question_answer

A condenser of capacity \[20\mu F\] is first charged and then discharged through a \[10\text{ }mH\] inductance. Neglecting the resistance of the coil, the frequency of the resulting vibrations will be

A)  \[356\,cycle/h\]

B)  \[356\,cycle/s\]

C)  \[356\times {{10}^{3}}\,cycle/s\]

D)  \[3.56\,cycle/s\]

Correct Answer: B

Solution :

Frequency of vibration for L-C circuit is given by              \[n=\frac{1}{2\pi }\frac{1}{\sqrt{LC}}\]                                   where L is coefficient of self-inductance, C the capacitance. Given, \[C=20\mu F=20\times {{10}^{-6}}F,\] \[L=10mH=10\times {{10}^{-3}}H\] \[\therefore \] \[n=\frac{1}{2\times 3.14}.\frac{1}{\sqrt{20\times {{10}^{-6}}\times 10\times {{10}^{-3}}}}\] \[\Rightarrow \] \[n=356\,cycle/s\]