Electromagnetic Induction And Alternating Current Ques 75

  1. 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) $\frac{R}{\omega _0 C}$

Show Answer

Answer:

Correct Answer: 75.(b)

Solution:

Formula:

Quality Factor:

$$ Q=\frac{\omega _1-\omega _2}{\omega _0} $$

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.

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