Dielectric-barrier discharges (DBDs) in atmospheric pressure air have been studied by using a power-frequency voltage source. In this paper the electrical characteristics of DBDs using glass and alumina dielectrics have been investigated experimentally. According to the Lissajous figures of voltage-charges, it is discovered that the discharge power for an alumina dielectric is much higher than that for a glass dielectric at the same applied voltage. Also, the voltage-current curves of the glass and alumina dielectrics confirm the fact that the dielectric barriers behave like semiconducting materials at certain applied voltages.