The resistance \(R\) in Figure P3=59. is adjusted until maximum power is delivered to the load consisting of \(R\) and the \(12-\mathrm{k} \Omega\) resistor in parallel.

(a) Find the required value of \(R\).
(b) How much power is delivered to the load?
(c) Validate your answer using Multisim.
(d) How much power is delivered to the right \(12-\mathrm{k} \Omega\) resistor in the load?
(e) Compare this value to the power that would be delivered to the load if the resistor \(R\) did not exist.
(f) If the sole purpose of resistor \(R\) is to have the source deliver the most power to the right \(12-\mathrm{k} \Omega\) resistor, did it achieve the goal?

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50 mA 3 . R Load 12