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If one were to use a transformer to increase the voltage to a motor, while at the same time decreasing the maximum current to the motor. Would this have a similar effect as moving to a higher gear in car. Whereas the angular velocity of the motor would increase while the maximum tourque decreases.

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You don't get to set the voltage and current of a load at the same time.

What you propose might give a higher unloaded motor speed, since the motor will draw little current then. As the motor gets more loaded, eventually it will try to draw more current than the transformer can supply, which will cause the motor to stall. At that point, the voltage collapses too.

Basically, what you are really asking is how a motor behaves with a high voltage but high impedance supply.

Of course all this is only valid if the motor can run on AC. Some can, others can't.

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What you are describing is constant power operation. With an AC induction motor, that is achieved by increasing the frequency while keeping the voltage constant or raising the voltage only slightly. With a DC motor that is achieved by reducing the field excitation. When the motor is provided with the capability of operating at an increased speed but reduced torque, the maximum current remains relatively constant.

The load characteristics ultimately determines the operating torque at a given speed. In an electric vehicle, part of the torque is used to accelerate the vehicle inertia and climb hills. That part of the torque usage can be sacrificed for increased level-terrain speed. While using the constant-power part of the motor's speed range, fast acceleration is not possible and the speed must be reduced to climb a steep hill.

Increasing the constant power range is a major research topic in designing motors for electric vehicles.

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