During ion cyclotron resonance heating, the sheath power dissipation caused by ion acceleration in the radio frequency (RF) sheath is one of the main causes of RF power loss in the tokamak edge region. To estimate the power dissipation of an RF sheath in the ion cyclotron range of frequency (ICRF), a 1D fluid model for the multi-component plasma sheath driven by a sinusoidal disturbance current in the ICRF is presented. By investigation of the sheath potential and ion flux at the wall, it is shown that the larger frequency and lower amplitude of the disturbance current can cause smaller sheath power dissipation. The effect of the energetic ion on the sheath power dissipation depends on the disturbance current. For large amplitude of disturbance current, the increase in the concentration and energy of the energetic ion leads to a decrease in sheath power dissipation. While for a small disturbance current, the sheath power dissipation demonstrates non-monotonic variation with the concentration and energy of the energetic ion. In addition, the sheath power dissipation is found to have a small increase in the presence of light impurity ions with low valence.