What is the Energy/CO2 balance of using electric vehicles?
According to an article in the Zeit of 2014-01  the germany electric energy mix of 2014 creates 601g of CO2 per kWh.
A typical german VW Golf creates 169g of CO2 per kilometer.
A typical electric vehicle - Nissan Leaf is being used at 17.6 kWh per 100 kilometer which amounts to 106g of CO2 per kilometer at the 2014 electric energy mix. (See https://www.umweltbundesamt.de/themen/klima-energie/energieversorgung/strom-waermeversorgung-in-zahlen?sprungmarke=Strommix#Strommix for newer data)
On top of this energy per kilometer the energy to supply the fuel at the point of usage for the car and the energy to create and maintain the car needs to be added.
The energy for the supply of fuel amounts to 20% extra for the Golf example this would be 203 g of CO2 per km.
The full details of the needed energy amount to create the batteries for EVs are not know but there is an estimate by the IFEU Heidelberg  that assumes 125 kg per kWH capacity. For the leaft this would amount to 3 metric tons of CO2 and compared to a VW Golf it would take 28.000 km of operation before the Nissan Leaf operates more ecologic than the VW Golf.
A 2017 swedish study  estimates that it take 8.2 years for a 100 kWh Tesla to reach the point where it makes ecological sense to drive it.