Introduction to Electrical Engineering (ESO-203A)
(2015-16, Second Semester)
Assignment No. : 10
1. A 3-phase 50 Hz induction motor has a full-load speed of 1440 rpm. For this motor
calculate,
(a) The number of poles,
(b) full-load slip and rotor frequency and
(c) The speed of stator field with respect to the (i) stator structure and (ii) rotor
structure.
(Ans= (a) no. of poles =4, (b) slip at full load =0.04 and rotor frequency=2Hz (c)
(i) 1500rpm (ii)60rpm)
2. A 3-phase induction motor draws one fourth of the current at full load as it
draws at starting. If the starting torque is 1.5 times of the full load torque,
a) Find the full load slip.
b) Determine the slip at which motor develops maximum torque.
c) Determine the max. torque developed by motor as percent of full load torque.
(Ans= (a) 0.09375 (b) 0.3916 (c) 220.86% of full load torque)
3. A 3-phase, 11 kV, 50 Hz, 4 pole induction motor is taking 50 kW at 0.8 power
factor lagging when running at slip of 0.03. Stator copper loss is 500 Watt and
rotational loss is 1.5 kW. If stator core loss is negligible, Find
(a) Rotor copper loss
(b) Output power
(c) Efficiency
(d)
Shaft torque.
(ans= (a) 1.485kW (b) 46.515kW
(c) efficiency= 93.03% (d) shaft
torque=305.4Nm)
4. A 3-phase, 4-pole, 1440 rpm, 50 Hz induction motor has star-connected
rotor winding, having a resistance of 0.2Ω per phase and a standstill leakage
reactance of 1Ω per phase. When the stator is energized at rated voltage and
frequency, the rotor induced emf at standstill is 120 V/phase. Calculate the
rotor current, rotor power factor and torque both at starting and at full load?
(Ans= at starting rotor current =117.67A/ph, rotor power factor=0.196 lag and
torque =52.88Nm, at full load rotor current= 23.53A/ph, rotor power
factor=0.9806 lag and torque=52.88Nm)
5. A 3-phase, 6-pole, 50 Hz wound rotor induction motor has a full-load speed
of 960 rpm with its slip rings short-circuited. The motor drives a constant
torque load. If the rotor speed is reduced to (a) 800 rpm and (b) 400 rpm by
inserting external resistance in the rotor circuits, compute the ratio of the
rotor copper losses at these two reduced speeds with that at the full load.
(ans= (a) 5 (b) 15)
6. A 7.5 kW, 400 V, 3-phase, 50 Hz, 6-pole squirrel cage induction motor
operates at 4% slip at full load when rated voltage and frequency is applied.
Assuming a linear relationship between torque and slip in the operating region,
calculate the no-load speed of the motor when the supply voltage is reduced
to half its rated value. The no load torque is 6 N-m.
(Ans= no load speed=987.13rpm)
7. A three-phase, 208 V, 6-pole, 60 Hz induction motor has the following
equivalent circuit parameters R1= 0.075Ω, 𝑅2′ = 0.11Ω, 𝐿1 = 𝐿′2 =0.25 mH
and Lm=15 mH. The motor drives a fan. The torque required for the fan varies
as the square of speed and is given by,
2
𝑇𝑓𝑎𝑛 = 12.7 × 10−3 𝜔𝑚
Determine the speed, torque and power of the fan when the motor is
connected to a three-phase, 208 V, 60 Hz supply. Use the approximate
equivalent circuit shown below and neglect the rotational losses. For
operation at low slip, the motor torque can be considered to be proportional
to slip. (Ans= speed=1125.84rpm, torque=176.528Nm, power=20.8kW )
R1
I1
V1
Lm
X1
I 2
X 2
R 2
s
8. A 3 phase Induction machine has an efficiency of 0.9 when the load is 37kW. At
this load the stator cu loss and rotor cu loss each equals the iron loss. The
mechanical losses are one third of no load loss. Calculate the slip?
(ans= slip=0.0303)