Question

In a series LR circuit $X_L=R$ and power factor of the circuit is $P_1$. When capacitor with capacitance $C$ such that $X_L=X_C$ is put in series, the power factor becomes $P_2$. The ratio $\frac{P_1}{P_2}$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{\sqrt{3}}{\sqrt{2}}$
• D. $2:1$

Answer 1

Answer: (B)

In case of L-R circuit
$Z=\sqrt{X_L^2+R^2}\&$ power factor
$P_1=\cos \varphi =\frac{R}{Z}$
As $X_L=R$
$\Rightarrow Z=\sqrt{2}R$
$\Rightarrow P_1=\frac{R}{\sqrt{2}R}\Rightarrow P_1=\frac{1}{\sqrt{2}}$
In case of L-C-R circuit
$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$
As $X_L=X_C$
$\Rightarrow Z=R$
$\Rightarrow P_2=\cos \varphi =\frac{R}{R}=1$
$\Rightarrow \frac{P_1}{P_2}=\frac{1}{\sqrt{2}}$