I'm new to electronics and am having trouble understanding how power supplies convert 120AC into a safe, manageable DC voltage. So far, I understand that there's a transformer to step the voltage down, then a rectifier, followed by an IC voltage regulator. However, any way I look at it, it seems that even if you step the voltage down 10x (via transformer), the current going into the rectifier is 10x larger than the wall outlet. This seems dangerous, and also contradicts my impression that wall-power supplies like wall warts produce safe voltage/current.
Am I correct in thinking that the power output from a wall wart is equal to the power output from an electrical jack (IV = IV)? If so, is getting shocked from an outlet equally dangerous to getting shocked from a wall wart? If not, what's missing from my analysis?