Question:
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
Solution:
$\mathrm{Q}=\frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}}=\frac{\omega \mathrm{L}}{\mathrm{R}}=\frac{1}{\sqrt{\mathrm{LC}}} \frac{\mathrm{L}}{\mathrm{R}}=\frac{\sqrt{\mathrm{L}}}{\mathrm{R} \sqrt{\mathrm{C}}}$
$Q^{\prime}=\frac{\sqrt{2 L}}{\left(\frac{R}{2}\right) \sqrt{C}}=2 \sqrt{2} Q=2 \sqrt{2}(100)$
$=282.84$
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