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  4. In a series LCR circuit, the inductive reactance ( X L ) is 10 Ω and the capacitive reactance ( X C ) is 4 Ω. The resistance ( R ) in the circuit is 6 Ω. The power factor of the circuit is:

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Q. 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:

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Solution:

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We know that power factor is $\cos \phi$,
$\cos \phi=\frac{ R }{ Z }\,\,\,\,\dots(1)$
$Z =\sqrt{ R ^{2}+\left( X _{ L }- X _{ C }\right)^{2}} \ldots(2)$
$(\omega L -1 / \omega C )$
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$\Rightarrow Z=\sqrt{6^{2}+(10-4)^{2}}$
$\Rightarrow Z=6 \sqrt{2} \mid \cos \phi=\frac{6}{6 \sqrt{2}}$
$\cos \phi=\frac{1}{\sqrt{2}}$