Maximum direct current power Vdc, " EXO 3 Video 1, 1 "

Three different DC voltage sources, Vs1=1[Vcc], Vs2=2[Vcc] and Vs3=3[Vcc], simultaneously supply a load Rc via three identical resistors R.
Determine the values of Rc and R so that the load Rc receives maximum power Pmax=150[mW], then Pmax=1000[mW] from Vs1, Vs2 and Vs3 simultaneously.
To do this, we remove the load Rc and determine the Thévenin equivalent circuit literally as a function of R, finding Rth=R/3.
Then a nodal calculation yields Vth=2[Vcc].
The Thévenin equivalent circuit therefore consists of Rht=R/3 and Vth=2[Vcc].
We then connect the load Rc to the Thévenin equivalent circuit to deduce the value of Rc so that it can absorb maximum power. Rc must be equal to Rth for maximum power Pmax, i.e. Rc=R/3.
Knowing that Pmax=(Vsource)²/(4.Rc), hence :
Pmax=(Vth)² / 4.(R/3)=(2)²/ 4.(R/3).
The Thévenin equivalent circuit is used to calculate the maximum power Pmax, which is why (Vth)² must be taken as the voltage source, not (Vsource)², which belongs to the general formula. When the maximum powers are found, we replace them with Pmax=0.15[W] and Pmax=1[W] respectively in the maximum power formula, to finally deduce R and Rc.
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