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GATE 2023 EE – Question 22

Electrical Machines · Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors · 1 mark · Multiple choice

The four stator conductors (A, A′, B and B′) of a rotating machine are carrying DC currents of the same value, the directions of which are shown in the figure (i). The rotor coils a-a′ and b-b′ are formed by connecting the back ends of conductors ‘a’ and ‘a′’ and ‘b’ and ‘b′’, respectively, as shown in figure (ii). The e.m.f. induced in coil a-a′ and coil b-b′ are denoted by $E_{a\text{-}a'}$ and $E_{b\text{-}b'}$, respectively. If the rotor is rotated at uniform angular speed ω rad/s in the clockwise direction then which of the following correctly describes the $E_{a\text{-}a'}$ and $E_{b\text{-}b'}$?

Diagram for GATE 2023 EE question 22
  1. $E_{a\text{-}a'}$ and $E_{b\text{-}b'}$ have finite magnitudes and are in the same phase
  2. $E_{a\text{-}a'}$ and $E_{b\text{-}b'}$ have finite magnitudes with $E_{b\text{-}b'}$ leading $E_{a\text{-}a'}$
  3. $E_{a\text{-}a'}$ and $E_{b\text{-}b'}$ have finite magnitudes with $E_{a\text{-}a'}$ leading $E_{b\text{-}b'}$
  4. $E_{a\text{-}a'}=E_{b\text{-}b'}=0$

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Correct answer: (D) $E_{a\text{-}a'}=E_{b\text{-}b'}=0$

Explanation

The current directions (A into the page, A′ out, B into, B′ out, going round the stator) alternate every 90°, so the stator field is a 4-pole pattern with a pole pitch of 90° mechanical. Each rotor coil spans 180° mechanical, i.e. two pole pitches, so its two sides always sit under poles of the same polarity and their emfs cancel. Both coil emfs are zero.