In this paper, the influences of an external pulse on the variation of the quantum state of a mesoscopic RLC circuit are investigated emphatically. Our research result indicates that the transition probabilities of the variation of the quantum state are adjusted by controlling the variation of the pulse parameters when the parameters of the mesoscopic circuit are constant. We point out that the quantum state of a system is stable when the width of the pulse is equal to the integral times of the minimum fixed value. The minimum fixed value is not related to the altitude of pulse but the circuit parameters. The larger the resistance, the wider the minimum fixed width of the external pulse.