GATE EE 2015 Set 2 — Question 31
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Electrical Machines → DC Machines → Generator & Motor Characteristics
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Question
A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to directly drive a load whose load torque depends on its rotational speed (in radian/second), such that . Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is ___________.
Correct answer
177 to 183
Solution
For a shunt motor, the induced EMF is . Since it's a shunt motor at constant terminal voltage, the flux is constant, so is constant.
Also .
Induced EMF .
Also .
Equating the two expressions for :
rad/s.
The given range is 177 to 183.
1.No-load condition: At no-load, , so .
2.Rated condition: Nm at rad/s. Torque , so .
Induced EMF . Also .
3.Steady-state with load :
In steady state, motor torque .Induced EMF .
Also .
Equating the two expressions for :
rad/s.
The given range is 177 to 183.
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