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R1 = 2 ohm

R2 = 5 ohm

What value of R3 maximizes the dissipation rate in resistance 3? (battery is ideal -> no internal resistance)

DIAGRAM:

_______________

|.........|...........|

R1.......R2.........R3

|.........|...........|

_ +......|...........|

- -.......|...........|

|.........|...........|

_______________

Someone posed this question on the forums years ago, but the answer wasn't entirely helpful. I couldn't reconcile some missing pieces of information.

I've established that the equivalent resistance in the whole circuit (expressed in terms of R3) is:

(7R3 + 10)/(R3 + 5)

I know that the power is maximized when the derivative of the power function is equal to zero, but the distinct absence of current is holding me back. I've also tried to use Kirchoff's laws to establish some equations to solve for current, but it introduces three new unknown values and several of the equations render themselves useless upon application.

Can someone help me with this?

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# Maximizing dissipation rate

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