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Why is it that we have a 12 volt battery? Why not say 1.5 or 3 volts? Because if current is all that matters, then we could achieve higher current values to power one load (or multiple loads) with lower resistor values, no? Is it that a higher voltage battery can handle more loads for a certain amount of time or or does it have to do with the power rating of the loads we are attempting to run.

My initial guess is that sure we could use a 1.5 volt battery to say run a motor or other multiple loads (with lower resistance) but that battery would be drained fairly quickly in terms of amp hours. Am I thinking right?

PS: I am trying to think of this problem without use of transformer.