Problems on Induction
Motors
Find the speed of a 4pole induction motor
working at 50Hz supply at a slip of 3%.
Given : Number of poles P= 4
Frequency f= 50Hz
Slip s= 3%
Solution:
Ns 
120 f
P
𝑁𝑟 = (1 − 𝑠)𝑁𝑠
𝑁𝑠 =
120 𝑥 50
4
=1500rpm
𝑁𝑟 = 1 − 0.03 1500 = 1455rpm
A 3phase induction motor has 2poles and is connected
to 400V, 50Hz supply. Find the speed of rotor and
frequency of rotor induced emf at 4%slip.
Given:
Supply freq f = 50Hz
Number of poles P=2
slip s = 4%
Solution:
Ns 
𝑁𝑠 =
120 f
P
𝑁𝑟 = (1 − 𝑠)𝑁𝑠
120𝑥50
= 3000𝑟𝑝𝑚
2
𝑁𝑟 = 1 − 0.04 3000 =2880 rpm
𝑓𝑟 = 0.04x50=2Hz
𝑓𝑟 = 𝑠𝑓
A 3phase 6pole 50Hz star connected Induction Motor has
rotor resistance/phase 0.3Ohm and reactance at
standstill is 1.5Ohm/phase.EMF measured between
sliprings is 175 on open circuit in rotor at standstill.
Calculate i) rotor emf/phase ii) slip at 950rpm iii)rotor
freq ,rotor impedance and rotor current at 950rpm.
Given: Poles P =6 supply freq=50Hz R2=0.3Ω/phase X2=1.5 Ω/phase
rotor speed Nr =950rpm E2=175V (line qty.)
Solution:
Ns 
𝐸2 =
120 f
P
175
3
𝑁𝑠 =
120𝑥50
= 1000𝑟𝑝𝑚
6
𝑁𝑠 − 𝑁𝑟
𝑥100%
𝑁𝑠
𝑓𝑟 = 𝑠𝑓
1000 − 950
%𝑠 =
𝑥100% = 5% = 0.05
1000
= 101𝑉
𝑅𝑜𝑡𝑜𝑟𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑐𝑒𝑍 =
%𝑠 =
𝑅22 + (𝑠𝑋2 )2
𝑅𝑜𝑡𝑜𝑟𝑐𝑢𝑟𝑟𝑒𝑛𝑡/𝑝ℎ𝑎𝑠𝑒 =
𝑠𝐸2
𝑅22
+
𝑠 2 𝑋22
𝑅𝑜𝑡𝑜𝑟𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑐𝑒𝑍 =
𝑓𝑟 = 0.05x50=2.5Hz
(0.3)2 +(0.05𝑥1.5)2 =0.807Ohm
𝑅𝑜𝑡𝑜𝑟𝑐𝑢𝑟𝑟𝑒𝑛𝑡 0.05𝑥101
=
= 6.257𝐴
𝑝ℎ𝑎𝑠𝑒
0.807