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What will happen to an electric fan if it is switched on in a vacuum room? Assume the the motor used in fan is dc motor and the current is also dc. Will its angular acceleration approach to a limit when the time increases?

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The DC fan motor will accelerate until it reaches its design speed, which occurs when the back EMF generated as it turns equals the applied source voltage. At that point the speed stabilizes and the current drawn by the motor from the source falls to almost zero.

This has to do with the principles of operation of a DC motor and not with the fact that it is sitting in a vacuum. The vacuum means that the motor cannot perform any useful work because there is no air to "load" the fan blades with.

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