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Find the quality factor of a circuit with capacitance `C=2.0 mu F` and inductance `L=5.0 mH` if the maintenance of undamped oscillations in the circuit with the voltage amplitude across the capacitor being equal to `V_(m)=1.0 V` requires a power `( :P: )=0.10m W`. The damping of oscillations is sufficiently low |
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Answer» Given `V=V_(m) e^(-betat)sin omegat, omega~= omega_(0) betaTlt lt 1` Power loss `=(" Energy loss per cylcle")/(T)` `~=(1)/(2) CV_(m)^(2)xx2 beta` `(` energy decreasesas `W_(0) e^(-2betat) ` so loss per cycle is `W_(0)xx2 betaT)` Thus `lt P gt =(1)/(2)CV_(m)^(2)xx(R)/(L)` or `R=(2lt P gt)/( V_(m)^(2))(L)/(C)` Hence `Q=(1)/(R) sqrt((L)/(C))=sqrt((C)/(L))(V_(m)^(2))/(2lt P gt)=100` on putting the vales. |
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