Simple LC Circuit

I consider that anyone who can analyse correctly circuits involving inductors is an electronics guru. Inductors (and their by products like transformers) are one of the most dreaded circuit elements in electronics. Here I would like to share one of my favourite and innocent looking circuits: an inductor and capacitor connected in series to a battery through a switch. What is the voltage and current waveforms when the switch is closed?

Before you check the answer please try if you can get it yourself. Check out if your basics are correct!!

Since this is a series resonant circuit, the waveforms are going to be sinusoidal with the frequency being the resonant one.

Help Points:

1. Inductor opposes a change in its current. Hence Ibat at t = 0 is 0 amps.

2. At any time Vc + VL = Vbat.

3. Average voltage across inductor = 0 and so the average voltage across capacitor = Vbat

The inductor voltage VL is sinusoidal varying between +Vbat and -Vbat and 90 degree leading Ibat.

Capacitor voltage is sinusoidal with a DC shift, varying between 2Vbat and 0 and 90 degree lagging Ibat.