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  • In a series LCR circuit, the inductive reactance (XL) is 10and the capacitive reactance (XC) is 4. The resisatnce (R) in the circuit

In a series LCR circuit, the inductive reactance (XL) is 10\Omegaand the capacitive reactance (XC) is 4\Omega. The resisatnce (R) in the circuit is 6\Omega. The power factor of the circuit is:
Option: 1 \frac{1}{2\sqrt{2}}
Option: 2 \frac{\sqrt{3}}{2}
Option: 3 \frac{1}{2}
Option: 4 \sqrt{\frac{1}{2}}

Answers (1)

best_answer

\\ \text{We know that power factor is} \ \ \ cos \phi,

\begin{array}{l} \cos \phi=\frac{R}{Z} \ldots \ldots .(1) \\ \\ Z =\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}} \ldots .(2) \end{array}

\begin{array}{l} \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}} \end{array}

 

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Deependra Verma

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