Why Should Load Reactance Match Generator Reactance for Maximum Power Transfer?

[tnho]

Homework Statement

An alternating current electrical generator has a fixed internal impedance $$R_{g}+iX_{g}$$ and is used to supply power to a passive load that has an impedance $$R_{g} +iX_{l}$$, where $$i = \sqrt{-1}$$, $$R_{g}\neq 0$$, and $$X_{g} \neq 0$$. For maximum power transfer between the generator and the load, $$X_{l}$$ should be equal to...

The answer is $$X_{l}=X_{g}$$.

However, I don't know how come up with this answer. It seems that the maximum power transmission occur with the imaginary part of the total impedance of the system vanishes. But Why??

Thanks a lot=)

 

[George Jones]

Homework Statement

An alternating current electrical generator has a fixed internal impedance $$R_{g}+iX_{g}$$ and is used to supply power to a passive load that has an impedance $$R_{g} +iX_{l}$$, where $$i = \sqrt{-1}$$, $$R_{g}\neq 0$$, and $$X_{g} \neq 0$$. For maximum power transfer between the generator and the load, $$X_{l}$$ should be equal to...

The answer is $$X_{l}=X_{g}$$.

However, I don't know how come up with this answer. It seems that the maximum power transmission occur with the imaginary part of the total impedance of the system vanishes.

From your last sentence above, it seems that you forgot a negative sign in the equation above.

But Why??

It's a two variable max/min problem from mutivariable calculus.

The power delivered to the load is $P=|I^2| R_l$. What is I?