The exact solution of time evolution operator is obtained by applying the gauge transform of algebra dynamic. Such an operator describes the quantum state of time dependence of mesoscopic LC circuit containing voltage source. The coherence of quantum state of mesoscopic LC circuit is taken into account. The result showed that the probability of charge stored in capacitor is a motional Gauss wave-packet. The relation between centre charge of wave-packet and voltage source is given. The special example in which the circuit is driven by single rectangle pulse is investigated.