Series LC Circuit: Charging Capacitor & Current Flow w/ 0V Inductor

[likephysics]

In a series LC ckt, the capacitor charges to the applied voltage V after some time t1secs. Now there is no voltage across the inductor.
How can the inductor keep supplying current to the capacitor, when the potential difference across it is zero.
The capacitor is charged up to 2V. Why just 2V?

 

[JoAuSc]

I feel like I'm missing information. What's "2V" referring to? Is there a power source in this circuit? Do we charge the capacitor, then add it to the circuit after it's charged?

 

[likephysics]

Well I have 2 cases:
1.
Just an LC circuit connected to a voltage source thru a switch.
switch is closed and capacitor is charged to supply voltage V.
Now the switch is opened, the inductor opposes this change and an emf is developed across it
which is equal to - L. di/dt
This will continue charging the capacitor in the -ve direction. Why does the capacitor get charged to 2 times V.

2. Just an LC ckt with a switch (no voltage source) with the capacitor charged to V volts. When the switch is closed, the capacitor starts discharging thru the inductor. When the cap current reaches zero, the inductor begins charging the cap. The capacitor is charged up to 2V.
why 2V. why not more. conservation of energy?

Link: http://www.walter-fendt.de/ph11e/osccirc.htm [Broken]

 

[Bob S]

In the first case, the capacitor is charged to the battery voltage V, and then the battery is disconnected. The inductor current and inductor voltage is initially zero. The capacitor is switched to the inductor. The capacitor discharges through the inductor, and when the capacitor voltage is zero, the inductor current is maximum (down direction). The inductor then begins discharging its stored energy into the capacitor. Eventually, half a cycle later, the capacitor is fully charged to -V (note sign), and the inductor current is again zero (no stored energy). The capacitor is never charged to 2 times V. It oscillates between +V and -V. Because there is no resistor in the LC circuit, the stored energy is constant.
E = (1/2)C V² + (1/2)L I² = constant.
The equation for the inductor is
V_capacitor = L dI/dt. (positive current flows down through inductor)
Whenever the capacitor has a positive voltage, the current through the inductor is increasing (dI/dt>0), and whenever the voltage across the capacitor is negative, the current through the inductor is decreasing (dI/dt<0).