A) \[1007\,\,Hz\]
B) \[100\,\,Hz\]
C) \[109\,\,Hz\]
D) \[500\,\,Hz\]
Correct Answer: A
Solution :
Key Idea: In the state of resonance inductive and capacitive reactance?s are equal. \[{{X}_{L}}={{X}_{C}}\] \[\Rightarrow \] \[\omega L=\frac{1}{\omega C}\] \[\Rightarrow \] \[2\pi fL=\frac{1}{2\pi fC}\] \[\Rightarrow \] \[{{f}^{2}}=\frac{1}{4{{\pi }^{2}}LC}\] \[\Rightarrow \] \[f=\frac{1}{2\pi }\sqrt{\frac{1}{LC}}\] \[\left( resonant\,\,frequency \right)\] Given, \[L=0.25\,\,H,\]\[C=0.1\,\mu \,F=0.1\times {{10}^{-6}}\,F\] \[\therefore \] \[f=\frac{1}{2\pi }\sqrt{\frac{1}{0.25\times 0.1\times {{10}^{-6}}}}\] \[f=1007\,\,Hz\]
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