Problem + Hard 58-1    Source:   Problem 61 - List of RLC Problems - Discipline Electrical Circuits of the School of Engineering - UFRGS - 2017 - Prof. doctor Valner Brusamarello.

When the circuit is in resonance I_T = 15 A. Furthermore, the voltage drop on the 3 Ω resistor is 30 volts and on the 1.5 Ω resistor is 19.84 volts, as shown in the circuit below. Determine   X,   X_C   and   R' so that the circuit is in resonance.

Attention - In the list of exercises at UFRGS, the answer to this problem has a typo. The correct answer is:   X = 12,   X_C = 4.96   and   R' = 2.57.

Problem + Hard 58-2    Source:   Problem elaborated by the website author

Given the quadrupole equations A below, determine Z so that I is maximum.