A) \[f\]/4
B) 8\[f\]
C) \[f\]/\[2\sqrt{2}\]
D) \[f\]/2
Correct Answer: C
Solution :
In a series LC circuit, frequency of LC oscillations is given by \[f=\frac{1}{2\pi \sqrt{LC}}\] or \[f\alpha \frac{1}{\sqrt{LC}}\] \[\Rightarrow \] \[\frac{{{f}_{1}}}{{{f}_{2}}}=\sqrt{\frac{{{L}_{2}}{{C}_{2}}}{{{L}_{1}}{{C}_{1}}}}\] Given \[{{L}_{1}}=L,\,{{C}_{1}}=C,\,{{L}_{2}}=2L,\,{{C}_{2}}=4C,\,{{f}_{1}}=f\] \[\therefore \] \[\frac{f}{{{f}_{2}}}=\sqrt{\frac{2L\times 4C}{LC}}=\sqrt{8}\] \[\Rightarrow \] \[{{f}_{2}}=\frac{f}{2\sqrt{2}}\]
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