Gus, your typical home solar system will take way too long to charge a Tesla electric vehicle.
For example, the mid range Tesla model S has a battery pack capacity of 60kWh (kilowatt hours).
http://en.wikipedia.org/wiki/Tesla_Model_S#Battery
Let's assume you have one of the larger home solar installations, ie 5kW. According to the following link it will typically produce 18 to 25kWh of energy per day. Lets assume a round number of 20kWh for this example.
http://www.solargain.com.au/how-much-does-solar-energy-save-you
If we use all of that energy to charge the battery, leaving none to power the house appliances and none fed back to the grid, it's still going to take an average of over three days to charge (65/20). That's three days off the road. IMO this is still optimistic since there are some inefficiencies in the charging process.
This is why there is so much talk about charging stations. So called super-charging stations will charge the battery in around one hour, but the amount of current that charger system will draw from the electricity grid is rather scary.
