A) \[f/4\]
B) \[8f\]
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 \[f\,\propto \,\,\frac{1}{\sqrt{LC}}\] |
| \[\Rightarrow \] \[\frac{{{f}_{1}}}{{{f}_{2}}}=\sqrt{\frac{{{L}_{2}}{{C}_{2}}}{{{L}_{1}}{{C}_{1}}}}\] |
| 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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