question_answer

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

A)  \[356\text{ }cycle/h\]                  

B)  \[356\text{ }cycle/s\]

C)  \[356\times {{10}^{3}}cycle/s\]                

D)  \[3.56\text{ }cycle/s\]

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, \[C=20\text{ }\mu F=20\times {{10}^{-6}}F,\] \[L=10\text{ }mH=10\times {{10}^{-3}}H\] \[\therefore \]  \[n=\frac{1}{2\times 3.14}.\frac{1}{\sqrt{20\times {{10}^{-6}}\times 10\times {{10}^{-3}}}}\] \[\Rightarrow \]               \[n=356\text{ }cycle/\text{ }s\]