Q109 / 150 · MHT CET 2012 · Physics

The $Q$ -factor of a resonant circuit is equal to

  • A
    $\frac{1}{L} \sqrt{\frac{R}{C}}$
  • Correct answer
    B
    $\frac{1}{R} \sqrt{\frac{L}{C}}$
  • C
    $\frac{1}{R L} \sqrt{C}$
  • D
    $\frac{1}{C} \sqrt{\frac{R}{L}}$

Solution

The quality factor (Q-factor) of a resonant circuit $$ Q=\frac{\omega_{0} L}{R} $$ At resonance, $\omega_{0}=\frac{1}{\sqrt{L C}}$ $$ Q=\frac{1}{\sqrt{L} C} \cdot \frac{L}{R}=\frac{1}{R} \sqrt{\frac{L}{C}} $$

Hence, the correct answer is option: 'B'.

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