Question

In a series $LCR$ circuit, the inductive reactance is twice the resistance and the capacitive reactance is $\frac{1}{3^{rd}}$ of the inductive reactance. The power factor of the circuit is________

• A. 1.5
• B. 1.15
• C. 0.6
• D. 0.5

Answer 1

Answer: (C)

In $L-C-R$ circuit,
$X_L=2R\text{ and }{X}_C=\frac{X_L}{3}$
Impedance of $L-C-R$ circuit is given as
$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$
$=\sqrt{R^2+{\left(X_L-\frac{X_L}{3}\right)}^2}$
$=\sqrt{R^2+{\left(\frac{2X_L}{3}\right)}^2}=\sqrt{R^2+\frac{4X_L^2}{9}}$
$=\sqrt{R^2+\frac{4}{9}(2R{)}^2}=\sqrt{R^2+\frac{16}{9}{R}^2}$
$=\sqrt{\frac{25R^2}{9}}\Rightarrow Z=\frac{5}{3}R$
Power factor $=\cos \phi$
$=\frac{R}{Z}=\frac{R}{5R/3}=\frac{3}{5}=0.6$