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Also, electric vehicles can be charged at home, which (for most of us, anyway) can't be said of petrol-powered ones.
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The energy required to recharge a battery enough to do 100 miles in the average electric car will be about 40kWh. That's quite a bit of power to be using from your home mains supply, but if you charge overnight for 12 hours it is just about do-able via a standard 13A socket.
If however you want significantly more than 100 miles worth of power, and if you want to charge it more quickly, you'll find that it quickly reaches currents that your house supply will not be able to accommodate. e.g. to charge for a 300 mile range in 2 hours would need a 240V supply rated at 250 amps - that's more than the wires entering most houses can carry.
Even overnight charging will be problematic if everyone in the neighbourhood has an electric car. All those cars charging at the same time will almost certainly overload the local substation.
Even if a car battery were to be developed that could be charged from flat in, say, 15 minutes (which I'd say is the longest you'd want to wait to refuel on a long journey), the national grid would not be able to supply the refuelling stations without a huge upgrade. To recharge just 10 cars at once, each with an 100kWh battery, would need a power drain from the grid of around 4 MW.
Swapping out the battery at the service station is really the only practical model (in which case charging time does not matter), with the flat batteries being physically shipped to a central power station for recharging. Each battery could have a tamper-proof monitor so that customers only pay for the amount of electricity that they had used from the battery they were swapping.