If the two batteries have the same voltage, than the power the bulb draws will be the same - 10W. It doesnt matter how many watts your power source is capable of, only the voltage matters.Studiot: Hm. I think I see the direction you're going. But let me ask with a simplistic example: Let's say we have a basic battery based circuit with a small 10 watt bulb and 2 batteries: one that is able to produce (or be drawn from) 30W and another at 20W. First you use the 30W battery in the circuit and you get a X lumens. Then, using the same 10W bulb, you switch to the 20W battery but this time you get an increase to Y lumens (I changed my example a bit).