JEE Mains · Physics · STD 12 -Alternating current
- JEE Mains 2021
- Medium
- MCQ
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 :
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
We know that power factor is \(\cos \phi\)
\(\cos \phi=\frac{ R }{ Z }\)
\(Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}} \quad \ldots\)
\(\Rightarrow Z =\sqrt{6^{2}+(10-4)^{2}}\)
\(\Rightarrow Z =6 \sqrt{2} \mid \cos \phi=\frac{6}{6 \sqrt{2}}\)
\(\cos \phi=\frac{1}{\sqrt{2}}\)
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