A coupling that makes electrical connections across a joint joining adjacent tubular members, such as drill pipe sections in a drill string. A male sleeve, made from an electrical insulating material, is attached to the male end of one pipe section. A number of axially spaced apart male contact members, such as ring segments or buttons, are formed on the outside surface of the male end. The male contact members are spring biased radially outward. Each of the male contact members is radially displaced from the axial centerline of the pipe section by a progressively increasing amount. A female sleeve, also made from an electrical insulating material, is attached to the female end of the other pipe section. A number of female contact members, such as ring segments or buttons, are formed on the inside surface of the female end. Each of the female contact members is radially displaced from the axial centerline of the pipe section by a progressively increasing amount. The axial spacing and radial displacements of the male and female contact members is such that when the pipe section are assembled by threading the male end into the female end, each male contact member makes electrical contact with its intended mating female contact member without ever having contacted any of the other female contact members. Deformable cleaning elements formed on one of the ends wipe clean the contact members formed on the other end as the joint is being assembled. The debris wiped clean is deposited in a groove located in front of the wiper.