Here's my general understanding:
electric = runs on electricity, electronic (specific term) [electric car, electric fan, electric appliance, etc. Also metaphorically: exciting, energetic]
electrical = having to do with/concerning electricity (broader term) [electrical engineer, electrical wiring, electrical tape, electrical shortage, electrical energy, etc.]
I'm sure there are many exceptions, of course. One that springs to my mind is "electric company" for the organization that runs a power-plant. Sometimes the two words may be used interchangeably, as "electrical/electric shock".