Non-Standard AC Power Optimization

An ideal AC voltage source drives a load consisting of a resistor R R and an inductive reactance X X in series. Let the active power consumed by the load be P P , and let the reactive power consumed by the load be Q Q .

What ratio of X R \frac{X}{R} maximizes the quantity ( P + Q ) (P + Q) ?

Note: R R and X X are both positive numbers with units of ohms.


The answer is 0.4142.

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