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If the fan has a DC motor then it should be powered from a voltage source, not a current source.
The motor needs a high current to start running and a lower current when it is up to speed. A current source with a current high enough to start the motor will supply too much voltage and current when the motor is up to speed.
With a voltage source the motor will start and the speed is adjusted by the voltage.
Every voltage source has an equivalent current source and every current source has an equivalent voltage source.
As the load is increased (such as when the motor starts), the voltage across the load will fall, whether the load is driven by a current source, or a voltage source -- unless the sources are ideal (and no real-world source is ideal).