Cooling rate effects on the electrical properties of $BaTiO_3$ positive temperature coefficient of resistance (PTCR) were analyzed using dc resistivity and AC complex impedance spectroscope. PTCR $BaTiO_3$ was fabricated at different cooling rates : 6, 12, 25, 50, and 100℃/h. As the cooling rates decreased, the dc resistivity of the sample, the slope of the PTCR curve and the resistivity jump increased. AC complex impedance spectra showed that the observed dc increase was mainly due to the grain boundary resistivity increase. The grain resistivity also exhibited relatively weak PTCR behavior. The average grain size of the samples decreased as the cooling rate increased. The builtin potential and the depletion layer width were analyzed using the AC complex impedance data. Slow cooling rate produced higher built-in potential and large depletion layer width. The relationship between the built-in potential and the depletion layer width at different temperatures were analyzed and used to explain the observed grain boundary resistivity change. The resistivity decrease in low temperature region was due to the depletion layer width decrease. The resistivity jump over the temperature was due to both the built-in potential and the depletion layer width changes.
