A) \[\text{1}{{0}^{\text{3}}}\text{ rad}/\text{s}\]
B) \[\text{1}{{0}^{4}}\text{ rad}/\text{s}\]
C) \[\text{1}{{0}^{2}}\text{ rad}/\text{s}\]
D) \[\text{1}{{0}^{5}}\text{ rad}/\text{s}\]
Correct Answer: B
Solution :
At resonance, inductive reactance \[({{X}_{L}})\] is equal to capacitive reactance \[({{X}_{C}})\]. Therefore, \[{{X}_{L}}={{X}_{C}}\] \[\omega L=\frac{1}{\omega C}\Rightarrow \omega =\frac{1}{\sqrt{LC}}\] Given, \[L=1\,mH=1\times {{10}^{-3}}H\], \[C=10\,\mu F=10\times {{10}^{-6}}F\] \[\therefore \] \[\omega =\frac{1}{\sqrt{{{10}^{-3}}\times 10\times {{10}^{-6}}}}\] \[\Rightarrow \] \[\omega ={{10}^{4}}rad/s\]You need to login to perform this action.
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