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This relates to max power transfer. Here’s my circuit:

schematic

simulate this circuit – Schematic created using CircuitLab

My goal is to try and find the value of R for the maximum power that can be delivered to it. Then I’ll calculate that power as well. I have tried drawing the circuit with an a port on the left of the R resistor and a b port on the right of the R resistor and then trying to calculate Rth by shorting the independent voltage sources, but each time I do that and apply KCL or KVL I get equations that equal zero or not enough equations to solve for all the unknowns.

That’s just Rth, I do not even know where to get started for calculating Vth for this circuit. My best guess is that I will ignore the R or load resistor and then apply nodal analysis or some other techniques but I’m not sure which one to use.

I know these equations:

    \[V_{oc}=V_{th};;;;;;I_N=I_{sc};;;;;;R_N=R_{th}={V_{oc}over I_{sc}};;;;;;R_L=R_{th};;;;;;p_{max}={V_{th}^2 over {4R_{th}}};;;;;;When;;;R_L ne R_{th};;;p=i^2R_L=({V_{th}over{R_{th}+R_L}})^2R_L\]

I know those equations but just do not know how to get them correctly.

Sorry I can’t show work or explain it more, this is as far as I can get right now. Any help would be very appreciated. Thank you!

Right now I’m most familiar with superposition, Thevenin, Norton, Nodal, Mesh, and Ohm’s law.

EDIT: in case anyone is still reading this, I’m still stuck and every time I try to solve for Voc or Isc I get a system of equations that can’t be solved.