A comprehensive analytical model is developed for a functionally graded piezoelectric (FGP) curved bar which is in a closed electrical circuit. Piezoelectric coefficient is assumed to vary in the radial direction according to a power law unlike the corresponding studies in the literature. This assumption constitutes one of the basic novelties of the present investigation. For the verification, the numerical results of the mathematical model for an FGP curved actuator are compared with those of a related study on a linear FGP curved bar in the literature. Next, the model is used to determine the deformation and electrical behaviours of an FGP curved sensor under a couple at its free end section. The presentation of the numerical results for the curved sensors is another novelty of the present study since the numerical results in the related studies in the literature were presented just for the actuators. Results are compared with bimorph piezoelectric curved sensors and the effect of the grading parameter on the mechanical and electrical fields is examined. Numerical results show that FGP curved sensor provides several advantages in terms of the mechanical behavior of the material, and the distribution and production of electric potential in the sensor are affected significantly with the variation of grading parameter.