problem, in initial considerations, it is known that X_C = R_C, because the impedance angle Z_C is equal to 45°. Then:

Item c

In the figures below, graphs of currents and voltages relevant to the circuit are shown.