JEE Mains · Physics · STD 12 -7. Alternating current
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 .........
- A \(200\)
- B \(100\)
- C \(300\)
- D \(400\)
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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