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schematic

simulate this circuit – Schematic created using CircuitLab

Can we apply Maximum Power transfer theorem if we are given two networks both with voltage sources. In solution it was said that for maximum power transfer the voltage across the network B should be half of Vin and current through R1 should be same as if a resistor resistor of 5 ohms is connected across boundary port of Network A and Network B.I don't know if I can trust it.I cannot prove it .

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  • \$\begingroup\$ For this circuit to mean anything, the voltage across r3 must be lower than V2. If the voltage drop across r3 is equal to 12V, then R2 is zero ohms. Ohms law could be used to find r2. \$\endgroup\$ – drtechno May 19 at 17:39
  • \$\begingroup\$ @drtechno: Your comment makes no sense at all. It is certainly possible for V2 to absorb power rather than deliver power, and it makes sense for it to do so in the context of the question. \$\endgroup\$ – Dave Tweed May 20 at 20:54
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Yes, Mr. Gupta is correct. Spice simulation shows the maximum power r2 to be 5.2 ohms

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  • \$\begingroup\$ Putting R2 as 5.2 and calculate I am getting Power transferred as 125 W. \$\endgroup\$ – SUNITA GUPTA May 20 at 2:32
  • \$\begingroup\$ Yes, 5.2 ohms is the correct answer, but using a simulator to find the solution numerically is "cheating" -- what is the analytical justification for this answer? \$\endgroup\$ – Dave Tweed May 20 at 20:35
  • \$\begingroup\$ I guess that the answer to this question does not reveal any particular overriding principle of circuits, like the "maximum power transfer theorem". However, if you analyze the circuit with R2 as a free parameter, find the sum of the powers dissipated in R2 ,R3, and V2, and then find a maximum of this function based on R2, you can solve for the R2 that maximizes the function, which turns out to be 26/5 in this case. \$\endgroup\$ – user69795 May 22 at 13:29

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