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  4. 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 (Approximate the answer to the nearest integer)

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Q. 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___ (Approximate the answer to the nearest integer)

NTA AbhyasNTA Abhyas 2022

Solution:

Quality factor $=\frac{X_{L}}{R}=\frac{\omega L}{R}$
$Q=\frac{1}{\sqrt{L C}}\frac{L}{R}$
$Q=\left(\frac{1}{\sqrt{C}}\right)\frac{\sqrt{L}}{R}$
$Q=\frac{X L}{R}=\frac{\omega L}{R}=\frac{1}{\sqrt{L C}}\frac{L}{R}=\frac{1}{R}\frac{\sqrt{L}}{\sqrt{C}}$
$Q^{'}=\frac{\sqrt{2 L}}{\left(\frac{R}{2}\right) \sqrt{C}}=2\sqrt{2}Q$
$Q^{'}=282.84$