Question

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

• A. 0.8 $\Omega$
• B. 1.4 $\Omega$
• C. 2 $\Omega$
• D. 2.8 $\Omega$

Answer 1

The correct option is A 0.8 $\Omega$

Redrawing the diagram


Current through R will be

$i=\frac{10-3}{2+R}=\left(\frac{7}{2+R}\right)A$

Current through 3 V source is

$i_1=(i-\frac{3}{-j1})=i-3j$

So power delivered to circuit B by circuit A is

$P=i^{2}R+i_1\times 3$

$P={\left(\frac{7}{2+R}\right)}^2.R+(\frac{7}{2+R}-3j)3$

for P to be maximum $\frac{\partial P}{\partial R}$ will be zero.

$\frac{\partial P}{\partial R}=0$

${\left(\frac{7}{2+R}\right)}^2-\frac{98R}{(2+R{)}^3}-\frac{21}{(2+R{)}^2}=0$

49(2 + R) - 98R - 21(2 + R) = 0

98 - 42 = 49R + 21R

$R=\frac{56}{70}=0.8\Omega$