A) \[\frac{1}{2\pi }\frac{1}{\sqrt{LC}}\]
B) \[\frac{1}{2\pi }\,\sqrt{LC}\]
C) \[\frac{1}{\,\sqrt{LC}}\]
D) \[\sqrt{LC}\]
Correct Answer: A
Solution :
Natural frequency is nothing but resonant frequency. In this case \[{{X}_{L}}={{X}_{C}}\] \[\Rightarrow \] \[{{\omega }_{0}}L=\frac{1}{{{\omega }_{0}}C}\] \[\Rightarrow \] \[\omega _{0}^{2}L=\frac{1}{LC}\] \[\Rightarrow \] \[{{\omega }_{0}}=\frac{1}{\sqrt{LC}}\] \[\Rightarrow \] \[2\pi f=\frac{1}{\sqrt{LC}}\] or \[f=\frac{1}{2\pi \sqrt{LC}}\]
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