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A six-pole, 3−ϕ,50 Hz induction motor has a rotor resistance and rotor reactance of 0.02Ω and 0.13Ω respectively at standstill. The external resistance to be added in the rotor circuit to get 75% of maximum torque at starting is
  • a)
    0.02 Ω
  • b)
    0.038 Ω
  • c)
    0.059 Ω
  • d)
    0.38 Ω
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A six-pole, 3−ϕ,50 Hz induction motor has a rotor resistance and roto...
sm =
sm =
sm = 0.453
sm = R/X = 0.453
R = 0.453 x 0.13
R = 0.058Ω
So, the external resistance to be connected to the rotor circuit would be
Rext = 0.058 x 0.02 = 0.038 Ω
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Most Upvoted Answer
A six-pole, 3−ϕ,50 Hz induction motor has a rotor resistance and roto...
Given data:
- Number of poles (p) = 6
- Frequency (f) = 50 Hz
- Rotor resistance (Rr) = 0.02 Ω
- Rotor reactance (Xr) = 0.13 Ω

Calculating synchronous speed (Ns):
Synchronous speed (Ns) of an induction motor is given by the formula:
Ns = 120f / p

Substituting the given values:
Ns = 120 * 50 / 6
Ns = 1000 RPM

Calculating slip (s):
Slip (s) is given by the formula:
s = (Ns - N) / Ns

Where N is the actual speed of the rotor.

Given that the motor is at standstill, N = 0 RPM. Therefore, the slip at standstill is 1.

Calculating rotor impedance (Zr):
Rotor impedance (Zr) is given by the formula:
Zr = √(Rr^2 + Xr^2)

Substituting the given values:
Zr = √(0.02^2 + 0.13^2)
Zr = √(0.0004 + 0.0169)
Zr = √0.0173
Zr = 0.1316 Ω

Calculating external resistance (Re):
To get 75% of maximum torque at starting, the slip (s) should be 0.25. Therefore, the actual speed of the rotor (N) can be calculated as:
s = (Ns - N) / Ns
0.25 = (1000 - N) / 1000
N = 750 RPM

The rotor impedance (Zr) at this speed can be calculated using the formula:
Zr = √(Rr^2 + Xr^2)

Substituting the given values:
0.1316 Ω = √(0.02^2 + Xr^2)
0.1316^2 = 0.04 + Xr^2
0.0173 - 0.04 = Xr^2
Xr^2 = 0.0227
Xr = √0.0227
Xr = 0.1508 Ω

The total impedance (Z) of the rotor circuit can be calculated as:
Z = Rr + Xr
Z = 0.02 + 0.1508
Z = 0.1708 Ω

The external resistance (Re) to be added in the rotor circuit can be calculated as:
Re = Z - Zr
Re = 0.1708 - 0.1316
Re = 0.0392 Ω

Therefore, the correct answer is option 'B' (0.038 Ω).
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A six-pole, 3−ϕ,50 Hz induction motor has a rotor resistance and rotor reactance of 0.02Ω and 0.13Ω respectively at standstill. The external resistance to be added in the rotor circuit to get 75% of maximum torque at starting isa)0.02 Ωb)0.038 Ωc)0.059 Ωd)0.38 ΩCorrect answer is option 'B'. Can you explain this answer?
Question Description
A six-pole, 3−ϕ,50 Hz induction motor has a rotor resistance and rotor reactance of 0.02Ω and 0.13Ω respectively at standstill. The external resistance to be added in the rotor circuit to get 75% of maximum torque at starting isa)0.02 Ωb)0.038 Ωc)0.059 Ωd)0.38 ΩCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A six-pole, 3−ϕ,50 Hz induction motor has a rotor resistance and rotor reactance of 0.02Ω and 0.13Ω respectively at standstill. The external resistance to be added in the rotor circuit to get 75% of maximum torque at starting isa)0.02 Ωb)0.038 Ωc)0.059 Ωd)0.38 ΩCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A six-pole, 3−ϕ,50 Hz induction motor has a rotor resistance and rotor reactance of 0.02Ω and 0.13Ω respectively at standstill. The external resistance to be added in the rotor circuit to get 75% of maximum torque at starting isa)0.02 Ωb)0.038 Ωc)0.059 Ωd)0.38 ΩCorrect answer is option 'B'. Can you explain this answer?.
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