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In this paper, we study the response of an inductive quantum circuit with discrete charge to a stochastic electromotive force. We show that the discreteness of the charge causes a totally different behavior of the quantum circuit with respect to the classical circuit case. In particular, we show that in the case of fluctuating phase of a harmonic voltage source, the mesoscopic circuit would generate a quantum current with the same frequency of the voltage source one. Possible practical applications of mesoscopic circuits could be modeling the Josephson junction as discussed in this paper.