A capacitor is charged to a potential difference of Vo by connecting it across a battery and then is allowed to discharge through an inductor of inductance L.
In starting charge on the plates of the capacitor qo = CVo
At any instant, let the charge flown through the circuit be q and the current in the circuit be i. operating Kirchhoff's law![627_l c circuit1.png](https://www.expertsmind.com/../CMSImages/627_l c circuit1.png)
Differentiating w.r.t. time we get
![1721_l c circuit2.png](https://www.expertsmind.com/../CMSImages/1721_l c circuit2.png)
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![2379_l c circuit.png](https://www.expertsmind.com/../CMSImages/2379_l c circuit.png)
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The charge q on the plates of the capacitor and current I in the circuit vary sinusoidally as q = q0 sin (wt + f) and I = q0 w cos (wt + f). where f is the initial phase and it depends on initial conditions of the circuit and w = 1/√LC.
The net power of the system remains conserved
![116_l c circuit3.png](https://www.expertsmind.com/CMSImages/116_l%20c%20circuit3.png)
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