GATE 2024 EE Q.17: solution and answer

GATE 2024 · EEQ.17 · 1 mark · MCQ

A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is

(A)
92
(B)
94
(C)
96
(D)
98

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Answer and solution

ANSWER

The percentage efficiency of the motor is 96% (Option C).

Official answer: CSource: Official answer key, GATE 2024 EE (IISc Bengaluru)

Synchronous speed: $N_{s} = \frac{120 f}{P} = \frac{120 \times 50}{6} = 1000 rpm$
Slip: $s = \frac{N _{s} - N}{N _{s}} = \frac{1000 - 960}{1000} = 0.04$
Since stator copper loss, core loss, and rotational loss are all neglected, the only loss present is the rotor copper loss.
The air-gap power splits as $P_{a g} = P_{m ec h} + P_{r o t or, c u}$ , with $P_{r o t or, c u} = s P_{a g}$ and $P_{m ec h} = (1 - s) P_{a g}$ .
Because there are no stator losses, input power equals air-gap power, so efficiency $= \frac{P _{m ec h}}{P _{a g}} = (1 - s)$ .
$η = (1 - 0.04) \times 100% = 96%$

KEY IDEA

When stator copper loss, core loss, and rotational (mechanical) loss are all neglected, the only loss remaining is the rotor copper loss, which equals the slip fraction of the air-gap power. Since there are no stator losses, the input power equals the air-gap power, and the developed mechanical output power equals (1-s) times the air-gap power. Hence efficiency = 1 - s exactly.

WATCH OUT FOR

Confusing slip loss fraction with efficiency directly, or computing efficiency as Pmech/Pinput using an incorrect power balance (e.g., forgetting that with stator losses neglected, input power to the rotor equals air-gap power, so efficiency simplifies neatly to (1-s)).

From the GATE 2024 EE paper. Every question of this paper · Download the full paper · All 2 Losses & efficiency questions, with notes