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I'm having a little trouble understanding the concept of impedance matching to maximise energy transfer. I understand that the reactance of a capacitor is [tex]X_c= \frac{1}{\omega C }[/tex] and that it is always 90 degrees lagging of the current in the complex plane which leads to a capacitors complex impedance being defined as [tex]X_c= \frac{-j}{\omega C }[/tex]. I also understand the reactance of an inductor is [tex] X_L= \omega L [/tex] and since it leads the current by 90 degrees, it has a complex inductance defined as [tex] X_L=j \omega L [/tex].

Since the reactance of the inductor and capacitor are always antiparallel to each other, but perp to the reactance of a normal resistor, you find the impedence of an LRC circuit to be [tex] Z=sqrt( R^2+(\omega L -\frac{1}{\omega C})^2 ) [/tex].

That's the point where my knowlege of AC circuits ends. Why does matching the output impedance of a generator with my load circuit maximise power transfer?

What are the conditions for this matching?

To make the discussion more concrete my motivation is this question http://grephysics.net/ans/8677/64 from an old GRE paper, that Im trying to wrap my head around.

Please help a poor theorist who hasnt seen circuits for many a year out.

Thanks