Why is there current in LC Circuits? When we connect two electric sources (positive to positive and negative to negative) then the current that runs the circuit is calculated as follows:

$ I = (E1-E2)/(2r + R) $
In case of an LC circuit the second source is considered to be the inductor because of lenz's law(?) The picture we get then is something like this:

So what we learn in textbooks is that the Voltage of the capacitor and the voltage of the inductor are equal.
$ Vc = E $ 
Then as with the tow connected sources.
$ Imax = (Vc-E)/R $
So, $Imax$ should be equal to zero.
Sorry if i have that all confused...maybe you could help me out! 
 A: You made an assumption that the potential difference (voltage) across capacitors and inductors are equal, which is untrue for a series circuit. It appears to me that the textbooks you looked up are probably describing the case of a parallel circuit, where such an equality is indeed true. However, you are analysing a series circuit, for which the constant physical quantity is current and the sum of the potential difference(s) across the whole circuit equals zero. In other words, the potential difference across the inductor is proportional to its rate of change of current, with the constant of proportionality $L$ being the inductance. Summing the potential difference in an anti-clockwise fashion from the node between the resistor and the inductor, we obtain
$$
V_R + V_C = -L\frac{\mathrm{d}I}{\mathrm{d}t}
$$
where $V_R$ and $V_C$ are the potential difference(s) across the resistor and capacitor respectively.
Ohm's Law states $V=IR$ and the definitions of capacitance $C=Q/\Delta V$ and current $I=\mathrm{d}Q/\mathrm{d}t$ collectively gives the following second-order linear homogeneous ordinary differential equation (ODE):
$$
\frac{\mathrm{d}^2Q}{\mathrm{d}t^2} + \frac{R}{L}\frac{\mathrm{d}Q}{\mathrm{d}t} + \frac{Q}{LC} = 0
$$
Solving the ODE yields the steady-state solution which takes on three possible forms - over-damping, critical damping and under-damping - depending on the relative values of resistance, inductance and capacitance.
The general idea which agrees with intuition is that the current goes to zero eventually due to power loss as joule heat (i.e. from the resistor).
