Maximum direct current power Vdc, " EXO 5 Video 1, 2 "

We have a quadripole circuit, like transistors, with an independent voltage source and a dependent voltage source. The left and right sides of the circuit are simply connected by a common ground. However, whatever the circuit configuration, it can always be transformed into an equivalent Thévenin circuit consisting of an equivalent resistor Rth and an equivalent voltage source Vth.
Both the resistor Rth and the source Vth can be positive or negative. For the purposes of this exercise, Vth is negative; simply invert the voltage arrow representing it.
When the Thévenin circuit is found, we connect it to the load Rc to deduce the maximum power absorbed by Rc, when Rc = Rth.
Knowing that Pmax= (Vsource)² /4.Rth where Vsource = Vth since we've replaced the original circuit with Thévenin's.
Note: Rc must be equal to Rth to obtain the maximum power Pmax. If Rc is slightly higher or lower than Rth, the power absorbed by Rc will not be maximum.