When you talk about operating an electrical device over time, that is "work". Work requires "energy", for all intents and purposes work equals energy. In the case of your hundred-watt light bulb, over one hour it will take 400 watt-hours of energy to operate. You'll note that you're charged for your power in units of kilowatt-hours. A kilowatt-hour is a unit of energy and it will do a certain amount of work.
Now a watt is a unit of "power". Power is the RATE at which you do work. (Specifically a watt is one joule of work per second, but we seldom use the unit of joules because a joule is very small.) So to use an analogy, power is to work as speed (miles per hour) is to distance (miles). If you take the product of power over time, you get energy. 100 watts times 4 hours equals 400 watt-hours. In theory, your 400 watt inverter should be able to operate four 100 watt light bulb forever as long as it is supplied with a source of energy. So how long you can maintain your light doesn't depend on the inverter, but rather the inverter's source of power. So you have to know how much energy is stored in the battery to determine how long you can operate the light. Battery energy ratings are given not in watts, but rather amp-hours. You have to know the voltage rating and the amp-hour rating to figure out how much energy is in the battery. Energy happens to be equal to voltage times current, so if we multiply the voltages time the battery's amp-hour rating, we get the battery's energy in watts. So if I have a 12 volt, 50 ampere-hour battery, it should hold 600 watt-hours of energy. IN THEORY, those 600 watt-hours will operate a 100 watt light bulb for six hours.
Now when you start operating a load from a battery through an inverter, you get all sorts of things that mess up your calculations. First, the amp-hour rating of a battery is always very optimistic and assumes a very light load that will maximize the rating. Also, the battery's voltage drops as it is discharged and will eventually fall below what the inverter requires to operate long before the battery is fully discharged. The last thing is the efficiency of the inverter, which is probably not very good.
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Today's Featured Article - Restoration Story: Fordson Major - by Anthony West. George bought his Fordson Major from a an implement sale about 18 years ago for £200.00 (UK). There is no known history regarding its origins or what service it had done, but the following work was undertaken alone to bring it up to show standard. From the engine number, it was found that this Major was produced late 1946. It was almost complete but had various parts that would definitely need replacing.
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