Electrical aspects of cell function manifest in many ways. The most widely studied is the cell membrane potential, V_m, but others include the conductance and capacitance of the membrane, the conductance of the enclosed cytoplasm, as well as the charge at the cell surface (an electrical double layer) producing an extracellular electrical potential, the ζ-potential. Empirical relationships have been identified between many of these, but not the mechanisms that link them all. Here we examine relationships between V_m and the electrical conductivities of both the cytoplasm and extracellular media, using data from a suspensions of red blood cells. We have identified linear relationships between extracellular medium conductivity, cytoplasm conductivity and V_m. This is in contrast to the standard model of a resting membrane potential which describes a logarithmic relationship between V_m and the concentration of permeable ions in the extracellular medium. The model here suggests that V_m is partially electrostatic in origin, arising from a charge imbalance at an inner electrical double-layer, acting across the membrane and double-layer capacitances to produce a voltage. This model describes an origin for coupling between V_m and ζ, by which cells can alter their electrostatic relationship with their environment, with implications for modulation of membrane ion transport, adhesion of proteins such as antibodies and wider cell–cell interactions.