GATE EE 2015 Set 2 — Question 58
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Electrical Machines → DC Machines → Speed Control & Starting
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Question
With an armature voltage of and rated field winding voltage, the speed of a separately excited DC motor driving a fan is , and its armature current is . The armature resistance is . The load torque of the fan load is proportional to the square of the rotor speed. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to is _______.
Correct answer
47.5 to 47.5
Solution
For a separately excited DC motor, the back EMF is given by .Step 1: Calculate initial back EMF ()
Given: , , , and .Step 2: Determine the relationship between back EMF and speed
Since the field voltage is rated and constant, the flux is constant.
We know , so .
For :Step 3: Determine the relationship between armature current and speed
The electromagnetic torque is , so (since is constant).
The fan load torque is given as .
At steady state, , which implies .Step 4: Calculate the required armature voltage ()
Given: , , , and .Step 2: Determine the relationship between back EMF and speed
Since the field voltage is rated and constant, the flux is constant.
We know , so .
For :Step 3: Determine the relationship between armature current and speed
The electromagnetic torque is , so (since is constant).
The fan load torque is given as .
At steady state, , which implies .Step 4: Calculate the required armature voltage ()
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