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 \[=2\pi \times \frac{Total\,energy\,stored\,in\,the\,circuit}{Loss\,in\,energy\,in\,each\,cycle}\] 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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