Electromagnetic Induction and Alternating Current 6 Question 4
4. For an $R-L-C$ circuit driven with voltage of amplitude $v _m$ and frequency $\omega _0=\frac{1}{\sqrt{L C}}$, the current exhibits resonance. The quality factor, $Q$ is given by
(2018 Main)
(a) $\frac{C R}{\omega _0}$
(b) $\frac{\omega _0 L}{R}$
(c) $\frac{\omega _0 R}{L}$
(d) $\frac{R}{\omega _0 C}$
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Answer:
Correct Answer: 4. (b)
Solution:
$$ Q=\frac{\omega _1-\omega _2}{\omega _0} $$
Here, $\omega _1-\omega _2=$ bandwidth $=\frac{R}{L}$
Substituting the values, we get
$$ Q=\frac{\omega _0 L}{R} $$
Alternative solution $\frac{\omega _0 L}{R}$ is the only dimensionless quantity, hence it must be the quality factor.
