# the *answer*

The amp_hour rating on batteries is really the amperes times the number of hours *at* that particular voltage. So it is really a measure of the electrochemical energy (units are power multiplied by time) in the battery. Energies will be additive. Your series linked batteries will be able to give the same number of amps for the same number of hours but at twice the voltage and so there will be twice as much energy delivered to the circuit.

Amp-hours are only useful in comparing batteries at the same voltage. With the series set-up you will now have a 400 amp-hour battery but at twice the voltage so it will deliver twice the energy. You could get an 800 amp-hour setup at the original voltage of a single battery if you put them in parallel. The best way to think of this is by considering the energy which equals amps*volts*time. Two batteries gives you twice the energy which you can choose to deliver any way you want to.

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