GATE Electrical 2024 | Question: 7

Question

​​​​​A three phase, $50 \mathrm{~Hz}, 6$ pole induction motor runs at $960 \mathrm{rpm}$. 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. $98$

Answer 1

Step 1: Calculate Synchronous Speed (Ns)

 

The synchronous speed of an induction motor is given by:

 

Ng 120x f P

 

where:

 

• f = 50 Hz (supply frequency),

 

• P = 6 (number of poles).

 

Ns 120×50 6 = 1000 rpm

 

Step 2: Calculate Slip (s)

 

Slip is defined as:

 

S= Ns-Nr/ Ns

 

where:

 

• N = 960 rpm (actual rotor speed),

 

• Ns = 1000 rpm

Eff. = (1 - s) * 100

 

Substituting s = 0.04 :

 

Eff. = (1 - 0.04) * 100 = 96%

 

Final Answer:

 

The percentage efficiency of the motor is 96%.