The impedance of a battery can be modelled with an elegant fractional-capacitor or “constant phase element” (CPE) equivalent circuit and a series resistor. In this manuscript, we present new evidence that suggests that a linear model similar to Randles’ comprised solely of this impedance network is able to predict both the charge-voltage relationship epitomised by the familiar hysteresis curve of voltage as a function of charge as a battery charges and discharges through its linear region, and the recovery or “equilibration” transient that results from a step change in load current. The proposed model is unique in that it does not contain a source, either voltage or current, nor any purely reactive elements. There are important potential advantages of a passive battery model.