Question

In series LR circuit $X_L=3R$ and R is resistance. Now a capacitor with $X_C=R$ is added in series. Ratio of new to old power factor is?

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

Answer 1

The correct option is D $\sqrt{2}$

Power factor

$\cos \varphi =\frac{R}{Z}$

impedance $Z=\sqrt{x_2^2+R^2}=\sqrt{10R^2}$

$\cos {\varphi }_1=\frac{R}{\sqrt{10}R}=\frac{1}{100}$

$Z_2=\sqrt{(X_L-X_C{)}^2+R^2}$

$=\sqrt{5}R$

$\cos {\varphi }_2=\frac{R}{Z_2}=\frac{1}{\sqrt{5}}=\frac{\cos {\varphi }_2}{\cos {\varphi }_1}=\sqrt{2}$.