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It sounds nice, but that’s a virtual impossibility. Solar panels only work efficiently when the sun is shining, and at the right angle – perhaps 6 hours per day. In the northern US, you might only have 6 months of efficient electricity production.
So the big problem is what to do at night when there is no sun. You can’t store electricity, so you need some type of firm energy source, such as hydro, nuclear, or coal to make up for that shortfall.
Georock is correct that storage would be required. Pumped hydro is the most efficient way of storing power at this level – surplus power is used to pump water to an elevated reservoir, then reclaimed by draining the water through a turbine. The need for storage can be decreased also by carrying the electric grid through multiple time zones so the time that there is no sunlight on the grid is decreased.
CIA figures show U.S. electrical consumption at just over 4 trillion KwHr per year. At about 2000 hours sunlight per panel per year (conservative estimate) that means about 2 trillion watts of solar panel. Retail prices right now are about $3.50/watt, so a one-time cost of $7 trillion would give us fossil-fuel electricity in the states. There isn’t that much solar panel fabrication capability in the world yet. Seems like a better investment than a lot of others we’ve been making at that scale, though.
The area is a bit tricky – the newer thin-film photovoltaic panels will be lots cheaper when the bcome available in bulk (that’s production capacity limited right now) but the take up to 10x the area of the silicon photovoltaics. Figuring in silicon, at around 10 watts/square foot, it’s 200 billion square ft. or about 7200 Square miles. That’s the size of the eastern 1/3 of San Bernadino county, which is mostly Mojave desert.
Another possibility is solar thermal, which uses mirrors to focus sunlight on a boiler. This is a powerplant-sized solution with about the same efficiency as the photovoltaic. Some designs incorporate enough thermal storage to allow overnight continuous operation.
Wouldnt cost anything, solar power is free
Running the entire US on Solar power is not very practical, as others have mentioned, but since that was not the question lets address the question of cost. In about half of the US the cost of solar power is roughly equivalent to the retail cost of electricity (assuming the solar cells have a life expectancy of 25 years and considering the cost over the life of the system). So virtually half of the US could convert to solar power without paying any extra money over the next 25 years (you have to pay up front on the initial installation, so the method of payments is different, but total cost might be the same).
However, you then have a major problem. These homes and businesses would be connected to the grid. The idea is that during the day they generate more power than they need, sell it to the grid, and then at night they buy it back at the same price. This works great when few people have solar, but if everyone does, who pays for the grid? Why is the power company still generating power if everyone has solar? In that case there would be new costs of paying for the grid and paying to store excess power produced during the day for use at night.
So the costs would be neglible for installing the solar power, but could become much greater if we had to then subsidize the grid and create storage for power that is generated.
It gets worse because solar power is very seasonal. There is much less power generated in the winter than in the summer. Are you going to store the power for several months?