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(B) For better tuning of a series $LCR$ circuit,the quality factor $(Q)$ should be as high as possible.The quality factor is given by the formula: $Q

Vedclass · Accepted Answer

$R=15 \Omega, L=3.5 	ext{ H}, C=30 \mu	ext{F}$

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(B) For better tuning of a series $LCR$ circuit,the quality factor $(Q)$ should be as high as possible.The quality factor is given by the formula: $Q = \frac{1}{R} \sqrt{\frac{L}{C}}$.To maximize $Q$,we need a small resistance $(R)$ and a large ratio of inductance $(L)$ to capacitance $(C)$.Let us calculate the factor $F = \frac{1}{R} \sqrt{\frac{L}{C}}$ for each option:$A: F = \frac{1}{20} \sqrt{\frac{1.5}{35 	imes 10^{-6}}} \approx 10.35$$B: F = \frac{1}{15} \sqrt{\frac{3.5}{30 	imes 10^{-6}}} \approx 22.79$$C: F = \frac{1}{25} \sqrt{\frac{2.5}{45 	imes 10^{-6}}} \approx 9.43$$D: F = \frac{1}{15} \sqrt{\frac{2.5}{45 	imes 10^{-6}}} \approx 15.71$Comparing the values,option $B$ provides the highest quality factor,which indicates better tuning.

For better tuning of a series $LCR$ circuit in a communication system,the preferred combination is

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