Third-order RLC circuit with dual power supply, " EXO 12 Vidéo 1, 2 "

A circuit composed of several circuits of the ‘RL and RLC’ type is supplied by a cosine voltage source and a sinusoidal current source, determine the current passing through a specific element of the circuit, the calculations will be carried out using a Thévenin equivalent circuit.
We begin by removing the load Z, whose value is unknown, to calculate the equivalent Thévenin impedance Zth at the connection points of Z, without the load Z. We then calculate the Thévenin equivalent voltage Vth at the same connection points of the load Z, without the load Z. When Vth and Zth have been found, the Thévenin equivalent circuit is drawn using the values of Vth and Zth, and the load Z is connected to the Thévenin equivalent circuit in order to determine its value, bearing in mind that the maximum power will be transmitted to Z when Z is equal to the conjugate of Zth, i.e. Z=Zth*.
And when Z=Zth* the maximum power is: Pmaxi= V²/(8.Rth)
Note: A capacitor C or an inductor L is a reactive element. If a circuit has only one reactive element, the circuit is said to be of the first order; if it has ‘N’ reactive elements, the circuit is said to be of the Nth order. In this case we have two inductors and a capacitor, so the circuit is of the third order.