Max power delivered to variable resistor

AI Thread Summary
To determine the maximum power delivered to the variable resistor in the circuit, first identify the Thevenin equivalent voltage (V_th) and resistance (R_th). Redraw the circuit to clarify node connections and find R_th by shorting the voltage source and calculating the equivalent resistance between the specified nodes. For V_th, calculate the open circuit voltage across the nodes with the voltage source included, which was found to be 30V. Once both V_th and R_th are established, apply the maximum power transfer theorem to find the maximum power delivered to the variable resistor. This method ensures accurate calculations for circuit analysis.
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Homework Statement


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Determine the maximum power that can be delievered to the varaible resistor R in the circuit of Fig 4.139.


Homework Equations





The Attempt at a Solution



I am not sure how to handle this because the resistor is in that diamond structure. I need to find V thev and R thev Any advice or a hint to get started?
 
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To find R_{th}, short the voltage source. That means drawing a vertical line connecting the blue nodes in your 2nd diagram. Then you must find the equivalent resistance between the red nodes. You have to redraw the circuit in order to solve it easily.

Next to find V_{th}, from the original diagram find the open circuit potential difference across the red nodes with the voltage source added back in. That would be the thevenin voltage. You can use nodal analysis to solve this. I got 30V for this. Once you got both, you can use the formulae for the maximum power theorem to get the answer.
 
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