Determine the load resistance for which the power delivered to the circuit is a maximum. Graph the dependence of the power on the load resistance.

Explanation

The power `R_("tot")=epsi^2//(R+r)` is at its maximum in conditions of short-circuit (R =0). The short circuit power is `R_("sh.e")=epsi^2//r`.
The power in the external circuil is at its maximum when R = r.
To check this consider the extremum of the expression `P_(ex)=(epsi^2)/(r). (Rr)/((R+r)^2=(epsi^2)/(ry)`
We have
`y=((R+r)^2)/(Rr)=R/r+2+r/R=R/r-2+r/R+r=`
`=(sqrt(R/r)-sqrt(r/R))^2+4`
Obviously, y= 4 for R = r is minimum value. In this case the power in the external circuit is maximum. The corresponding graphs are shown in Fig. 26.13.