An implantable system, such as a neural stimulator or a cochlear implant system, includes a rechargeable battery configuration having improved recharging and lifetime characteristics. The battery is housed within the implant's case and has first and second electrode plates. Each electrode plate has a plurality of slits that extend across a substantial portion of the plate's surface area. The slits in the electrode plates reduce the magnitude of eddy currents induced in the plates by external ac magnetic fields allowing faster battery recharging times. Alternatively, the electrode plates are wrapped in a spiral configuration such that, in the plane of the spiral, the electrode plates have a small cross-sectional area and no closed current loops. Additionally, the implant device may be housed in a case formed of a high-resistivity material and a circuit included in the implant device is configured to avoid large current loops that would result in eddy current heating. As a backup option, the circuitry of the implant device may optionally be powered from an external battery that inductively couples energy to the same coil that is used to charge the internal battery. In one embodiment, the implantable system is partitioned into first and second implantable cases, each having electrical circuitry therein, and only one having a rechargeable power source therein, facilitating its subsequent replacement for repair or upgrading purposes. The two cases are coupled together when the system is in use. Coupling is achieved either magnetically and/or with a detachable electrical cable. In one embodiment, power is transferred from one implant case to the other using a 3-phase transmission scheme.