Question 166 of 190

In a series LCR circuit, the inductive reactance $\left({X}_{L}\right)$ is $10\Omega$ and the capacitive reactance $\left({X}_{C}\right)$ is $4\Omega$. The resistance $(R)$ in the circuit is $6\Omega$. The power factor of the circuit is :

A$\dfrac{1}{2}$B$\dfrac{1}{2\sqrt{2}}$C$\dfrac{1}{\sqrt{2}}$D$\dfrac{\sqrt{3}}{2}$

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Answer: (C) $\dfrac{1}{\sqrt{2}}$

We know that power factor is $\cos \phi$,
$\cos \phi =\dfrac{R}{Z}...\left(1\right)$
$Z=\sqrt{{R}^{2}+{\left({X}_{L}-{X}_{C}\right)}^{2}}...\left(2\right)$

$\Rightarrow Z=\sqrt{{6}^{2}+(10-4{)}^{2}}$
$\Rightarrow Z=6\sqrt{2}∣\cos \phi =\dfrac{6}{6\sqrt{2}}$
$\cos \phi =\dfrac{1}{\sqrt{2}}$