The maths behind the sun powering my toaster while I bathe

Maths are a lot like karate.  It’s just cooler when an Asian is doing it.

But I needed to do some calculations or I wouldn’t have enough amperage to do anything useful.  Also I wanted to know just how the hell much this was going to cost.
First, I did want to calculate the amp hours that would be needed.  All of these calculations are done assuming 12v battery storage.
First, I’m going with the national average for household power consumption.  I know that I probably use more than this, but this will be the rough baseline.  The average consumption is 1000 watts at any given point in time.  So that’s 1kW/h.  At 12 volts and thanks to Ohm, storing 1kWh would require storing 83.3Ah.
83.3Ah * 24 hours = 2000Ah on the nose
As I’m only going to assume that I’ll have 5 hours of direct sunlight per day, I’ll need to come up with 2000Ah at a rate of 400A/h.
Incidentally that’s enough power to kill 20,000-40,000 people.  The collective State of Texas now has a boner.
I’m tired of going over this, it works out to me needing 400 square feet of grade A solar panels at a cost of $1700-$2400.  And a lot of  2 guage wire, which is somewhat impractical.  So small scale time, lets make around 80-100 watts.
The goal is to be able to generate 100 watts for $100.  
More to come…
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