Abstract: The present invention relates to improvements in an apparatus for supplying electricity, which can supply the electricity to the compressor after a predetermined time period has passed from an initiation of the acceleration of the vehicle. The apparatus includes an outer cylinder, an intermediate cylinder and an inner cylinder. The intermediate cylinder is slidably mounted within the outer cylinder, and the inner cylinder is slidably mounted within the intermediate cylinder. The outer cylinder has a pair of terminals thereon. One of the terminals is connected to a relay, and the other is connected to a battery. A rod of the intermediate cylinder projects from the outer cylinder, and the rod is displaced by the movement of an accelerator pedal or a throttle valve. The intermediate cylinder includes a pair of contacts and a check valve thereof, and the pair of contacts are respectively connected to the pair of terminals. The inner cylinder includes an orifice and a connector.