alternating-currents Question 13
Question: Q. 1. Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?
(a) $R=20 \Omega, L=1.5 H, C=35 \mu \mathrm{F}$.
(b) $R=25 \Omega, L=2.5 H, C=45 \mu \mathrm{F}$.
(c) $R=15 \Omega, L=3.5 H, C=30 \mu F$.
(d) $R=25 \Omega, L=1.5 H, C=45 \mu F$.
[NCERT Exemplar]
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Solution:
Ans. Correct option : (c)
Explanation : Quality factor $(Q)$ of an $L-C-R$ circuit is given by, $\quad Q=\frac{1}{R} \sqrt{\frac{L}{C}}$ Tuning of an $L-C-R$ circuit depends on quality factor of the circuit. Tuning will be better when quality factor of the circuit is high.
As, quality factor $(Q)$ of an $L-C-R$ circuit is given by,
$$ Q=\frac{1}{R} \sqrt{\frac{L}{C}} $$
For $Q$ to be high, $R$ should be low, $L$ should be high and $C$ should be low.
