The back emf in a motor is 120 V when the motor is turning at 1680 rev/min. What is the back emf when the motor turns at 3360 rev/min? (Ans: 240 V). 



Data Given:

1st Back emf in motor at angular speed "1 = Ɛ1 = 120 V

1st Angular speed = 1 = 1680 rev per min 

= 16802πrad60s 168023.1416rad60s = 175.93 rad s⁻¹

2nd Angular speed = 2 = 3360 rev per min 

= 3360 2πrad60s 3360 23.1416rad60s = 351.86 rad s⁻¹



To Find:


Back emf in the motor at angular speed "2" = Ɛ2 = ?


Solution:

As the angular speed and back emf are proportional and their ratio will be equal, thus

Ɛ1Ɛ2  = 12


or

Ɛ2 Ɛ121


Putting the corresponding values 

Ɛ2  120V351.86rads¹175.93rads¹

Ɛ2  42223.2V175.93

Ɛ2  = 240 V ----------------Ans.



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