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There is provided a portable electrical system including primary and secondary devices, the primary device having a first, lithium cobalt oxide battery, and the secondary device having a second, lithium iron phosphate or lithium titanate battery, wherein the primary and secondary devices are configu

There is provided a portable electrical system including primary and secondary devices, the primary device having a first, lithium cobalt oxide battery, and the secondary device having a second, lithium iron phosphate or lithium titanate battery, wherein the primary and secondary devices are configured to allow recharging of the second battery from the first battery at a rate of between 2C and 16C.

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1. A portable electronic smoking system, comprising: rechargeable primary and secondary devices, the primary device comprising a housing and having a first battery, andthe secondary device being an electrically heated tobacco device and comprising a second battery and a heater configured to heat an

1. A portable electronic smoking system, comprising: rechargeable primary and secondary devices, the primary device comprising a housing and having a first battery, andthe secondary device being an electrically heated tobacco device and comprising a second battery and a heater configured to heat an aerosol-forming substrate, said secondary device being configured to be received within the housing of the primary device during a recharging cycle,wherein the primary device and secondary device are configured to be coupled together and to form a charging circuit,wherein a capacity of the first battery is between five times and forty times a capacity of the second battery,wherein the primary and secondary devices are configured to recharge the second battery from the first battery, andwherein the primary device further comprises: a pair of output terminals configured to connect to the second battery;a DC power source;a voltage regulator connected between the DC power source and to the output terminals and being configured to control a charging voltage; anda microprocessor coupled to the voltage regulator and to the output terminals, and being configured to: control the voltage regulator to supply a first charging voltage and, after the first charging voltage has reached a predetermined voltage level, determine an internal resistance of the charging circuit by measuring a current in the charging circuit at the first charging voltage and at a second charging voltage, wherein the second charging voltage is lower than the first charging voltage, and limit the first charging voltage supplied by the voltage regulator to a maximum charging voltage based on the determined internal resistance and on a predetermined maximum voltage of the second battery. 2. The portable electronic smoking system according to claim 1, wherein the microprocessor is further configured to: calculate the maximum charging voltage based on the determined internal resistance and the predetermined maximum voltage of the second battery; andadjust the first charging voltage to maintain a predetermined charging current until the first charging voltage reaches the calculated maximum charging voltage, thereafter adjust the first charging voltage to a level at or below the calculated maximum charging voltage, and thereafter periodically or continuously recalculate the calculated maximum charging voltage and adjust the first charging voltage to maintain the first charging voltage at a level at or below the recalculated maximum charging voltage. 3. The portable electronic smoking system according to claim 1, wherein the microprocessor is further configured to determine the second charging voltage by reducing a voltage from the first charging voltage by a predetermined voltage difference. 4. The portable electronic smoking system according to claim 1, wherein the microprocessor is further configured to recalculate the internal resistance periodically. 5. The portable electronic smoking system according to claim 1, wherein the second battery has a diameter of 10 mm and a length of 37 mm. 6. A method of charging a second battery in a secondary electrically heated tobacco device from a first battery in a primary device comprising a housing, said secondary device comprising a heater configured to heat an aerosol-forming substrate, the primary and secondary devices forming a portable electronic smoking system, wherein a capacity of the first battery is between five times and forty times a capacity of the second battery, the method comprising: connecting the secondary device to the primary device having an adjustable voltage source, to form a charging circuit;controlling a first charging voltage supplied by the voltage source to provide a predetermined charging current to the second battery;determining an internal resistance of the charging circuit by measuring a current in the charging circuit at the first charging voltage and at a second charging voltage, wherein the second charging voltage is lower than the first charging voltage;calculating a maximum charging voltage based on the determined internal resistance and on a predetermined maximum voltage of the second battery; andadjusting the first charging voltage to maintain the predetermined charging current until the first charging voltage reaches the maximum charging voltage, and thereafter adjusting the first charging voltage to maintain the first charging voltage at a level at or below the maximum charging voltage,wherein the steps of determining the internal resistance and calculating the maximum charging voltage are carried out only after the first charging voltage has reached a predetermined voltage level. 7. The method according to claim 6, wherein the second charging voltage has a predetermined voltage difference from the first charging voltage. 8. The method according to claim 6, wherein the steps of calculating the maximum charging voltage and adjusting the first charging voltage are carried out a plurality of times during a single charging cycle. 9. The method according to claim 6, wherein the steps of calculating the maximum charging voltage and adjusting the first charging voltage are carried out continuously after the first charging voltage first reaches the maximum charging voltage during a single charging cycle. 10. The method according to claim 6, wherein the step of determining the internal resistance is carried out periodically. 11. The method according to claim 6, further comprising the step of returning the secondary device to the primary device for recharging the second battery after a single smoking session. 12. The method according to claim 11, wherein the single smoking session lasts 7 minutes. 13. The method according to claim 11, further comprising the step of recharging the second battery for less than 6 minutes.