A) \[\frac{R}{\omega L}\]
B) \[\frac{\omega L}{R}\]
C) \[\frac{R}{\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}}\]
D) \[\frac{\omega L}{\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}}\]
Correct Answer: B
Solution :
| We define the quality factor of the circuit as follows: |
| Quality factor Q |
| \[=2\pi \times \frac{\text{Total}\,\text{energy}\,\text{stored}\,\text{in}\,\text{the}\,\text{circuit}}{\text{Loss}\,\text{in}\,\text{energy}\,\text{in}\,\text{each}\,\text{cycle}}\] |
| But the total energy stored in circuit \[LI_{rms}^{2}\] |
| and the energy loss per second \[=I_{rms}^{2}R\] |
| So, loss in energy per cycle \[=\frac{I_{rms}^{2}R}{f}\] |
| Hence, quality factor \[Q=2\pi \times \frac{LI_{rms}^{2}}{I_{rms}^{2}\,R/f}\] |
| \[=\frac{2\pi \,f\,L}{R}=\frac{\omega L}{R}\] |
| Note: Evidently, Q is a dimensionless quantity. |
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