GATE 2023 EE Q.16: solution and answer

GATE 2023 · EEQ.16 · 1 mark · MCQ

A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is

(A)
100 Hz
(B)
95 Hz
(C)
10 Hz
(D)
5 Hz

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Answer and solution

ANSWER

The frequency of induced rotor currents due to the backward field is 95 Hz — option B.

Official answer: BSource: Official answer key, GATE 2023 EE (IIT Kanpur)

Synchronous speed: $N_{s} = \frac{120 f}{P} = \frac{120 \times 50}{10} = 600 RPM$
Slip with respect to the forward rotating field: $s = \frac{N _{s} - N}{N _{s}} = \frac{600 - 540}{600} = 0.1$
By the double revolving field theory, the rotor's slip with respect to the backward field is $(2 - s) = 2 - 0.1 = 1.9$
Frequency of rotor currents induced by the backward field: $f_{b} = (2 - s) f = 1.9 \times 50 = 95 Hz$

KEY IDEA

By the double revolving field theory, a single-phase induction motor's pulsating mmf is resolved into two counter-rotating fields (forward and backward), each behaving like a separate 3-phase-equivalent field. If the rotor slip with respect to the forward field is $s$ , its slip with respect to the backward field is $(2 - s)$ , so the backward-field rotor current frequency is $f_{b} = (2 - s) f$ .

WATCH OUT FOR

Using slip $s$ (instead of $2 - s$ ) with the line frequency for the backward-field current, which gives $f_{b} = s f = 5 Hz$ — this is actually the frequency due to the forward field's own slip-frequency rotor current, not the backward field's.

From the GATE 2023 EE paper. Every question of this paper · Download the full paper · All 17 Induction machines questions, with notes

GATE 2023 EE Q.16: solution and answer

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