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Thanks wind_magic! I think I understand most of what you're saying. Except I am confused about...
You say "if a TV uses 30 watts"... how do you know how many watts it uses? And is that "per hour"? Or is that "while it's on". I guess I'm confused about if watts is a measure of "flow" or a measure of "amount". (Like "gallons per hour", or just "gallons")
So how much "power" does the TV suck out of the batteries if on for 3 hours? And what unit of measure do you use to express the absolute amount of power still in the battery, volts? or watts?
And about the engines... how many watts does a modern, 30HP marine engine produce? (I assume it's actually an alternator making the electricity, correct? Or do marine engines use something different?)
I'm learning... little by little...
Watt is a measure of work, you can think of it like flow. In terms of the water analogy volts is the speed the water moves at and amps is the size of the river, and multiplying flow rate times size gives you volume [edit, really it is more like flow, or total inertia, not volume], which is sort of like what watts are.
How many watts does the motor produce, that depends on the alternator which is the electrical generator on the motor. Your alternator will be rated to produce a certain number of amps, you can look up the model of your alternator and see what it will produce. You can also change the alternator to get a bigger one, usually, that will produce even more power. The alternator typically uses very little of the power generated by your motor so a lot of power gets wasted unless you are also using the motor to actually move the boat somewhere, in which case the electrical power is kind of "free" since you're using the motor anyway.
How much power do things use ? Turn your television around and look at the back and it will have a little plate saying how many watts it uses. Or you can look in the manual that came with it. Or if it is something small you can look at the little wall wart (the power adapter) that came with it and see how many amps that generates. Or you can just get a table of common values and guess. Or you can get something like a "watts up" meter and actually measure how much power the device is using.
Power usage is while it is on, typically, so if it uses 30 watts for 1/2 hour then that is the same as using 15 watts for a full hour, or 60 watts for 15 minutes. Does that make sense ? 30 watts at 12 volts is about 2.5 amps, so if you want to run it for an hour you need 2.5 amp hours of battery capacity, so a 100 amp hour battery (in theory) would run a 2.5 amp load for 40 hours before being completely discharged.
Power usage isn't always constant - there are usually two kinds of power usage, one when you are using it, and one when it sits idle. So for example your old VCR player might use 20 watts while you are using it but still use 0.2 watts when it is turned off (to keep the clock set, etc), so even if you aren't using something it may be using small amounts of power. Usually this is called "standby" power and you can find it in the documentation that came with whatever device it is.
Keep asking questions and I or someone else will answer them ...