The quantum wave function of mesoscopic RLC circuit with power source is obtained by the method of representational transformation, and with the wave function, the quantum fluctuation of the mesoscopic circuit was obtained. Meanwhile, the quantum effect of mesoscopic circuit with power source is investigated using the double wave function. By comparing between two kinds of methods, we confirm that the fluctuation is connected with the state of a circuit. This can be seen from the method of double wave function. The average values of ensemble solved by double wave function are just the expected values solved by the method of representational transformation.