The research work on the quantum effects in mesoscopic circuits has undergone a rapid developmentrecently,however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electriccharge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-differenceSchrodinger equation of the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, theSchrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of thesystem are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. Theresults show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application ofthe whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the designof the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopicquantum states. The research work on the quantum effects in mesoscopic circuits has undergone a rapid developmentrecently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electriccharge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. Theresults show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the designof the miniation circuits, especially on the purpose of reducing quantum noise coher ent controlling of the mesoscopic quantum states.