Question

Consider the circuit shown in the figure below,
Assume $V_s=\left(250\sin 500t\right)V$ and $Z_0=(100-j200)\Omega$. If $Z_L$ be a parallel combination of R and C, then the value of R and C such that the maximum power transfer takes from source to load are respectively

• A. $R=8\Omega andC=500\mu F$
• B. $R=100\Omega andC=10\mu F$
• C. $R=250\Omega andC=250\mu F$
• D. $R=500\Omega andC=8\mu F$

Answer 1

The correct option is D $R=500\Omega andC=8\mu F$

$Z_L=R||(-j{X}_C)=\frac{R(-j{X}_C)}{R-j{X}_C}=\frac{R(-j{X}_C)}{R-j{X}_C}\times$

$\frac{R+j{X}_C}{R+j{X}_C}$

$=\frac{R{X}_C^2}{R^2+X_C^2}-j\frac{R^2{X}_C}{R^2+X_C^2}...\left(i\right)$

For maximum power transfer $Z_L=Z_0^{\ast }$

$\because Z_0=100+j200$

$\therefore Z_L=100-j200....\left(ii\right)$

On comparing equation (i) and (ii), we get,

$\frac{R{X}_C^2}{R^2+X_C^2}=100and\frac{R{X}_C^2}{R^2+X_C^2}=200$

on solving , we get $X_C=250\Omega$

$C=\frac{1}{500X_C}=8\mu F$

and $R=500\Omega$