This paper addresses an application of the potential game theory to a power-aware mobile sensor coverage problem where each sensor tries to maximize a probability of target detection in a convex mission space. The probability of target detection depends on a sensing voltage of each mobile sensor as well as its current position. While a higher sensing voltage improves the target detection probability, this requires more power consumption. In this paper, we assume that mobile sensors have different sensing capabilities of detecting a target and they can adaptively change sensing areas by adjusting their sensing voltages. We consider an objective function to evaluate a trade-off between improving the target detection probability and reducing total power consumption of all sensors. We represent a sensing voltage and a position of each mobile sensor using a barycentric coordinate over an extended strategy space. Then, the sensor coverage problem can be formulated as a potential game where the power-aware objective function and the barycentric coordinates correspond to a potential function and players' mixed strategies, respectively. It is known that all local maximizers of a potential function in a potential game are equilibria of replicator dynamics. Based on this property of potential games, we propose decentralized control for the power-aware sensor coverage problem such that each mobile sensor finds a locally optimal position and sensing voltage by updating its barycentric coordinate using replicator dynamics.