If I have two batteries at 2 volts at 1 Ah, and I strap them together, will I get 4 volts at 2 Ah, or 4 volts at 1 Ah?
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it depends on how you tack the batteries together.
Check out http://www.bfafairfax.com/~pfeiffer/Physics/EandM/electriccircuits.html to answer your question more thoroughly.
HTH
one negative terminal to te other's positive terminal, i.e
+|cell|- +|cell|-
In series, 4 volts at 1Ah. In parallel, 2 volts at 2Ah.
Series means one after the other, the plus of one connected to the minus of the other, then the free plus and minus ends to the device. Parallel means side by side, ie the plus and minus of both batteries are connected to the same points on the device.