How many watts will the battery give?

Question

Batteries

Let's say there are two batteries:
1. 4.5Ah 12V
2. 860mAh 3.7V
There is a 100W 220V lamp, theoretically, how long will each of the batteries work from the battery (using a converter)?

Answer 1

Multiply amps by volts to get watts.
Multiply by hours to get watts*hours.
Divide by the load power and get how much it will work in the ideal case. W * h / W \u003d h
Another thing is the load ... An incandescent lamp has a non-linear resistance, depending on the heating of the spiral. If powered directly from the battery, then most likely the current will depend on the resistance of the cold coil (there will not be any 100W there, stupidly it has little voltage to work with).
If you feed the lamp through a good booster / inverter, then the time will depend on the current consumed by the lamp and the efficiency of the converter. (Assume 4.5A * h * 12V = 54W * h, when operating at 100W, the load will work for 0.54 hours, and taking into account the efficiency of the percent converter of 80, we get 0.4 hours, i.e. 25 minutes).
Option 2 is unlikely to be able to give 100W at all, this is 100W load / 3.7Vaccum = 27A of current consumption

Answer 2

With a converter efficiency of 90 percent, the following theoretical results are obtained:
1. 4.5Ah 12V 100W 220V - 29min
2. 860mAh 3.7V 100W 220V - 1.9 min
and in practice - option 2 will not work even :)