Question

A series $LR$ circuit is connected to an ac source of frequency co and the inductive reactance is equal to $2R$. A capacitance of capacitive reactance equal to $R$ is added in series with $L$ and $R$. The ratio of the new power factor to the old one is :

• A. $\sqrt{\frac{2}{3}}$
• B. $\sqrt{\frac{2}{5}}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\sqrt{\frac{5}{2}}$

Answer 1

Answer: (D)

$Powerfacto{r}_{\left(old\right)}$
$=\frac{R}{\sqrt{R^2+X_{L^2}}}=\frac{R}{\sqrt{R^2+{\left(2R\right)}^2}}=\frac{R}{\sqrt{5}R}$
$Powerfacto{r}_{\left(new\right)}$
$=\frac{R}{\sqrt{R^2+{\left(X_L-X_C\right)}^2}}=\frac{R}{\sqrt{R^2+{\left(2R-R\right)}^2}}$
$=\frac{R}{\sqrt{2}R}$
$\therefore \frac{Newpowerfactor}{Oldpowerfactor}=\frac{\frac{R}{\sqrt{2}R}}{\frac{R}{\sqrt{5}R}}$