During drilling of an earth borehole, resistance measurements may be made at the drill bit through use of a bottom hole assembly that includes a drill bit having a sensor, such as an electrode, located generally at an exterior surface of the drill bit. The current will be induced in the formation from multiple transmitters, at least one of which will be supported on, or very close to the drill bit. Connection mechanisms are described that enable the releasable engagement of electrical conductors to circuitry within the drill bits. The obtained resistivity measurements at the drill bit can be used for many purposes, including formation imaging and geosteering of the drilling operation.