Maximum Power Transfer

Thread Starter


Joined Nov 16, 2006
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?




Joined Apr 2, 2007
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?


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