A) \[\frac{2}{\pi }\times {{10}^{5}}Hz\]
B) \[\frac{{{10}^{5}}}{\pi }Hz\]
C) \[\frac{5}{\pi }\times {{10}^{3}}Hz\]
D) \[\frac{{{10}^{-5}}}{\pi }Hz\]
Correct Answer: C
Solution :
: Maximum power is dissipated at resonant frequency. Resonant frequency, \[{{\upsilon }_{r}}=\frac{1}{2\pi \sqrt{LC}}\] Here, \[L=5mH=5\times {{10}^{-3}}H\] \[C=2\mu F=2\times {{10}^{-6}}F\] \[\therefore \] \[{{\upsilon }_{r}}=\frac{1}{2\pi \sqrt{5\times {{10}^{-3}}\times 2\times {{10}^{-6}}}}=\frac{1}{2\pi \sqrt{{{10}^{-8}}}}\] \[=\frac{{{10}^{4}}}{2\pi }=\frac{5}{\pi }\times {{10}^{3}}Hz\]
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