In a series \(LCR\) resonant circuit, the quality factor is measured as \(100\) If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be .........

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Answer & Solution

Correct Answer

(D) \(400\)

Step-by-step Solution

Detailed explanation

\(Q =\frac{ X _{ L }}{ R }=\frac{\omega L }{ R }=\frac{1}{\sqrt{ LC }} \frac{ L }{ R }=\frac{\sqrt{ L }}{ R \sqrt{ C }}\)

\(Q ^{\prime}=\frac{\sqrt{2 L }}{\left(\frac{ R }{2}\right) \sqrt{ C }}=2 \sqrt{2} Q =2 \sqrt{2}(100)\)

\(=282.84\)

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