With no resistance, the full voltage is applied to the fan, and you get mechanical work done, at whatever efficiency the fan itself is capable of. Never minding the fan itself, so far as the electrical aspect goes, you could say it's 100% efficient.
With resistance in the system, for example about equal to the resistance of the fan, you have less current flowing through the system. Half as much. Same voltage. So the system is using half the power. The fan, now one part of a voltage divider circuit, is getting half the voltage, and getting half the current. It runs slower, doing less, doing about 1/4 the work. 1/4 of the fan action divided by 1/2 power going into the system means that the system is 50% efficient.
Imagine a lot of resistance in the system, megohms. You'll have only a trickle of current, say a microamp. The fan barely moves. The system will be using very little power, but most of that little power is just making the resistor hot. Or rather, a small fraction of a degree warmer than ambient temperature. The system efficiency is close to zero.
I have checked the power consumption for various speed of fan.
It consumes $80 W$ at full speed $45 W$ at second speed and subsequently reduced at lower speed.
This I have measured from the Digital Electrical Meter.
Best Answer
The power generated by a wind turbine is proportional to $v^3$. Turbines use wind to generate power, fans simply operate on the reverse principle - generating wind using power. Therefore, the power consumed by a fan is proportional to the cube of the wind speed it generates.