# Induction Machine



## applepieordie (Aug 22, 2017)

Hello,

What equation is being used in the solution? (question from Kaplan sample exam)







Is max torque synonymous to max power? 

In Graffeo's book I see the formula: Slip at which Pmax occurs at = Sp = Rrotor/(Rrotor + Zeq), where Zeq = Zmotor + Zstator. But this equation seems slightly different than the one used int he solution.

Also, if you have good machine references (such as a formula sheet) to share it would be greatly appreciated.

Thanks!


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## rg1 (Aug 22, 2017)

From the equivalent circuit of Induction motor, we see that Pmax or Tmax occurs when (Rexternal+r2)/slip= IZeqI. where Zeq is (r1+j(x1+x2)) . IMHO this is the basic equation. This also available in Wildi. From this equation the answer at slip 1 comes Rexternal+.333=IZeqI= sqrt((.645)**2+(1.11+.978)**2)=1.37 on primary side.


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## rg1 (Aug 22, 2017)

rg1 said:


> From the equivalent circuit of Induction motor, we see that Pmax or Tmax occurs when (Rexternal+r2)/slip= IZeqI. where Zeq is (r1+j(x1+x2)) . IMHO this is the basic equation. This also available in Wildi. From this equation the answer at slip 1 comes Rexternal+.333=IZeqI= sqrt((.645)**2+(1.11+.978)**2), gives Rexternal=1.37 ohms on primary side.


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## Omer (Aug 22, 2017)

rg1 said:


> From the equivalent circuit of Induction motor, we see that Pmax or Tmax occurs when (Rexternal+r2)/slip= IZeqI. where Zeq is (r1+j(x1+x2)) . IMHO this is the basic equation. This also available in Wildi. From this equation the answer at slip 1 comes Rexternal+.333=IZeqI= sqrt((.645)**2+(1.11+.978)**2)=1.37 on primary side.


Yes, you are right.

I think book answer is wrong including r2 in the calculation of Zeq.

Wildi is the best.


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## cos90 (Aug 22, 2017)

Where did you get this Kaplan? Kaplan changed their name to Brightwood and the book I purchased from them looks nothing like this.


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## Stephen2awesome (Aug 22, 2017)

rg1 said:


> From the equivalent circuit of Induction motor, we see that Pmax or Tmax occurs when (Rexternal+r2)/slip= IZeqI. where Zeq is (r1+j(x1+x2)) . IMHO this is the basic equation. This also available in Wildi. From this equation the answer at slip 1 comes Rexternal+.333=IZeqI= sqrt((.645)**2+(1.11+.978)**2)=1.37 on primary side.


rg1,  what page are you getting that equation from in Wildi?


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## rg1 (Aug 22, 2017)

Stephen2awesome said:


> rg1,  what page are you getting that equation from in Wildi?


It is Chapter 15. Not a big chapter. Page no 322 arround


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## applepieordie (Aug 24, 2017)

cos90 said:


> Where did you get this Kaplan? Kaplan changed their name to Brightwood and the book I purchased from them looks nothing like this.


I didn't purchase if from Brightwood. I got this exam (in pdf format) from a colleague and was told it is the Kaplan exam. 

My guess is it is probably an older sample exam as it has many errors. I found this thread dated 2010 in the forum where a poster called cableguy made an errata list and it matches the errors I see in the pdf I have:


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