Fan Speed and Electricity Consumed

Current drawn by an electric motor is roughly proportional to the torque. And for a fan, torque is going to scale roughly as a square of the speed. So yes, at higher fan speed, it will draw more power.

 

Another way of looking at it: the fan moves more air at higher settings, and moves it faster. Greater mass undergoing greater acceleration, means more enegry is being used.

 

That would be a terrible way to build a speed controller. It would mean that at any setting other than full, power is being completely wasted.

Since a typical household fan will run on AC power, best speed controller will be one using a transformer. In that case, the power loss will be very small at all settings. Another way is using resistors. That would work for both AC and DC, but it would result in higher power losses, especially at low settings. Still, the power drawn at low settings will be lower than at full speed even in this case.