GATE 2022 IN Q.29: solution and answer

GATE 2022 · INQ.29 · 1 mark · NAT

A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is _______ (round off to one decimal place)

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Answer and solution

ANSWER

The full-load rotor speed is 1440.0 rpm.

Official answer: 1440.0Source: Official answer key, GATE 2022 IN (IIT Kharagpur)

Synchronous speed: $N_{s} = \frac{120 f}{P} = \frac{120 \times 50}{4} = 1500 rpm$
Slip relates synchronous and rotor speed as $N = N_{s} (1 - s)$ , so $N = 1500 (1 - 0.04)$
$N = 1500 \times 0.96 = 1440.0 rpm$

KEY IDEA

Rotor (mechanical) speed of an induction motor is related to synchronous speed and slip by $N = N_{s} (1 - s)$ , where $N_{s} = \frac{120 f}{P}$ depends only on supply frequency and number of poles — the voltage, power rating and winding connection given in the stem are not needed for this calculation.

WATCH OUT FOR

Forgetting to convert slip into the (1-s) factor correctly, or mistakenly using the number of pole pairs instead of poles in the synchronous speed formula (using P=2 instead of P=4).

From the GATE 2022 IN paper. Every question of this paper · Download the full paper · All 17 Induction machines questions, with notes

GATE 2022 IN Q.29: solution and answer

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