Question

The impedance of an AC circuit is Z=$100\angle {30}^{\circ }$. The resistance od circuit is :

Answer 1

$Z=\sqrt{R^2+(X_L-X_C{)}^2}\angle {\tan }^{-1}\frac{X_L-X_C}{R}$

$\Rightarrow R^2+(X_L-X_C{)}^2={100}^2$(equation $1$)

$\frac{X_L-X_C}{R}=\tan {30}^o=\frac{1}{\sqrt{3}}$

$\Rightarrow X_L-X_C=\frac{R}{\sqrt{3}}$(equation $2$)

Putting equation $2$ in $1$

$R^2+\frac{R^2}{3}={100}^2$

$\Rightarrow 4R^2=3\times 100\times 100$

$\Rightarrow R^2=3\times 25\times 100$

$\Rightarrow R=86.6\Omega$