Question

Two ac sources feed a common variable resistive load as shown in figure. Under the maximum power transfer condition, the power absorbed by the load resistance $R_L$ is

• A. 2200 W
• B. 1250 W
• C. 1000 W
• D. 625 W

Answer 1

The correct option is D 625 W

For obtaining maximum power absorbed by $R_L$, we find thevenin's equivalent circuit across $R_L$.



$Z_{th}$ is calculated by short-circuting the voltage sources.

$Z_{th}=(6+j8)||(6+j8)=3+j4\Omega$



$\frac{V_{th}-100\angle 0^o}{6+j8}+\frac{V_{th}-90\angle 0^o}{6+j8}=0$

$V_{th}=100\angle 0^{o}V$



For maximum power transfer,

$R_L=\sqrt{R_{th}^2+X_{th}^2}=\sqrt{3^2+4^2}=5\Omega$

$I=\frac{V_{th}\angle 0^{\circ }}{(3+j4)+R_L}=\frac{100}{8+j4}$

$=11.18\angle -{26.56}^{o}A$

Power absorbed by $R_L$(max.)

$=I^2{R}_L={11.18}^2\times 5$

= 625 W