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Question:
In a series LCR circuit, the inductive reactance $\left(\mathrm{X}_{\mathrm{L}}\right)$ is $10 \Omega$ and the capacitive reactance $\left(\mathrm{X}_{\mathrm{C}}\right)$ is $4 \Omega$. The resistance (R) in the circuit is $6 \Omega$. The power factor of the circuit is :
Correct Option: , 3
Solution:
We know that power factor is $\cos \phi$,
$\cos \phi=\frac{R}{Z}$ ..........(1)
$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$ .......(2)
$(\omega \mathrm{L}-1 / \omega \mathrm{C})$
$\Rightarrow Z=\sqrt{6^{2}+(10-4)^{2}}$
$\Rightarrow Z=6 \sqrt{2} \mid \cos \phi=\frac{6}{6 \sqrt{2}}$
$\cos \phi=\frac{1}{\sqrt{2}}$
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