# Question about amp-hour and batteries in series

I am a little confused about this wiring batteries in series and parallel and the effect of this on total time that these batteries can last(I suppose this is called amp-hour, correct me if I'm wrong)

I'll keep it simple; Let's consider we have lamps and batteries that are totally identical(battery's inner resist is 0) and we are preparing three different scenarios.

First: We are wiring two batteries parallel to each other and then to one lamp.

Second: We are wiring two batteries in series to one lamp.

Last: We are wiring one battery to one lamp.

What would be the max brightness of First, Second, and Last lamp and what would be the amount of time they would last comparing to each other?

My guess is that clearly Second will be brightest and the two other will be negligibly similar and no problem here.

But when it comes to time, my answer was parallel would be the longest and other two would be same but in the book answer was parallel batteries are longest then one battery then two battery in series.( First one > Last one > Second one )

Let me say what I am thinking for this problem and so you can tell me where I am wrong; I thought that the batteries in series should increase their total voltage to 2x and so the amphere must increase 2x too until we have the same resistance, so let's say we increased it from 1A to 2A, in this case if the lamp stays ON for 1 hour with a current of 1A and consumes 1Ah of energy from one battery, two batteries that are creating 2A should last 1 hour aswell to create 2x of energy and that is 2Ah, but if they last less then 1 hour(as what the answer was in the book) then we wont get 2 amp hour of energy since the time will be shorter, and if that is right does this mean wiring batteries in series lower their potentiel energy?

Hope so my curiosity didn't mess things and this was clear enough, thanks.