Question from exam, couldn’t do this question and dont understand how to…

The discussion centers on determining the resistor value R that maximizes power delivery in a circuit containing a current-dependent voltage source and a current source. The problem is complex due to the presence of dependent sources and feedback loops, making Thevenin equivalent analysis challenging. Approaches suggested include using node and mesh analysis to write and solve circuit equations, differentiating power expressions to find maxima, and applying the maximum power transfer theorem where maximum power occurs when the load resistance equals the source (Thevenin) resistance. The circuit features a current-controlled voltage source (transresistance amplifier) and a 1-ampere current source in series with a 1-ohm resistor, which is effectively negligible. Stability analysis reveals a positive feedback loop involving the dependent source and resistors, with circuit stability dependent on R values; specifically, the circuit is stable for R > 1 Ω and unstable for R < 1 Ω. Sign conventions and correct interpretation of dependent sources are critical, as errors can lead to contradictory or unstable solutions. The problem is noted as difficult and somewhat artificial compared to practical real-world circuits.
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