Question

In a series $LCR$ circuit, the inductive reactance is twice the resistance and the capacitive reactance is $\frac{1}{3^{r d}}$ 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,
$X_{L}=2 R \text { and } X_{C}=\frac{X_{L}}{3}$
Impedance of $L-C-R$ circuit is given as
$Z =\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$
$=\sqrt{R^{2}+\left(X_{L}-\frac{X_{L}}{3}\right)^{2}}$
$=\sqrt{R^{2}+\left(\frac{2 X_{L}}{3}\right)^{2}}=\sqrt{R^{2}+\frac{4 X_{L}^{2}}{9}}$
$=\sqrt{R^{2}+\frac{4}{9}(2 R)^{2}}=\sqrt{R^{2}+\frac{16}{9} R^{2}}$
$=\sqrt{\frac{25 R^{2}}{9}} \Rightarrow Z=\frac{5}{3} R$
Power factor $=\cos \varphi$
$=\frac{R}{Z}=\frac{R}{5 R / 3}=\frac{3}{5}=0.6$