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  • 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 ______. Option: 1 282

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 ______.
Option: 1 282.84
Option: 2 369
Option: 3 123
Option: 4 876

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\begin{array}{l} \mathrm{Q}=\frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}}=\frac{\omega \mathrm{L}}{\mathrm{R}}=\frac{1}{\sqrt{\mathrm{LC}}} \frac{\mathrm{L}}{\mathrm{R}}=\frac{\sqrt{\mathrm{L}}}{\mathrm{R} \sqrt{\mathrm{C}}} \\ \\ \mathrm{Q}^{\prime}=\frac{\sqrt{2 \mathrm{~L}}}{\left(\frac{\mathrm{R}}{2}\right) \sqrt{\mathrm{C}}}=2 \sqrt{2} \mathrm{Q}=2 \sqrt{2}(100) \\\\ =282.84 \end{array}

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Deependra Verma

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