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The rotor resistance per phase of a 4 pole 50 Hz 3 phase induction motor are 0.024 ohm and.12 ohm respectively. Find the speed at maximum torque.also find the value of additional rotor resistance per phase required to develope 80 percentage of maximum torque at starting.?
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The rotor resistance per phase of a 4 pole 50 Hz 3 phase induction mot...
Calculation of Speed at Maximum Torque:

  • Given, rotor resistance per phase (Rr1) = 0.024 ohm and (Rr2) = 0.12 ohm

  • Number of poles (p) = 4

  • Frequency (f) = 50 Hz

  • Maximum torque occurs at slip (s) = 0.20

  • Formula for speed at maximum torque is,

    Ns = (1 - s) x (f/p) x 60

    where, Ns is synchronous speed

  • Substituting the given values, we get

    Ns = (1 - 0.20) x (50/4) x 60 = 900 rpm



Calculation of Additional Rotor Resistance:

  • Given, rotor resistance per phase (Rr1) = 0.024 ohm and (Rr2) = 0.12 ohm

  • Percentage of maximum torque (T) required at starting = 80%

  • Formula for percentage of maximum torque is,

    T = (1 - s)² / (1 + sRr

    where, Rr is total rotor resistance per phase

  • At starting, slip (s) = 1

    Substituting the given values,

    0.8 = (1 - 1)² / (1 + 1Rr

    Simplifying the equation, we get

    Rr = 0.6 ohm (approx.)

  • Additional rotor resistance required (Radd) = Rr - Rr1

    Substituting the values, we get

    Radd = 0.576 ohm (approx.)



Explanation:

  • The speed at maximum torque is calculated using the formula Ns = (1 - s) x (f/p) x 60, where Ns is synchronous speed, s is slip, f is frequency and p is number of poles.

  • The additional rotor resistance required to develop 80% of maximum torque at starting is calculated using the formula T = (1 - s)² / (1 + sRr)², where T is percentage of maximum torque and Rr is total rotor resistance per phase.

  • By solving the above equations, we get the required values of speed and additional rotor resistance.

Community Answer
The rotor resistance per phase of a 4 pole 50 Hz 3 phase induction mot...
Answer 1
S=R2/X2
gives Sm=0.2
speed = Synchronous speed*Slip
N=300rpm

Tst/Tm=2R2*X2/(R2^2+X2^2)
0.8= 2a/(1+(a)^2)

where a=X2/R2
gives Rext= 0.156Ohm
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The rotor resistance per phase of a 4 pole 50 Hz 3 phase induction motor are 0.024 ohm and.12 ohm respectively. Find the speed at maximum torque.also find the value of additional rotor resistance per phase required to develope 80 percentage of maximum torque at starting.?
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