The $Y_2O_3$ ceramics have been widely used as plasma resistant materials in the semiconductor industry. In this study, composites made of plasma resistant $Y_2O_3$ and electrically conductive carbon have been produced. The electrical properties of this composite were measured with respect to the size, volume fraction of the conductive carbon phase, and sintering temperature. When micro-sized carbon was used, the composites were insulating up to 5 wt% addition of the carbon. However, when nano-sized carbon of around 60 ~100 nm was used, the composites became conductive over threshold volume fraction of carbon, which increased with increasing sintering temperature. This behavior of electrical conductivity of the composites was discussed in terms of the percolation theory. The percolation threshold of the conductivity seemed to be affected by the grain growth and coalescences of dispersed conductive carbon phases with grain growth of matrix $Y_2O_3$.