Lowering the speed of a fan actually lowers down consumption of electric power

The speed of a fan can be controlled through the use of a regulator, which is a variable resistance. It is connected in series with the (coil of) the fan. When the rheostat value is zero, the fan gets all the voltage, it then rotates with the highest speed. But when the rheostat value is increased, the electric current lowers down and a portion of the total supply voltage is spent in the rheostat itself. The fan doesn’t get full voltage then. If the rheostat value is further increased, both the current (I) and terminal voltage difference (V) of the fan lower down. Since electric power, P = VI, hence the fan then will rotate with even less speed, i.e. less power. But the thing is that with an increase in rheostat value, the current will decrease and the total voltage drop will remain the same (220 V). Hence the fan and regulator system will then consume less power compared to the case when rheostat value was zero.