In a series LCR resonant circuit,the quality | vedclass

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(NONE) The quality factor $Q$ of a series $LCR$ circuit is given by the formula: $Q = \frac{1}{R} \sqrt{\frac{L}{C}}$.Initially,$Q = 100$.When the ind

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$400$

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(NONE) The quality factor $Q$ of a series $LCR$ circuit is given by the formula: $Q = \frac{1}{R} \sqrt{\frac{L}{C}}$.Initially,$Q = 100$.When the inductance $L$ is increased by two fold $(L' = 2L)$ and the resistance $R$ is decreased by two fold $(R' = R/2)$,the new quality factor $Q'$ becomes:$Q' = \frac{1}{R'} \sqrt{\frac{L'}{C}} = \frac{1}{(R/2)} \sqrt{\frac{2L}{C}} = 2 	imes \sqrt{2} 	imes \left( \frac{1}{R} \sqrt{\frac{L}{C}} ight)$.Substituting the initial value of $Q$:$Q' = 2 \sqrt{2} 	imes Q = 2 	imes 1.414 	imes 100 = 282.8$.

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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