GATE 2022 EE Q.35: solution and answer

GATE 2022 · EEQ.35 · 1 mark · NAT

The frequencies of the stator and rotor currents flowing in a three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is ________. (round off to nearest integer)

See the question in the paper

Tap to open full size

Answer and solution

ANSWER

The motor speed is 585 rpm.

Official answer: 580 to 590Source: Official answer key, GATE 2022 EE (IIT Kharagpur)

Given: stator (supply) frequency $f_{s} = 40 Hz$ , rotor current frequency $f_{r} = 1 Hz$ , number of poles $P = 8$ .
The rotor current frequency is related to slip by $f_{r} = s f_{s}$ , so the slip is $s = \frac{f _{r}}{f _{s}} = \frac{1}{40} = 0.025$
The synchronous speed is $N_{s} = \frac{120 f _{s}}{P} = \frac{120 \times 40}{8} = 600 rpm$
The actual motor (rotor) speed is $N = N_{s} (1 - s) = 600 (1 - 0.025) = 600 \times 0.975$
$N = 585 rpm$

KEY IDEA

In an induction motor, the rotor current frequency equals slip times the stator (supply) frequency: $f_{r} = s f_{s}$ . Once slip is found, the actual rotor speed is obtained from the synchronous speed as $N = N_{s} (1 - s)$ .

WATCH OUT FOR

Confusing rotor frequency relation direction (using $f_{s} = s f_{r}$ instead of $f_{r} = s f_{s}$ ), or forgetting to compute $N_{s}$ correctly for an 8-pole machine (using $P$ instead of pole pairs correctly in $N_{s} = 120 f_{s} / P$ ).

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

GATE 2022 EE Q.35: solution and answer

Answer and solution

More Induction machines questions