question_answer

In an ideal parallel LC circuit, the capacitor is charged by connecting it to a dc source which is then disconnected. The current in the circuit

A) Becomes zero instantaneously

B) Grows monotonically

C) Decays monotonically

D) Oscillates instantaneously

Correct Answer: D

Solution :

[d] \[\frac{q}{c}+L\frac{di}{di}=0\Rightarrow \,\frac{{{d}^{2}}q}{d{{t}^{2}}}+\frac{q}{LC}=0\] which is equation of oscillatory motion \[\Rightarrow \,\,\,\,\,q={{q}_{0}}\sin \omega t\Rightarrow \frac{dq}{dt}=i={{q}_{0}}\omega \cos \omega t\] here \[\omega =\frac{1}{\sqrt{LC}}\Rightarrow \] current starts oscillation.