LC oscillation:

 

1) In a circuit containing an inductor (L), when connected to a  charged capacitor (C), an oscillation starts happening.


2) This oscillation is the oscillation of electric charge and current in the circuit.


3) After connection of the charged capacitor with the inductor, charge on the capacitor decreases, this decrease in charge creates a current in the circuit.


4) Suppose at any moment t, the charge on the capacitor is q and current in the circuit is I




5) Now potential across the capacitor is 

Now potential across the inductor is  


-ve sign, tells that this emf is opposite to the direction of current flow.





6) So, applying Kirchhoff’s law:



 But we know 

 







We know from resonance





Therefore


  



7) this is similar to the equation simple harmonic oscillation




After solving we get



Where  q0  is the maximum charge of the capacitor. Now at

t = 0,   q = q0




So,



Therefore




8) Thus the perfect equation for charge in the circuit is





9) Now current in the circuit is




 




 

So the current in the circuit is



now comparing with




 

We get the maximum value of current is