An inductor of inductance $\mathrm{L}$, a capacitor of capacitance $\mathrm{C}$ and a resistor of resistance…

An inductor of inductance $\mathrm{L}$, a capacitor of capacitance $\mathrm{C}$ and a resistor of resistance $\mathrm{R}$ are connected in series to an ac source. The quality factor of the circuit is
  1. $\sqrt{\frac{\mathrm{L}}{\mathrm{CR}^2}}$
  2. $\sqrt{\frac{\mathrm{LR}^2}{\mathrm{C}}}$
  3. $\sqrt{\frac{\mathrm{LC}}{\mathrm{R}^2}}$
  4. $\sqrt{\frac{\mathrm{L}^2 \mathrm{C}}{\mathrm{R}}}$

Solution


Quality factor is given as $\mathrm{Q}=\frac{\omega_0 \mathrm{~L}}{\mathrm{R}}=\sqrt{\frac{\mathrm{L}}{\mathrm{R}^2 \mathrm{C}}}$

Asked in: AP EAMCET 2023 (18 May Shift 1)

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