Q111 / 125 · BITSAT 2021 · Physics

For an RLC circuit driven with voltage of amplitude $V_{m}$ and frequency $\omega_{0}=\frac{1}{\sqrt{\mathrm{LC}}}$ the current exhibits resonance the quality factor, $Q$ is given by

  • A
    $\frac{\omega_{0}}{\mathrm{~L}}$
  • Correct answer
    B
    $\frac{\omega_{0} \mathrm{~L}}{\mathrm{R}}$
  • C
    $\frac{\mathrm{R}}{\omega_{0} \mathrm{C}}$
  • D
    $\frac{\mathrm{CR}}{\omega_{0}}$

Solution

Total angular momentum of the system initially \(\mathrm{L}_{\mathrm{i}}=\mathrm{I}_{1} \mathrm{w}+\mathrm{I}_{2}(0)=\mathrm{I}_{1} \mathrm{w}\) Total angular momentum of the system finally \(\mathrm{L}_{\mathrm{f}}=\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right) \mathrm{w}_{2}\) According to conservation of angular momentum i.e. \(\mathrm{L}_{\mathrm{i}}=\mathrm{L}_{\mathrm{f}}\) \(\begin{aligned} &\Rightarrow \mathrm{I}_{1} \omega=\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right) \omega_{2} \\ &\Rightarrow \omega_{2}=\frac{\mathrm{I}_{1} \omega}{\mathrm{I}_{1}+\mathrm{I}_{2}} \end{aligned}\)

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

More Alternating Current Questions