Which of the following combinations should be | vedclass

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(A) The quality factor $(Q)$ of an $L-C-R$ circuit determines the sharpness of resonance or the tuning quality. It is given by the formula:$Q = \frac{

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The quality factor $(Q)$ of an $L-C-R$ circuit determines the sharpness of resonance or the tuning quality. It is given by the formula:$Q = \frac{1}{R} \sqrt{\frac{L}{C}}$For better tuning,the quality factor $Q$ should be as high as possible.Calculating $Q$ for each option:$1$. For option $(A)$: $Q_1 = \frac{1}{15} \sqrt{\frac{3.5}{30 	imes 10^{-6}}} = \frac{1}{15} \sqrt{\frac{3.5 	imes 10^6}{30}} = \frac{1000}{15} \sqrt{0.1167} \approx 22.77$$2$. For option $(B)$: $Q_2 = \frac{1}{25} \sqrt{\frac{1.5}{45 	imes 10^{-6}}} = \frac{1000}{25} \sqrt{\frac{1.5}{45}} = 40 \sqrt{0.0333} \approx 7.30$$3$. For option $(C)$: $Q_3 = \frac{1}{20} \sqrt{\frac{1.5}{35 	imes 10^{-6}}} = \frac{1000}{20} \sqrt{\frac{1.5}{35}} = 50 \sqrt{0.0428} \approx 10.35$$4$. For option $(D)$: $Q_4 = \frac{1}{25} \sqrt{\frac{2.5}{45 	imes 10^{-6}}} = \frac{1000}{25} \sqrt{\frac{2.5}{45}} = 40 \sqrt{0.0555} \approx 9.43$Comparing the values,$Q_1$ is the highest. Therefore,option $(A)$ provides the best tuning.

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

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