The exact solution of time evolution operator was obtained by applying the gauge transform of algebra dynamics. Such an operator describes the quantum state of time dependence of mesoscopic RLC circuit containing voltage source. The charge and current zero-state response of the import voltage signal in mesoscopic RLC circuit were acquired. The result shows that the system of mesoscopic RLC circuit has linear time invariant feature,and the response in mesoscopic RLC circuit is the same as that in the macroscopic RLC circuit.