# AC electrical generator

1. Oct 31, 2007

### tnho

1. The problem statement, all variables and given/known data
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=)

2. Nov 1, 2007

### George Jones

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

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?