A connector includes a socket in which a plurality of first splices are provided in parallel in an opening edge portion and a plug which has a flat shape. The plug is capable of being fitted in the opening edge portion of the socket. The plug includes a plurality of second splices press-fitted in press-in grooves provided in parallel at positions corresponding to the first splices in the plug. Each of the first splices is fitted and abuts on an inside surface of one of the press-in grooves. Each of the first splices is brought into elastic contact with one of the second splices to establish electrical connection.