# Maximum Power Transfer

#### mlkcampion

Joined Nov 16, 2006
59
Hey
I was reading through my copy of Schuams Outlines (Electric Circuits)
and i came across the theory of Maximum Power transfer, i have already
looked at the threads on this topic however my question regards the
equation used to describe the power absorb by the load.

I have scanned the small section from Schuams Outline. (see attachment)
I can't work out how you go from the first equation to the final one
which i have underlined in orange, i understand that the part inside
the square braces is the effeciency but still can't get to this result. Can someone explain?

Cheers

#### recca02

Joined Apr 2, 2007
1,212
one way to get to the expression RL=R
wud be
differentiating the PL expression(the simple one derived from power =sq(i).r) and equating to zero and u may even check with second derivative whether it implies a maxima or minima by finding if the value of second derivative is positive or negative.

edit: right now i can only explain how to reach that expression (manipulation has been my specialty).
multiply numerator and denominator by 4R.
now manipulate as (RL+R)^2 -(RL+R)^2= 4RL.R
rest shud be easy split the fraction in two parts and cancel (RL+R)^2 take out common factor V^2/4R.
got it?

#### mlkcampion

Joined Nov 16, 2006
59
Cheers recca
I see what your doing alright, though for some reason i end up with
4R^2 under the line!!

Mike

#### recca02

Joined Apr 2, 2007
1,212
do not try to simplify the denominator,
just cancel what'er term can be cancelled. do not mess with the brackets 