Can anyone help me with the theorem "Maximum Power Transfer" on DC and AC circuits.

I know that
\(R_{L}=R_{S}\)
and
\(X_{L}=-X_{S}\)

but why. I need a proof.
can anyone explain the derivative of dP/dR, or how it should be solved.
any information would be appreciated.

 

Can anyone help me with the theorem "Maximum Power Transfer" on DC and AC circuits.

I know that
\(R_{L}=R_{S}\)
and
\(X_{L}=-X_{S}\)

but why. I need a proof.
can anyone explain the derivative of dP/dR, or how it should be solved.
any information would be appreciated.

If you follow this link,

http://en.wikipedia.org/wiki/Maximum_power_transfer_theorem

Instead of solving for dP/dR, they simply solve for the when the denominator in the P(R) expression is minimized. (This gives the maximum P(R))

The same approach is applied for AC circuits, only holding RL at a fixed value.