  A solvable quantum $LC$ circuit with charge discreteness is studied. Two
discrete spectral branches are obtained: (i) the normal branch corresponding to
a charged capacitor with integer effective charge $k=q_{e}n$ ($q_{e}$
elementary charge, $n$ integer) and (ii) the anomalous branch where the energy
is related to non-integer effective charge $k=q_{e}(n-x)$ in the capacitor. For
usual mesoscopics data like quantum point contact we found $x\sim 0.7$.
