A self-consistent model for the dynamics of the capacitive radio-frequency (RF) plasma sheath driven by a sinusoidal current source is obtained under the assumptions of time-dependent,collisionless ion motion and inertialess electrons. The model consists of fluid equations describing the charge transport in the sheath coupled to an equivalent circuit model of the sheath to predict the characteristics of it at any RF frequency. Some numerical results have been obtained for the instantaneous sheath thickness, the instantaneous voltage and the ion flux density on the substrate, etc. It has been shown that when the RF frequency is less than the ion plasma frequency, the ion flux density will strongly depend on the time.