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)

$Power factor _{\left(old\right)}$
$=\frac{R}{\sqrt{R^{2}+X_{L^{2}}}} =\frac{R}{\sqrt{R^{2}+\left(2R\right)^{2}}} =\frac{R}{\sqrt{5 }R}$
$Power\, factor _{\left(new\right)}$
$=\frac{R}{\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}} =\frac{R}{\sqrt{R^{2}+\left(2R-R\right)^{2}}}$
$=\frac{R}{\sqrt{2}R}$
$\therefore \frac{New \,power\, factor}{Old \,power\, factor}=\frac{\frac{R}{\sqrt{2 }R}}{\frac{R}{\sqrt{5}R}}$