Consumption Through Rehostate.

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I was surprised when I opened a 12 volt DC windshield wiper motor housing and found three large resistors set out apart from each other in a large space for them to give off heat. Apparently the speeds of the wipers were changed by using different resistances in series with the wiper motor. At full speed, no extra resistance. At low speed, a large resistor burned off energy while the motor got a little power.

In a car this doesn't matter much, you would never notice that you are throwing away power for the convenience of having three speed wipers.

I wonder if this is how a blender works? All those speeds. Certainly they don't have different windings for each speed, do they?

The average home appliance, such as a blender, uses what is called a "Universal" motor, it's an AC fed motor that really runs as a DC motor. Speed is a function of Field voltage then, so simple voltage control is all you need for changing speeds. This was indeed done with rheostats at one time, now it is all done digitally via PWM techniques. But when done with rheostats, the voltage variation was only on the field voltage, not the armature, where most of the work is done. So although technically the power in that field circuit doesn't change, it just diverts through the resistance, the amount of power consumed in the field is relatively low compared to the armature power. But since the armature power is a function of the load and the load is less at a lower speed, then varying the speed with a rheostat on the field excitation does indeed reduce the power consumption. But remember, it is also doing less work too.

Using a rheostat to drop the incoming AC line voltage will not do the same thing. In that case all you will do is reduce the torque capability of any motor, which may lead to stalling, in which case you have not saved anything. Less energy because no work being performed can be more easily attained with the OFF switch!

If you drop the AC line voltage to incandescent lights, they will consume less energy, but again, they will produce less light. It's easier to just put in lower wattage bulbs. Reducing voltage to CFL or other electronically excited lights may cause their power supplies to shut down, in which case again, the OFF switch would have sufficed. Get the picture?

Normally, you will find resistors in old fan regulators - step regulators

Fan power consumption reduces with reduction in speed. & reduction in speed is brought by reducing voltage with insertion of resistors. definitely, if you compare the total power consumption with step 1 - low speed to step 2 - higher speed, step 1 will have low power consumption, even though, resistors are inserted.

As you have mentioned, power loss in resistor varies proportional with R

But power consumption of the fan reduces by cube root of speed N