It is shown that RC circuits are inappropriate for modelling the transient runtime characteristics of battery voltage. In contrast, impedance-frequency measurements suggest that a fractional capacitor or “constant phase element” (CPE) can represent battery impedance over a wide frequency range. In this paper, we present evidence that shows RC models of rechargeable batteries to be theoretically inappropriate. We then propose a fractional mathematical model which uses 3 parameters to predict charge-voltage characteristics or steady- state Q-V function of a Li-ion cell.