ABSTRACT
A Thévenin equivalent circuit is shown in Figure 35.1 with source internal impedance, z =(r + jx) and complex load Z =(R+ jX).
The maximum power transferred from the source to the load depends on the following four conditions. Condition 1. Let the load consist of a pure variable resistance R (i.e. let X =0). Then current I in the load is given by:
I = E (r + R)+ j x
and the magnitude of current, |I |= E√[(r + R)2 + x2] The active power P delivered to load R is given by
P = |I |2 R= E 2R
(r + R)2 + x2
To determine the value of R for maximum power transferred to the load, P is differentiated with respect to R and then equated to zero (this being the normal procedure for finding maximum or minimum values using calculus). Using the quotient rule of differentiation,
dP dR
= E2 { [(r + R)2 + x2](1)− (R)(2)(r + R)
[(r + R)2 + x2]2 }
= 0 for a maximum (or minimum) value.
